Blog

  • Using FIDIC construction contracts in Saudi Arabia

    Using FIDIC construction contracts in Saudi Arabia

    This continues a long-standing preference for FIDIC contracts in the Kingdom with the ‘Public Works Contract’ approved for use by Saudi government authorities since 1988 being largely based on FIDIC conditions of contract 3rd edition published in 1977.

    Although the vast majority of FIDIC contracts being used are amended versions of the forms, some are amended more than others. This can involve either bespoke amended general conditions or amendments sitting on top of the FIDIC standard general conditions, alongside requirements under Saudi law.

    Most FIDIC contracts used in the Kingdom are based on the 1999 suite rather than the latest, 2017, suite, with this edition having been used by government departments and quasi-governmental companies on projects including the Haramain High Speed Rail Project; contracts entered into by the Public Investment Fund (PIF) and the Ministry of Transport; and the Mecca Metro and the Riyadh Metro projects.

    More recently, the 1999 FIDIC contract has been used in the NEOM reimagined industrial city project, including the Line, Trojena and Oxagon elements as well as the New Murraba and Qiddiya projects in Riyadh.

    Common amendments adopted in KSA

    Commonly-seen amendments made to FIDIC forms used in the Kingdom include:

    Dispute resolution

    Most, but not all, Saudi FIDIC-based contracts we have seen in recent years have dispute resolution clauses which remove the dispute adjudication board (DAB) drafting and provide for a final dispute resolution stage of arbitration under rules of the Saudi Center for Commercial Arbitration (SCCA) in Riyadh.

    Latent defects

    In addition to a ‘standard’ defects notification period as per the unamended FIDIC contract, most FIDIC-based contracts in the Kingdom include a provision which attempts to replicate the decennial liability requirements of article 29 of the Saudi Building Code Implementing Regulations.

    This means that the designer or engineer supervising the execution of the works and the contractor become jointly liable for a period of 10 years from the completion of the works, compensating the owner for the total or partial demolition of their constructed buildings or facilities and any hidden defect that threatens the durability of the building and its safety.

    There is also often a bespoke provision requiring the contractor to be responsible for ‘latent’ defects for a period, which in some cases is even longer than the 10-year liability period under the Building Code Implementing Regulations. Latent defects are not always defined, but where they are, the term usually means any defects which could not have been discovered during the standard defects notification period.  This is onerous on contractors given that decennial liability under law attaches in respect of serious defects only, whereas contractual latent defects can apply to any defects, depending on how the clause is drafted.

    Financing charges for delayed payments

    Saudi FIDIC contracts often remove the standard wording in sub-clause 14.8 (Delayed Payment) entitling the contractor to receive “financing charges”, otherwise known as late payment interest, in respect of failures by the employer to make timely payments. This is because of the prohibition of ‘riba’ under Sharia law, which has survived the introduction of the Saudi Civil Transactions Law (CTL) and would likely make any such provision unenforceable in the Kingdom.

    While any language regarding financing charges is likely to be removed so as not to affect the enforceability of any later issued award, parties still attempt to find ways to include provisions requiring the employer to pay compensation for loss caused by delayed payments, and as our colleagues Nesreen Osman and Mark Raymont have previously commented on this could be permissible under the CTL’s provisions. 

    Local content

    Most, but not all, contracts now contain requirements reflecting the Local Content Law, as administered by the Local Content and Government Procurement Authority. These requirements are generally of two types: a ‘local content’ score to be achieved by the contractor based on total value of local labour, goods, services, material, equipment, assets and technology used; or a ‘national product procurement requirement’, with price preference to be given to Saudi products.

    These requirements tend not to be strict obligations, with opportunities for contractors to avoid contractual liability if evidence can be provided on why compliance was not possible.

    Interaction with the Civil Transactions Law

    The introduction of the Civil Transactions Law (CTL) in December 2023 was a ground-breaking moment in the Saudi legal landscape, being the first time that the pre-existing Sharia principles have been distilled into legal code similar to those of other jurisdictions in the Middle East region. It has a large number of provisions which govern commercial contracts, including construction contracts, and it is crucial that contracting parties keep the CTL provisions firmly in mind when negotiating the terms of their agreements.

    In the following paragraphs we set out just some of the ways that the CTL will interact with FIDIC construction contracts being used in the Kingdom.

    Good faith and abuse of rights

    The FIDIC ‘rainbow suite’ forms do not contain express obligations on the parties to act in accordance with ‘good faith’ or similar concepts, in contrast to other commonly used forms like the New Engineering Contract (NEC) forms, the current editions of the Institute of Chemical Engineers (IchemE) forms of contract and the Joint Contracts Tribunal (JCT) 2024 editions.

    Despite this, article 95 of the CTL codifies the Sharia principle of good faith, itself deriving from the Sharia principle of ‘ihsan’, providing that a contract must be carried out “in accordance with its terms and in a manner consistent with good faith practices”.

    Article 29 of the CTL also states that “a person may not exercise his right in an abusive manner” and lists examples of when this may be the case: including if a right is exercised only to cause harm to others; if the benefit generated from exercising the right is substantially disproportionate to the harm it causes to others; or if the right is exercised for an unlawful purpose or in an unlawful manner.

    Liquidated damages for delay and performance

    The FIDIC ‘rainbow suite’ contracts make provision for liquidated damages to be applied to specified programme delays and (with the exception of the construct-only ‘Red Book’, which is designed for works primarily designed by the employer)  specific  failures by the works to achieve performance guarantees.

