Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Gas de Bose diluït més enllà del límit d'universalitat

Planasdemunt Hospital, Martí

Published Jul 10, 2023• 0 citations
OpenAlex

Abstract

The Bose equation of state has not progressed significantly since the universality regime discovery in terms of the s-wave scattering length, a. Nowadays no expansion exists to calculate the energy at higher densities, which does not show universality anymore and differs depending on the interaction potential of the particles. Current proposals are reviewed to study the possibility of extending the universality in terms of the s-wave effective range, r_0, and p-wave scattering length, a_1. We do so by achieving agreement using the Diffusion Monte Carlo (DMC) method between the energies of systems presenting interaction potentials that share up to the aforementioned 2-body scattering parameters. It is obtained that potentials sharing at least the additional parameter r_0, of similar or less magnitude than a, show this better consensus in their energies at higher densities. Dependencies between the scattering parameters and the energy are explored to validate current theories and present a preliminary proposal for the next term in the series expansion.

Related papers

Equation of state of Bose gases beyond the universal regime

Jordi Pera, Jordi Boronat

The equation of state of dilute Bose gases, in which the energy only depends on the s -wave scattering length, is rather unknown beyond the universal limit. We have carried out a set of diffusion Monte Carlo calculations up to gas parameters of 10 − 2 to explore how the departure from the universality emerges. Using different model potentials, we calculate the energies of the gas in an exact way, within some statistical noise, and report the results as a function of the three relevant scattering parameters: the s -wave scattering length a 0 , the s -wave effective range r 0 , and the p -wave scattering length a 1 . If the effective range is not large, we observe universality in terms of a 0 and r 0 up to gas parameters of 10 − 2 . If r 0 grows, the regime of universality in these two parameters is reduced and effects of a 1 start to be observed. In the ( a 0 , r 0 ) universal regime we propose an analytical law that reproduces fairly well the exact energies. Published by the American Physical Society 2024

arXiv:2407.18059•Physical Review Research•Dec 30, 2024•1 citation

Equation of state of an interacting Bose gas at finite temperature: A path-integral Monte Carlo study

Sebastiano Pilati, K. Sakkos, Jordi Boronat +2 more

By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same $s$-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.

arXiv:cond-mat/0607721•Physical Review A•Oct 27, 2006•29 citations

Equation of state of atomic systems beyond s-wave determined by the lowest order constrained variational method: Large scattering length limit

Ryan M. Kalas, D. Blume

Dilute Fermi systems with large s-wave scattering length a_s exhibit universal properties if the interparticle spacing r_o greatly exceeds the range of the underlying two-body interaction potential. In this regime, r_o is the only relevant length scale and observables such as the energy per particle depend only on r_o (or, equivalently, the energy E_{FG} of the free Fermi gas). This paper investigates Bose and Fermi systems with non-vanishing angular momentum l using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of a l-dependent length scale ξ_l, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite l. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.

arXiv:0704.1804•Apr 13, 2007•0 citations

Universality in ultradilute liquid Bose-Bose mixtures

Viktor Cikojević, Leandra Vranješ Markić, G. E. Astrakharchik +1 more

We have studied dilute Bose-Bose mixtures of atoms with attractive interspecies and repulsive intraspecies interactions using quantum Monte Carlo methods at $T=0$. Using a number of models for interactions, we determine the range of validity of the universal equation of state of the symmetric liquid mixture as a function of two parameters: the $s$-wave scattering length and the effective range of the interaction potential. It is shown that the Lee-Huang-Yang correction is sufficient only for extremely dilute liquids with the additional restriction that the range of the potential is small enough. Based on the quantum Monte Carlo equation of state we develop a density functional which goes beyond the Lee-Huang-Yang term and use it together with the local density approximation to determine density profiles of realistic self-bound drops.

arXiv:1811.04436•Physical Review A•Feb 13, 2019•81 citations

Equation of state of cold atoms: A lowest-order-constrained variational study of systems with large non- s -wave scattering lengths

Ryan M. Kalas, D. Blume

Dilute Fermi systems with large $s$-wave scattering length ${a}_{s}$ exhibit universal properties if the interparticle spacing ${r}_{0}$ greatly exceeds the range of the underlying two-body interaction potential. In this regime, ${r}_{0}$ is the only relevant length scale and observables such as the energy per particle depend only on ${r}_{0}$ (or, equivalently, the energy ${E}_{\mathrm{FG}}$ of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum $l$ using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an $l$-dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite $l$. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.

