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

arXiv:cond-mat/9603029

Theory of Interacting Quantum Gases

Henk T. C. Stoof, M. Bijlsma, M. Houbiers

Published Mar 5, 1996• 2 citations
arXivHTMLPDF

Abstract

We present a unified picture of the interaction effects in dilute atomic quantum gases. We consider fermionic as well as bosonic gases and, in particular, discuss for both forms of statistics the fundamental differences between a gas with effectively repulsive and a gas with effectively attractive interatomic interactions, i.e.\ between a gas with either a positive or a negative scattering length.

DOI
10.48550/arxiv.cond-mat/9603029

Related papers

Theory of interacting quantum cases

Henk T. C. Stoof, M. Bijlsma, M. Houbiers

We present a unified picture of the interaction effects in dilute atomic quantum gases. We consider fermionic as well as bosonic gases and, in particular, discuss for both forms of statistics the fundamental differences between a gas with effectively repulsive and a gas with effectively attractive inter atomic interactions, i.e., between a gas with either a positive or a negative scattering length.

Journal of Research of the National Institute of Standards and Technology•Jul 1, 1996•54 citations

Interacting Fermi Gases and the BCS–BEC Crossover

Лев П. Питаевский, S. Stringari

Abstract This is the first of a series of chapters devoted to interacting Fermi gases, with special focus here on the effects of superfluidity. It starts with a brief discussion of the ideal Fermi gas and then focuses on the properties of dilute interacting Fermi gases. Topics include the weakly repulsive Fermi gas; the gas of composite bosons; the BCS limit of a weakly interacting Fermi gas; the strongly interacting, but still dilute, unitary Fermi gas where the scattering length is much larger than the average interatomic distance; the BCS–BEC crossover; and the Bogoliubov–de Gennes approach. A discussion of the main physical quantities predicted by mean-field theory and by quantum Monte Carlo simulations, including, in particular, the equation of state, the momentum distribution, and the condensation of pairs, is also presented.

•Jan 1, 2016•1 citation

Statistically interacting quantum gases in D dimensions

Geoffrey G. Potter

Chapter 1. Exact and explicit results are derived for the thermodynamic properties (isochores, isotherms, isobars, response functions, speed of sound) of a quantum gas in dimensions [special characters omitted] ≥ 1 and with fractional exclusion statistics 0 ≤ g ≤ 1 connecting bosons (g = 0) and fermions (g = 1). In [special characters omitted] = 1 the results are equivalent to those of the Calogero-Sutherland model, a gas with long-range two-body interaction. Emphasis is given to the crossover between boson-like and fermion-like features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. A phase transition along the isobar occurs at a nonzero temperature in all dimensions. The T-dependence of the speed of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential. Chapter 2. The exact thermodynamics (isochores, isotherms, isobars, response functions, speed of sound) is worked out for a statistically interacting quantum gas in [special characters omitted] dimensions. The results in [special characters omitted] = 1 are those of the thermodynamic Bethe ansatz for the Nonlinear Schrödinger model, a gas with repulsive two-body contact potential. In all dimensions the ideal boson and fermion gases are recovered in the weak-coupling and strong-coupling limits, respectively. For all nonzero couplings ideal fermion gas behavior emerges for [special characters omitted] >> 1 and, in the limit [special characters omitted] → ∞, a phase transition occurs at T > 0. Significant deviations from ideal quantum gas behavior are found for intermediate coupling and finite [special characters omitted]. Chapter 3. Methodology previously developed in the framework of the coordinate Bethe ansatz applied to integrable quantum gas models is employed to calculate some ground-state properties and elementary excitations for quantum gas models in [special characters omitted] = 1 dimensions with statistical interactions that are not equivalent to dynamical interactions. The focus in this comparative study is on modifications of the Calogero-Sutherland and Nonlinear Schrödinger models. Statistical interactions cannot be chosen arbitrarily. They must satisfy certain physicality conditions, which will be discussed in some detail.

Journal of Media Literacy Education•Jan 1, 2008•0 citations

Ground-State Energy of a Dilute Fermi Gas

Élliott H. Lieb, Robert Seiringer, Jan Philip Solovej

Recent developments in the physics of low density trapped gases make it worthwhile to verify old, well known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently developed techniques to give a rigorous derivation of the asymptotic formula for the ground state energy of a dilute gas of $N$ fermions interacting with a short-range, positive potential of scattering length $a$. For spin 1/2 fermions, this is $E \sim E^0 + (\hbar^2/2m) 2 πN ρa$, where $E^0$ is the energy of the non-interacting system and $ρ$ is the density.

arXiv:math-ph/0507049•Jul 19, 2005•0 citations

A dilute mixture of atoms and molecules

Sungkit Yip

We study a dilute gas with two species of Fermionic atoms of unequal concentrations, interacting via a short-range interaction with one deeply bound state. We study the properties of this system under the mean-field approximation. We obtain the effective interaction among the fermions and bosons, and discuss the collective modes of the system.