    Under article 178 of the CTL, contracting parties are permitted to pre-agree damages for specified breaches of the contract, except where the subject of the relevant contractual obligation is to make payment of certain sums of money, with late payment interest being a prime example.

    Under article 179, however, liquidated damages will not be payable where the obligor proves that there were no actual damages incurred. Moreover, the Saudi courts have the power to reduce the amount of liquidated damages if the obligor proves that these were “excessive” or that the obligation to which they relate was only partially performed.

    The courts can also increase the amount to match the actual damage incurred if the creditor establishes that an act of fraud or gross negligence by the obligor caused the damage to exceed the liquidated damages.

    Article 179 of the CTL is a mandatory provision, and thus contractual parties cannot agree otherwise or opt out of it. 

    Limits of liability

    Article 173 of the CTL allows contracting parties to limit liability for their failures and delays in performing the contract, but this is not permissible in cases of fraud or gross negligence.

    This is consistent with the clauses providing for a limit on the contractor’s overall liability under the contract contained in the FIDIC rainbow suite 2nd edition, where the cap on liability does not include for instances of “fraud, gross negligence, deliberate default or reckless misconduct”. The 1st editions contain the same wording, but do not refer to “gross negligence”.

    However, under article 173 of the CTL, no agreement can be made to exempt a party from liability for a “harmful act”. This may mean that the scope for which liability cannot be limited under the CTL is wider than the wording contained within the FIDIC contracts, as it encompasses ‘ordinary’ negligence and other tortious acts or omissions in contrast to “gross negligence” in the FIDIC 2nd editions and “deliberate default” and “reckless misconduct” in the 2nd and 1st editions.

    Change in circumstances

    The FIDIC ‘rainbow suite’ has various protections for contracting parties whose performance is impacted by changes in circumstances, including the force majeure clause in the 1st editions and clause 18 (Exceptional Events) in the 2nd editions.

    The employer’s risks clause, covered by subclauses 17.3 and 17.4 in the 1st editions and sub-clause 17.2 in the 2nd editions, deals with responsibility for the cost of repair or replacement of loss and damage to the works caused by a closed list of events, many of which overlap with those covered in the definitions of ‘force majeure’ and ‘exceptional event’.

    Force majeure and exceptional event relief under FIDIC is limited to:

    • relief from performing obligations which have been “prevented” by the relevant event, which is likely to be a high barrier and will not cover performance which is merely made more difficult;
    • an extension of time to the extent the contractor has been “prevented” from performing contractual obligations and has incurred delay in completing the works; and 
    • in respect of some but not all force majeure/exceptional events, compensation for cost incurred.

    Importantly, all three entitlements are conditional on the affected party complying with contractual notification requirements.

    Article 97 of the CTL codifies provisions relating to “extraordinary unforeseen circumstances”, which is potentially broader in application than the FIDIC provisions, allowing the Saudi courts to reduce a burdensome obligation in the absence of agreement between the parties.

    The CTL allows for an obligor to seek to renegotiate in circumstances where extraordinary events arise, which could not have been foreseen at the time of entering the contract and which cause the performance of a contractual obligation to become unduly onerous for the obligor such as to threaten them with exorbitant loss. In the meantime, the obligor must continue performing its obligations. If the parties cannot renegotiate the obligation, the court has the power to restore the obligation to what it considers to be a reasonable level.

    The ‘muqawala’ section of the CTL, covered in articles 461-478, also contains a clause which allows a court to adjust contractual obligations – including by extending the time for performance, changing the contract price upwards or downwards and even terminating the contract, where the balance of contractual obligations has been altered by extraordinary unforeseen circumstances.

    Continue Reading

  • NASA launches second phase of moon recycling competition

    NASA launches second phase of moon recycling competition

    A SpaceX Falcon 9 rocket flies by the “Pink Moon” as it launches its Starlink Satellites from the Kennedy Space Center, Florida on April 12. On Monday, NASA announced Phase 2 of its moon sustainability competition, the LunaRecycle Challenge, to remove trash from outer space. File Photo by Joe Marino/UPI | License Photo

    Aug. 11 (UPI) — NASA is launching the second phase of its moon recycling competition to clean up trash in space.

    The space agency’s LunaRecycle Challenge is looking for the brightest minds to figure out a way to recycle plastics, foams and metals left behind by ongoing activity and building in space.

    “NASA is eager to see how reimagining these materials can be helpful to potential future planetary surface missions,” said Jennifer Edmunson, acting program manager for Centennial Challenges at NASA’s Marshall Space Flight Center in Alabama.

    “I’m confident focusing on the most critical trash items — and integration of the prototype and digital twin competition tracks — will yield remarkable solutions,” Edmunson added, “that could enable a sustainable human presence off-Earth and transform the future of space exploration.”

    As the United States discusses replacing the International Space Station and placing a small nuclear reactor on the moon, the potential for increased waste in space is growing.

    LunaRecycle’s Phase 1 competition attracted record-breaking interest with more than 1,200 registrations. Seventeen teams, from five countries and nine U.S. states, were named winners in that challenge.

    For Phase 2, only U.S. individuals and teams may participate and must build a physical prototype to manage a year’s worth of trash. The challenge estimates a crew of four astronauts would produce more than 4,600 pounds of single-use waste to include food packaging and discarded clothing. The goal for competitors is to recycle the waste, while minimizing crew time and any hazards.

    Submissions for NASA’s LunaRecycle milestone round, which is being administered by the University of Alabama, are open now and due January 2026. Finalists from that round will be announced in February with up to 20 finalists competing in the challenge’s in-person prototype demonstrations next August. Successful solutions in both rounds could net winners cash prizes totaling $2 million.