Physical Review A•Jul 18, 2007•3 citations

Critical Temperature of Interacting Bose Gases in Two and Three Dimensions

Sebastiano Pilati, S. Giorgini, Nikolay V. Prokof'ev

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.

arXiv:0801.3424•Physical Review Letters•Apr 9, 2008•75 citations
The Bose equation of state has not progressed significantly since the universality regime discovery in terms of the s-wave scattering length, a. Nowadays no expansion exists to calculate the energy at higher densities, which does not show universality anymore and differs depending on the interaction potential of the particles. Current proposals are reviewed to study the possibility of extending the universality in terms of the s-wave effective range, r_0, and p-wave scattering length, a_1. We do so by achieving agreement using the Diffusion Monte Carlo (DMC) method between the energies of systems presenting interaction potentials that share up to the aforementioned 2-body scattering parameters. It is obtained that potentials sharing at least the additional parameter r_0, of similar or less magnitude than a, show this better consensus in their energies at higher densities. Dependencies between the scattering parameters and the energy are explored to validate current theories and present a preliminary proposal for the next term in the series expansion.
The equation of state of dilute Bose gases, in which the energy only depends on the s -wave scattering length, is rather unknown beyond the universal limit. We have carried out a set of diffusion Monte Carlo calculations up to gas parameters of 10 − 2 to explore how the departure from the universality emerges. Using different model potentials, we calculate the energies of the gas in an exact way, within some statistical noise, and report the results as a function of the three relevant scattering parameters: the s -wave scattering length a 0 , the s -wave effective range r 0 , and the p -wave scattering length a 1 . If the effective range is not large, we observe universality in terms of a 0 and r 0 up to gas parameters of 10 − 2 . If r 0 grows, the regime of universality in these two parameters is reduced and effects of a 1 start to be observed. In the ( a 0 , r 0 ) universal regime we propose an analytical law that reproduces fairly well the exact energies. Published by the American Physical Society 2024
By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same sss-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.
Dilute Fermi systems with large s-wave scattering length a_s exhibit universal properties if the interparticle spacing r_o greatly exceeds the range of the underlying two-body interaction potential. In this regime, r_o is the only relevant length scale and observables such as the energy per particle depend only on r_o (or, equivalently, the energy E_{FG} of the free Fermi gas). This paper investigates Bose and Fermi systems with non-vanishing angular momentum l using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of a l-dependent length scale ξ_l, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite l. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.
We have studied dilute Bose-Bose mixtures of atoms with attractive interspecies and repulsive intraspecies interactions using quantum Monte Carlo methods at T=0T=0T=0. Using a number of models for interactions, we determine the range of validity of the universal equation of state of the symmetric liquid mixture as a function of two parameters: the sss-wave scattering length and the effective range of the interaction potential. It is shown that the Lee-Huang-Yang correction is sufficient only for extremely dilute liquids with the additional restriction that the range of the potential is small enough. Based on the quantum Monte Carlo equation of state we develop a density functional which goes beyond the Lee-Huang-Yang term and use it together with the local density approximation to determine density profiles of realistic self-bound drops.
Dilute Fermi systems with large sss-wave scattering length as{a}_{s}as​ exhibit universal properties if the interparticle spacing r0{r}_{0}r0​ greatly exceeds the range of the underlying two-body interaction potential. In this regime, r0{r}_{0}r0​ is the only relevant length scale and observables such as the energy per particle depend only on r0{r}_{0}r0​ (or, equivalently, the energy EFG{E}_{\mathrm{FG}}EFG​ of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum lll using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an lll-dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite lll. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.
We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.