arXiv:cond-mat/0203582•Mar 28, 2002•0 citations

Interactions in quantum fluids

Thierry Giamarchi

In these notes I review the basic concepts of the effects of interactions on quantum particles. I focuss here mostly on the case of fermions, but several aspects of interacting bosons are mentioned as well. These notes have been voluntarily kept at an elementary level and should be suitable for students wanting to enter this field. I review the concept of Fermi liquid, and then move to a description of the interaction effects, as well as the main models that are used to tackle these questions. Finally I study the case of one dimensional interacting particles that constitutes a fascinating special case.

arXiv:1007.1030•Oxford University Press eBooks•May 5, 2011•1 citation
We present a unified picture of the interaction effects in dilute atomic quantum gases. We consider fermionic as well as bosonic gases and, in particular, discuss for both forms of statistics the fundamental differences between a gas with effectively repulsive and a gas with effectively attractive interatomic interactions, i.e.\ between a gas with either a positive or a negative scattering length.
Abstract This is the first of a series of chapters devoted to interacting Fermi gases, with special focus here on the effects of superfluidity. It starts with a brief discussion of the ideal Fermi gas and then focuses on the properties of dilute interacting Fermi gases. Topics include the weakly repulsive Fermi gas; the gas of composite bosons; the BCS limit of a weakly interacting Fermi gas; the strongly interacting, but still dilute, unitary Fermi gas where the scattering length is much larger than the average interatomic distance; the BCS–BEC crossover; and the Bogoliubov–de Gennes approach. A discussion of the main physical quantities predicted by mean-field theory and by quantum Monte Carlo simulations, including, in particular, the equation of state, the momentum distribution, and the condensation of pairs, is also presented.
Chapter 1. Exact and explicit results are derived for the thermodynamic properties (isochores, isotherms, isobars, response functions, speed of sound) of a quantum gas in dimensions [special characters omitted] ≥ 1 and with fractional exclusion statistics 0 ≤ g ≤ 1 connecting bosons (g = 0) and fermions (g = 1). In [special characters omitted] = 1 the results are equivalent to those of the Calogero-Sutherland model, a gas with long-range two-body interaction. Emphasis is given to the crossover between boson-like and fermion-like features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. A phase transition along the isobar occurs at a nonzero temperature in all dimensions. The T-dependence of the speed of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential. Chapter 2. The exact thermodynamics (isochores, isotherms, isobars, response functions, speed of sound) is worked out for a statistically interacting quantum gas in [special characters omitted] dimensions. The results in [special characters omitted] = 1 are those of the thermodynamic Bethe ansatz for the Nonlinear Schrödinger model, a gas with repulsive two-body contact potential. In all dimensions the ideal boson and fermion gases are recovered in the weak-coupling and strong-coupling limits, respectively. For all nonzero couplings ideal fermion gas behavior emerges for [special characters omitted] >> 1 and, in the limit [special characters omitted] → ∞, a phase transition occurs at T > 0. Significant deviations from ideal quantum gas behavior are found for intermediate coupling and finite [special characters omitted]. Chapter 3. Methodology previously developed in the framework of the coordinate Bethe ansatz applied to integrable quantum gas models is employed to calculate some ground-state properties and elementary excitations for quantum gas models in [special characters omitted] = 1 dimensions with statistical interactions that are not equivalent to dynamical interactions. The focus in this comparative study is on modifications of the Calogero-Sutherland and Nonlinear Schrödinger models. Statistical interactions cannot be chosen arbitrarily. They must satisfy certain physicality conditions, which will be discussed in some detail.
Recent developments in the physics of low density trapped gases make it worthwhile to verify old, well known results that, while plausible, were based on perturbation theory and assumptions about pseudopotentials. We use and extend recently developed techniques to give a rigorous derivation of the asymptotic formula for the ground state energy of a dilute gas of NNN fermions interacting with a short-range, positive potential of scattering length aaa. For spin 1/2 fermions, this is E∼E0+(ℏ2/2m)2πNρaE \sim E^0 + (\hbar^2/2m) 2 πN ρaE∼E0+(ℏ2/2m)2πNρa, where E0E^0E0 is the energy of the non-interacting system and ρρρ is the density.
In these notes I review the basic concepts of the effects of interactions on quantum particles. I focuss here mostly on the case of fermions, but several aspects of interacting bosons are mentioned as well. These notes have been voluntarily kept at an elementary level and should be suitable for students wanting to enter this field. I review the concept of Fermi liquid, and then move to a description of the interaction effects, as well as the main models that are used to tackle these questions. Finally I study the case of one dimensional interacting particles that constitutes a fascinating special case.