    Continue Reading

  • Study identifies risk factors that increase risk of death in children with Fontan circulatory failure

    Study identifies risk factors that increase risk of death in children with Fontan circulatory failure

    A multi-center study has identified critical risk factors that increase the likelihood of death in children with a heart defect who are awaiting or have recently undergone heart transplantation, according to findings published in Circulation.

    Fontan circulatory failure (FCF) is a long-term complication in children born with single-ventricle heart defects who have undergone a series of surgeries that culminates with the Fontan procedure. While this surgery helps reroute blood flow and extend life expectancy, it can lead to chronic health problems, including heart failure and damage to other organs. Many of these patients eventually require a heart transplant.

    The new study, conducted across 20 U.S. medical centers, offers new insights into how specific health complications affect survival in children with the condition, said co-author Anna Joong, MD, cardiologist at Ann & Robert H. Lurie Children’s Hospital of Chicago and Associate Professor of Pediatrics at Northwestern University Feinberg School of Medicine.

    “We have a strong interest in understanding patients with Fontan circulatory failure: how we can better manage their heart failure, when the ideal time is to list them for a heart transplant, and what the risk factors are while waiting for a transplant,” Dr. Joong said.

    In the study, investigators analyzed data from 409 patients who had undergone a Fontan procedure and were listed for heart transplant between 2008 and 2022. They tracked outcomes from the time of waitlisting through one year after transplant. They found that 5.9 percent died awaiting a transplant, and among those transplanted, 8.5 percent died within the first year.

    The investigators also found that certain pre-existing conditions significantly increased the risk of death, including:

    • Repeated hospitalizations in the year before being listed for transplant doubled the risk of death.

    • Clinical cyanosis – a condition in which oxygen levels in the blood are dangerously low – was associated with a fivefold increase in mortality risk.

    • Sleep apnea, mental health conditions requiring treatment, and anatomical complications like Fontan pathway obstruction were all linked with a higher risk of death.

    Overall, survival has improved for patients who have single ventricle physiology and who had a Fontan. A really novel finding of this study was that patients with low oxygen levels were associated with poor outcomes. That’s an important thing for clinicians and families to know about, as an additional risk factor and when to refer to advanced heart failure therapies.”


    Dr. Anna Joong, MD, cardiologist at Ann & Robert H. Lurie Children’s Hospital of Chicago and Associate Professor of Pediatrics at Northwestern University Feinberg School of Medicine

    The findings should guide clinicians in identifying high-risk patients earlier and considering more aggressive interventions, including earlier heart failure team and transplant referral, Dr. Joong said. Overall, the study lays the groundwork for improving transplant outcomes and tailoring care to the specific needs of children born with single-ventricle heart defects.

    Moving forward, Joong and her collaborators will continue to study children post-heart transplant to understand their quality of life and address any functional limitations, she said.

    The study was supported by a grant from the Additional Ventures and Enduring Hearts organizations and a gift from the Van Hooser family.

    Source:

    Ann & Robert H. Lurie Children’s Hospital of Chicago

    Journal reference:

    Schumacher, K. R., et al. (2025). The Impact of Fontan Circulatory Failure on Heart Transplant Survival: A 20-Center Retrospective Cohort Study. Circulation. doi.org/10.1161/circulationaha.124.072961.

    Continue Reading

  • Dual-function organic molecule may advance display technologies and medical imaging

    Dual-function organic molecule may advance display technologies and medical imaging

    Researchers at Kyushu University have developed a novel organic molecule that simultaneously exhibits two highly sought-after properties: efficient light emission suitable for advanced displays and strong light absorption for deep-tissue bioimaging. This breakthrough addresses a long-standing challenge in molecular design, paving the way for next-generation multifunctional materials. T

    This image depicts the structure of the proposed organic molecule, alongside the energy level diagrams of two-photon absorption (left side) and thermally activated delayed fluorescence (right side).

    Youhei Chitose/Kyushu University

    Organic light-emitting diodes (OLEDs) are at the forefront of modern display and lighting technologies, powering nearly everything from smartphone screens to large televisions and monitors. A key phenomenon that is actively being researched to enhance OLED efficiency is thermally activated delayed fluorescence (TADF). This process occurs when absorbed energy trapped in a non-light-emitting state (triplet state) is shifted into a light-emitting state (singlet state) using heat from the surroundings. In simple terms, materials exhibiting TADF can efficiently produce light from energy that would normally be lost, leading to brighter and more energy-efficient devices.

    Beyond displays, the ability to capture sharp images of biological tissues while causing minimal harm is crucial for medical diagnostics and research. To this end, techniques leveraging two-photon absorption (2PA) have proven useful. In 2PA, instead of absorbing a single high-energy photon, a molecule absorbs two lower-energy photons simultaneously from a high-intensity laser to reach an excited state capable of emitting fluorescence. Light with lower-energy photons and longer wavelengths, like near infrared, is ideal for biomedical imaging, since it can penetrate much deeper into tissues without scattering. As a bonus, 2PA means that only a small portion of tissue at the laser’s focal point is excited, causing less damage to living cells.

    Although TADF and 2PA are both desirable properties in organic materials—one for efficient light emission, and the other for superior imaging—combining both in a single molecule has been extremely challenging. This is because these mechanisms impose conflicting design requirements. Strong TADF calls for a twisted molecular structure that physically separates electron orbitals to facilitate energy conversion. In contrast, 2PA typically requires a more planar structure with significant orbital overlap to enable effective light absorption.

    “Recognizing that these two functions have complementary advantages but conflicting molecular requirements, I was motivated to design a material that could harmonize both, ultimately aiming to create new multifunctional materials that could link the fields of electronics and life sciences,” says Dr. Youhei Chitose, Assistant Professor of the Graduate School of Engineering at Kyushu University, Japan, and the lead author of the study.

    To fill this knowledge gap, the research team employed a clever molecular design strategy. They created a molecule called CzTRZCN that acts as a molecular switch, changing its structure and properties depending on whether it’s absorbing or emitting light. Their approach involved combining an electron-rich carbazole (Cz) compound with an electron-deficient triazine (TRZ) core. The researchers were able to finetune how the electrons grouped into orbitals within the structure by also adding cyano (CN) groups, which exert a strong pull onto electrons.

    The end result meant that during light absorption, CzTRZCN maintains enough orbital overlap between its components to efficiently absorb two photons simultaneously. After excitation, the molecule undergoes structural changes that separate these components, enabling TADF.

    Through a combination of theoretical calculations and experimental validation, the team demonstrated that their newly designed material achieved remarkable dual functionality. When integrated into an OLED device, CzTRZCN achieved an external quantum efficiency of 13.5%, establishing a new benchmark among triazine-based TADF materials. Moreover, it exhibited a high 2PA cross-section (a measure of 2PA efficiency) and high brightness, signifying its potential for medical imaging.

    “The proposed molecule is a metal-free organic compound with low toxicity to cells and high biocompatibility. This makes it ideal for use in medical probes for precise cancer and neurological diagnostics, especially through time-resolved fluorescence microscopy,” highlights Chitose.

    Overall, this study represents an important step toward developing versatile organic materials that bridge the fields of photoelectronics and bioimaging. Beyond medical use, the proposed molecular design strategy for achieving different orbital characteristics for absorption and emission can be widely applied to other multifunctional materials.

    “Moving forward, we aim to expand this molecular design approach to cover a broader range of emission wavelengths. We also plan to collaborate with researchers in biomedical and device engineering fields to explore the implementation of these materials in practical applications such as in vivo imaging, wearable sensors, and OLEDs,” concludes Chitose.

    Continue Reading

  • New Canadian guideline highlights expanded role of obesity medications

    New Canadian guideline highlights expanded role of obesity medications

    “Pharmacotherapy can help people living with obesity improve overall health, not just lose weight,” says Dr. Sue D. Pedersen, MD, endocrinologist and obesity medicine specialist in Calgary, and lead author of this guideline. “The goal of obesity medications is to improve metabolic, mechanical, and/or mental health, and improve quality of life, incorporating treatment goals that are important to each individual patient.”

    The guideline includes 6 new and 7 revised recommendations, reflecting the latest evidence since the 2022 and 2020 versions of the guideline. It takes the emphasis off body mass index (BMI) and focuses on an individualized approach that uses additional indicators, such as waist circumference, waist-to-hip ratio, waist-to-height ratio, adjusted for sex and ethnicity where appropriate, and the presence of obesity-related complications.

    Obesity pharmacotherapy is a safe and effective option to support long-term obesity care. It is one of three pillars of treatment outlined in the full Canadian Adult Obesity Clinical Practice Guideline, with other pillars being behavioural and psychological and surgical approaches. Obesity treatment should always be tailored to each person’s specific health needs, values, and preferences. Recommendations also support sustained use of obesity pharmacotherapy as part of a long-term strategy to maintain improvements in health and quality of life.”


    Dr. Sue D. Pedersen, MD, endocrinologist and obesity medicine specialist in Calgary

    Recommendations include two new medications, tirzepatide and setmelanotide, as well as new recommendations for obesity-related complications such as atherosclerotic cardiovascular disease, heart failure with preserved ejection fraction, osteoarthritis, and more.

    The guideline recommends against using compounded obesity medications because of concerns about content, safety, efficacy, and quality.

    The guideline panel notes that only Alberta recognizes obesity as a chronic disease. Barriers to access – such as cost, stigma, and limited drug plan coverage – continue to prevent Canadians from receiving medication and support.

    “The lack of recognition of obesity as a chronic disease by public and private payers, health systems, the public, and media has a trickle-down effect, limiting access to treatment (e.g., related to medication costs),” the authors conclude.

    Source:

    Canadian Medical Association Journal

    Journal reference:

    Pedersen, S. D., et al. (2025) Pharmacotherapy for obesity management in adults: 2025 clinical practice guideline update. CMAJ. doi.org/10.1503/cmaj.250502.

    Continue Reading

  • Shortcut to weight loss? Scientists discover ‘hidden’ brain shortcut without nausea |

    Shortcut to weight loss? Scientists discover ‘hidden’ brain shortcut without nausea |

    Weight loss is the kind of ever-evolving and ever-elusive goal we keep on chasing throughout our whole lives. Whether it’s due to reasons related to better health or just for the sake of a better appearance, weight loss ranks quite high on our to-do list. Simultaneously, shedding pounds is one of the hardest tasks to do, especially if it’s the stubborn visceral fat you’re trying to lose. Even with proper diet, rigorous workout, and other wellness rituals, losing a considerable amount of weight is a tough job. Unless you’re resorting to fast solutions like Ozempic, Mounjaro, and medications of a similar kind.But they do come with their fair share of downsides. Enter nausea, vomiting, and whatnot! But, imagine losing weight without the nausea that often makes popular drugs like Ozempic impossible to stick with.

    5 Exercises for quick weight loss

    A team led by Syracuse University’s Prof. Robert Doyle has identified a brain peptide that can curb appetite and improve glucose control, without causing nausea or vomiting.Read on to know more.

    A ‘shortcut’ to weight loss: What’s the science?

    Semaglutide (Ozempic, Wegovy) is an anti-diabetic medication used for the treatment of type 2 diabetes and an anti-obesity medication used for long-term weight management. It is a peptide similar to the hormone glucagon-like peptide-1, modified with a side chain. It can be administered by subcutaneous injection or taken orally.

    Weight loss (14)

    Now, these traditional weight-loss drugs, such as GLP-1 receptor agonists (e.g., Ozempic, Wegovy), focus on neurons in the brain’s hindbrain region. While effective at curbing appetite, they often cause nausea and vomiting, which causes about 70% of patients to stop treatment within a year.Enter the research team from Syracuse University, led by chemistry professor Robert Doyle. They looked beyond neurons to explore the role of brain “support cells,” like glia and astrocytes, cells that don’t transmit electrical signals but help neurons function properly.Talk about introducing science and smart work, packed together!

    The appetite-suppressing molecule: ODN to TDN

    The research team discovered that astrocytes in the hindbrain generate a natural peptide, octadecaneuropeptide (ODN), which reduces appetite and improves glucose metabolism in lab animals. Because ODN itself isn’t suitable for human use, researchers created a modified version named tridecaneuropeptide (TDN). When injected into obese mice and musk shrews, TDN triggered weight loss and better blood sugar control, without causing nausea or vomiting.

    Weight loss (15)

    Why is this a shortcut?

    Doyle compares current drugs to running a marathon from the very start. They must navigate many steps, some causing side effects, before appetite suppression occurs. TDN, in contrast, starts the race halfway through by directly activating downstream support cells, skipping the early neuron-focused steps that provoke nausea.As quoted by Science Daily, Doyle explained, “Instead of running a marathon from the very beginning like current drugs do, our targeting downstream pathways in support cells is like starting the race halfway through, reducing the unpleasant side effects many people experience,” adding, “If we could hit that downstream process directly, then potentially we wouldn’t have to use GLP-1 drugs with their side effects. Or we could reduce their dose, improving the toleration of these drugs. We could trigger weight loss signals that happen later in the pathway more directly.”

    Weight loss (13)

    What’s next

    This discovery opens the door to new obesity and diabetes treatments that are potentially more tolerable and easier to stick with. To bring this to reality, a new biotech company called CoronationBio has been formed. It holds the licensing rights from Syracuse University and the University of Pennsylvania, and plans to start human clinical trials around 2026–2027.

    Why this discovery is ‘groundbreaking’

    Syracuse University’s discovery of a brain “shortcut” via support cells marks a potential turning point in obesity treatment. Why? Without nausea, patients may stick to treatment longer, which means better compliance and quality of life. Moreover, TDN or similar drugs could make obesity treatments safer and more appealing to more people. Additionally, bypassing the neuron-heavy path might allow lower doses of traditional drugs when combined with this approach. Bonus point? Shifting focus from neurons to support cells could inspire more targeted approaches in brain-related treatments.


    Continue Reading

  • Exact collective occupancies of the Moshinsky model in two-dimensional geometry

    Exact collective occupancies of the Moshinsky model in two-dimensional geometry

    We consider a system of N bosons in a two-dimensional isotropic harmonic potential, interacting with a force proportional to the square of the distance between the particles. The Hamiltonian of this system has the form11

    $$begin{aligned} mathscr {H} = sum _{i=1}^Nleft[ -{hslash ^2over 2m}nabla ^{2}_{textbf{r}_{i}} + {m omega ^2textbf{r}^2_{i}over 2}+sum _{j=i+1}Lambda |textbf{r}_i-textbf{r}_j|^2right] , end{aligned}$$

    (1)

    which can be transformed into a dimensionless form using the spatial coordinates expressed in (sqrt{hslash /momega }), the interaction parameter (Lambda) in (m omega ^2) and the energy in (hslash / omega).

    One-particle reduced density matrix

    The integral representation of the one-particle reduced density matrix is as follows

    $$begin{aligned} rho (textbf{r},textbf{r}^{‘})=int Psi ^{*}(textbf{r},textbf{r}_{2},…,textbf{r}_{N})Psi (textbf{r}^{‘},textbf{r}_{2},…,textbf{r}_{N})dtextbf{r}_{2}…dtextbf{r}_{N}. end{aligned}$$

    (2)

    Their eigenvectors (u_{k}(textbf{r})) (natural orbitals) and eigenvalues (lambda _{k}) (occupancies) are determined by the following integral eigenproblem

    $$begin{aligned} int rho (textbf{r},textbf{r}^{‘})u_{k}(textbf{r}^{‘})dtextbf{r}^{‘}=lambda _{k}u_{k}(textbf{r}).end{aligned}$$

    (3)

    These eigenvalues can be interpreted as expansion coefficients in the Schmidt decomposition, while the corresponding eigenfunctions represent the natural orbitals of the system

    $$begin{aligned} rho (textbf{r},textbf{r}^{‘})=sum _{k}lambda _{k}u^{*}_{k}(textbf{r}^{‘})u_{k}(textbf{r}).end{aligned}$$

    (4)

    The eigenvalues (lambda _{k}) are widely employed to quantify correlation effects in many-body systems and to distinguish between various quantum phases, including condensed and fragmented states. In the system under consideration, the one-particle reduced density matrix can be derived analytically in Cartesian coordinates19 and is conveniently expressed in polar coordinates as follows

    $$begin{aligned} rho (textbf{r},textbf{r}^{‘})=A exp left( -{Bover 2}(r^2+{r^{‘}}^{2})+{Cover 2} r r^{‘}textrm{cos}(varphi -varphi ^{‘})right) , end{aligned}$$

    (5)

    with the normalization constant

    $$begin{aligned} A=left( 2pi int _0^{infty } e^{-Br^2+frac{C}{2} r^2} r drright) ^{-1} = {omega over pi gamma }, end{aligned}$$

    (6)

    where

    $$begin{aligned} B={omega over gamma }+{Cover 2}, C=left( {1-omega over N}right) ^2{(N-1)over gamma }, end{aligned}$$

    (7)

    and

    $$begin{aligned} gamma ={(N-1+omega )over N}, omega =sqrt{1+2Lambda N}. end{aligned}$$

    (8)

    Diagonal representation of the one-particle reduced density matrix

    The objective of this study is to derive the Schmidt decomposition of Eq. (5) in polar coordinates, providing a diagonal representation of the one-particle reduced density matrix. To this end, we first expand Eq. (5) in a Fourier-Lagrange series.

    $$begin{aligned} rho (textbf{r},textbf{r}^{‘})={rho _{0}(r, r^{‘})over {2pi }}+sum _{l=1}{ rho _{l}(r,r^{‘}) textrm{cos}[l(varphi -varphi ^{‘})]over {pi }}, end{aligned}$$

    (9)

    where the l-partial wave component is given by the following integral

    $$begin{aligned} rho _{l}(r, r^{‘})=int _{0}^{2pi } rho (textbf{r},textbf{r}^{‘}) textrm{cos}(ltheta ) dtheta ,end{aligned}$$

    (10)

    wherein (theta =varphi -varphi ^{‘}), which results in

    $$begin{aligned} rho _{l}(r, r^{‘})=2Api exp left( -{Bover 2}(r^2+{r^{‘}}^2)right) I_{l}left( {C rr^{‘}over 2}right) ,end{aligned}$$

    (11)

    where we have employed an integral formula for the modified Bessel function of the first kind (I_{l}(z)), that is23

    $$begin{aligned} int _{0}^{2pi }dtheta exp left( z cos (theta ) right) cos (l theta )=2pi I_{l}(z). end{aligned}$$

    (12)

    A detailed analysis indicates that the Schmidt decomposition of the l-partial component, denoted as (rho _{l}) in Eq. (11), can be derived by direct comparison with the Hardy-Hille formula24

    $$begin{aligned} exp left( -{left( {1over 2}+{tover 1-t} right) (x+y)} right) I_{alpha }left( {2 sqrt{ xyt}over 1-t}right) = sum _{n=0} {n! t^{n+frac{alpha }{2}}(1-t)over (n+alpha )!}(xy)^{frac{alpha }{2}}exp left( -{(x+y)over 2} right) L_{n}^alpha (x)L_{n}^{alpha }(y), end{aligned}$$

    (13)

    where (L_{n}^{alpha }(x)) is the generalized Laguerre polynonomial and

    $$begin{aligned} t=-1+{4Bover C^2}left( 2B-sqrt{4B^2-C^2}right) . end{aligned}$$

    (14)

    By substituting (x = z^2r^2) and (y = z^2{r^{‘}}^2) into the formula (13), where

    $$begin{aligned} z={(4B^2-C^2)^{1over 4}over sqrt{2}},end{aligned}$$

    (15)

    we derive the matching condition

    $$begin{aligned} B=left( 1 + 2t(1 – t)^{-1}right) z^2, C=4sqrt{t}(1 – t)^{-1}z^2,end{aligned}$$

    (16)

    which, together with the requirement that Schmidt orbitals be normalized, yields

    $$begin{aligned} rho _{l}(r,r^{‘})=sum _{n} lambda _{n,l}v_{n,l}(r^{‘}) v_{n,l}(r),end{aligned}$$

    (17)

    with

    $$begin{aligned} v_{nl}(r)=sqrt{{2 n! z^2 over (n+|l|)!}}(z r)^{|l|}e^{-z^2r^2/2}L_{n}^{|l|}(z^2 r^2), end{aligned}$$

    (18)

    and

    $$begin{aligned} lambda _{nl}={Api t^{M}(1-t)over z^{2}}, qquad text {with} qquad M=n+frac{|l|}{2}.end{aligned}$$

    (19)

    Using the above expressions and the identity (cos (ltheta ) = (exp (i ltheta ) + exp (-i ltheta ))/2), where i is an imaginary unit, we can represent the 1-RDM as follows

    $$begin{aligned} rho (textbf{r},textbf{r}^{‘})=sum _{n=0}^{infty } sum _{l=-infty }^{infty } lambda _{n,l}u^{*}_{n,l}(textbf{r}^{‘})u_{n,l}(textbf{r}), end{aligned}$$

    (20)

    where

    $$begin{aligned} u^{}_{n,l}(textbf{r})={v_{n,l}(r)}{e^{i lvarphi }over sqrt{2pi }}. end{aligned}$$

    (21)

    The orbitals (21) form an orthonormal basis set

    $$begin{aligned} int _{0}^{2pi } int _{0}^{infty }dvarphi dr [r u^{*}_{n,l}(textbf{r})u^{}_{n^{‘}l^{‘}}(textbf{r})]=delta _{nn^{‘}}delta _{ll^{‘}},end{aligned}$$

    (22)

    and they can be recognized as the natural orbitals of the occupancies (19). The values of (lambda _{n,l}) are ((2M+1))-fold degenerate indicating that for given M, there exist exactly ((2M+1)) orthogonal orbitals corresponding to (lambda _{n,l}). We note that while the Schmidt decomposition uniquely determines the set of non-zero occupation numbers, the decomposition is not unique. Alternative forms of Schmidt orbitals can be constructed for the degenerate points (lambda _{n,l} = lambda _{n|l|}) as follows25,26

    $$begin{aligned} chi _{n,l}(textbf{r})= {left{ begin{array}{ll} frac{1}{sqrt{2}} (u_{n,-l}(textbf{r})+u_{n,l}(textbf{r})), & text {for} lne 0\ \ u_{n,0}(textbf{r}), & text {for} l=0 end{array}right. } qquad qquad xi _{n,l}(textbf{r}) = {left{ begin{array}{ll} frac{i}{sqrt{2}}(u_{n,-l}(textbf{r})-u_{n,l}(textbf{r})) , & text {for} lne 0\ \ 0, & text {for} l=0 end{array}right. }. end{aligned}$$

    (23)

    The family ({chi _{n,l}, xi _{n,l}}) forms a complete and orthonormal set. In terms of the orbitals (23), the 1-RDM takes the form

    $$begin{aligned} rho (textbf{r},textbf{r}^{‘})=sum _{l,n=0}^{infty } lambda _{n,l} left( chi _{n,l}(textbf{r})chi _{n,l}(mathbf {r’})+xi _{n,l}(textbf{r})xi _{n,l}(mathbf {r’})right) . end{aligned}$$

    (24)

    Collective occupancies, participation, and correlation

    There are many different quantities for studying the properties of many-body states. In the case of isotropic symmetry, one of them is the collective occupancy, defined as the sum of occupancies with angular momentum l27

    $$begin{aligned} eta _l= sum _n lambda _{n,l}=frac{n_{l}}{N}, end{aligned}$$

    (25)

    where (n_{l}) denotes the number of particles with that angular momentum. This quantity determines a fraction of particles with a given l. For the present system, the collective occupancy is given by the geometric series ((0< t < 1)) and can thus be accurately determined in closed analytical form

    $$begin{aligned} eta _l= frac{ pi A t^{frac{|l|}{2}}}{z^2}, end{aligned}$$

    (26)

    which gives us a unique opportunity to examine its behavior in the full interaction regime and the general case of N particles. Another closely related quantity is participation, defined as

    $$begin{aligned} K_{eta }= left( sum _{l} eta _l^2 right) ^{-1},end{aligned}$$

    (27)

    which measures the effective number of collective occupancies, i.e., the number of l fragments that contribute significantly. The collective occupancies and this tool offer insight into correlations in the single-particle angular momentum domain. For the same reason as for collective occupancy, this measure can be obtained analytically.

    $$begin{aligned} K_{eta }=frac{z^4(1-t)}{pi ^2 A^2 (1+t)}.end{aligned}$$

    (28)

    By contrast, participation

    $$begin{aligned} K=left( sum _{n,l} lambda _{n,l}^2 right) ^{-1} =frac{z^4}{pi ^2 A^2} end{aligned}$$

    (29)

    quantifies the effective number of natural orbitals and serves as an indicator of the degree of single-particle correlations28. More specifically, it assesses how a subsystem containing one particle correlates with a subsystem composed of the remaining particles.

    Fig. 1

    Graphs (a) and (b) show the behaviors of collective occupancies as functions of interaction strength (Lambda) for two different particle numbers (N=2) and (N=500), respectively. The dashed lines represent the approximation results (30). The strength of the interaction (Lambda) is expressed in units of (m omega ^2). The graphs (c) and (d) illustrate the corresponding results for the participation (K_{eta }), together with its approximation obtained from the expansion to infinity, (Lambda rightarrow infty): (K_{eta } approx 2beta ^{-1}(N)Lambda ^{1/4}) (dashed lines).

    Continue Reading

  • Former Pentagon official on Trump courting Pak Army chief – Firstpost

    Former Pentagon official on Trump courting Pak Army chief – Firstpost

    Former Pentagon official Michael Rubin said that the US administration under Trump should not consider Islamabad as a non-Nato ally

    read more

    Former Pentagon official Michael Rubin has likened Pakistan’s Army Chief Asim Munir to Al Qaeda’s Osama Bin Laden, days after the official threatened to “take down half the world” with its nuclear weapons.

    “Asim Munir is Osama Bin Laden in a suit and there will be no amount of concession that will be given to Pakistan that is going to change his ideology or the Pakistani elite he represents,” Rubin said.

    Munir’s comment came over the weekend during an event in Tampa, Florida, where he said, “We are a nuclear nation. If we think we are going down, we’ll take half the world down with us.”

    STORY CONTINUES BELOW THIS AD

    Rubin, reacting to Munir’s comments, said, “The fact that Pakistan is threatening half of the world with nuclear weapons is a clear indication that it has lost its right to be a legitimate state. It is time for the US to consider other policies.”

    The former Pentagon official added that the US administration under Trump should not consider Islamabad as a non-Nato ally.

    “Pakistan should be the first major non-NATO ally to be listed as a state sponsor of terrorism and should not be a member of the US Central Command anymore,” Rubin said.

    He also called for Munir to be declared a persona non grata in the US and should not get the American Visa “until he explains himself and apologises.”

    STORY CONTINUES BELOW THIS AD

    Trump courts Munir

    The
    Field Marshal’s recent trip to the US is the second such state visit to the country, turning heads over its potential implications.

    During a last visit, the world saw a rare instance of Trump sitting with the Army chief of a country in the Oval Office, treating him like a head of state. The rise of the newly appointed Pakistani Field Marshal in the span of a few years has many people comparing him to the country’s erstwhile dictatorial Army chiefs, General Zia Ul Haq, Ayub Khan and Pervez Musharraf, all of whom eventually toppled the then-governments and took the reins of Pakistan.

    STORY CONTINUES BELOW THIS AD

    Amid all the speculations, America is treating Munir as what some call a “de facto” leader of Pakistan. However, the Pakistani general is facing his share of challenges within the country, some of which are as follows.


    Continue Reading

  • Hailey Bieber shares insights into ‘perfect weekend’ at Kylie Jenner’s birthday

    Hailey Bieber shares insights into ‘perfect weekend’ at Kylie Jenner’s birthday

    Hailey Bieber posts snaps from her ‘perfect weekend’

    Hailey Bieber has spent some “perfect” time with her close pals Kylie Jenner and Kendall Jenner over the weekend.

    The model took to her Instagram account on Monday, August 11, to share some insights into her well-spent weekend, at the Kylie Cosmetics founder’s 28th birthday celebartions.

    In the candid post, she dumped photos of herself enjoying a warm, cozy weekend.

    The first snap of the carousel featured Hailey sitting on a bench in a laid-back position, wearing a white mini dress with red dots on it.

    She also posted a snap of her painting, in which she drew her face with yellow petals around. The painting appears to have been drawn at Kylie’s birthday bash as the reality star also posted a video of herself drawing the same painting.

    Hailey Bieber shares insights into perfect weekend at Kylie Jenners birthday

    Hailey Bieber shares insights into perfect weekend at Kylie Jenners birthday

    One of the photos in the series showed a snap of a FaceTime screen which read, “Kendall is unavailable,” with an ostrich picture set as a profile picture of Kendall’s FaceTime ID.

    Hailey also posted a snap of herself in an outdoor setting while stretching her body in casual attire, donning black loose trousers and a light blue crop top.

    Hailey Bieber shares insights into perfect weekend at Kylie Jenners birthday

    This came after Kylie posted a series of snaps and videos from her intimate birthday celebrations. In one of her videos, when the beauty mogul was seen blowing the candles on her raspberry cake, Hailey and her husband Justin Bieber could be seen, as the Rhode owner captured memories on her phone.


    Continue Reading

  • Asia Cup: 3 big stars set to miss out, Gill vs Axar in vice-captaincy tussle

    Asia Cup: 3 big stars set to miss out, Gill vs Axar in vice-captaincy tussle

    Shubman Gill is the flavour of the season after his stupendous show in the recent Test series against England but he will face a contender in Axar Patel for vice-captaincy in the Indian squad for the Asia Cup T20 scheduled in the UAE next month.

    Also, pace spearhead Jasprit Bumrah is set to play in the tournament and might be rested for the opening Test against the West Indies in early October.

    The Ajit Agarkar-led selection committee is likely to select the squad for the Asia Cup on August 19 or 20 depending on when the Centre of Excellence’s (CoE) Sports Science team sends the medical bulletin of all players, including that of skipper Suryakumar Yadav, who has already started batting at the nets in Bengaluru.

    There will be some tricky selection calls but the Indian selectors would certainly like to maintain continuity which has given them a lot of success from the time Suryakumar took over as T20 captain.

    While Axar was the designated vice-captain during India’s last series against England at home, Gill was the deputy when Suryakumar was first appointed full-time skipper of the T20 squad in Sri Lanka last year.

    It is understood that the selection committee won’t be too keen to tinker with the set-up as Abhishek Sharma, Sanju Samson, Suryakumar, Tilak Varma and Hardik Pandya form a solid top five.

    “Abhishek Sharma is world’s No. 1 T20 batter in last ICC rankings. Sanju Samson has been fantastic last season with both bat and gloves. So it will certainly be a tough call but Shubman in current form (although in Tests) can’t be ignored. He had a good IPL also. Problem for selectors is, there are too many performers at the top of the order,” a BCCI source privy to developments told PTI.

    With so many players in top-order, it would be very difficult to find a slot for Yashasvi Jaiswal and Sai Sudharsan.

    Even KL Rahul, who is now the first choice keeper in ODIs, is unlikely to be considered as he doesn’t bat in the middle-order.

    Second keeper’s slot

    While Samson is all but certain to be the first keeper, the choice for the second keeper’s slot will be between Jitesh Sharma and Dhruv Jurel. While Jurel was a part of the last T20 series, Jitesh had been impressive for RCB during their IPL winning campaign. He has also revelled in the role of a finisher.

    Reddy unlikely to be fit in time

    While Hardik Pandya remains India’s first choice white ball seam bowling all-rounder, Nitish Kumar Reddy, who suffered injury during the England series, is unlikely to get fit in time. Shivam Dube, who made a good comeback against England, is likely to find his place in the squad.

    Axar and Washington Sundar are set to be the other two spin-bowling all-rounders in the squad.

    Who will be third seamer, Prasidh Krishna or Harshit Rana?

    The main bone of contention will be the seam-bowling attack where Bumrah and Arshdeep Singh have locked their slots. The third slot is a fight between Prasidh Krishna, who has 25 wickets in last IPL, and the burly Harshit Rana, who has ability to bowl some really heavy deliveries.

    Likely contenders: Suryakumar Yadav (capt), Shubman Gill, Abhishek Sharma, Sanju Samson (wk), Tilak Verma, Shivam Dube, Axar Patel, Washington Sundar, Varun Chakravarthy, Kuldeep Yadav, Jasprit Bumrah, Arshdeep Singh, Harshit Rana/Prasidh Krishna, Hardik Pandya, Jitesh Sharma/Dhruv Jurel.


    Continue Reading