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:0803.1215 · Journal of Physics B Atomic Molecular and Optical Physics

Fermionic ground state at unitarity and Haldane exclusion statistics

R. K. Bhaduri, M. V. N. Murthy, M. Brack

Published May 20, 2008• 15 citations
arXivHTMLPDF

Abstract

We consider a few-particle system of trapped neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate the energies and the spatial densities of the few-body systems using a generalization of the extended Thomas–Fermi (ETF) method, and assuming the particles obey the Haldane–Wu fractional exclusion statistics (FES) at unitarity. This method is different from the scaled ETF version given by Chang and Bertsch (2007 Phys. Rev. A 76 021603). Our semiclassical FES results are consistent with the Monte Carlo calculations of the above authors, but can hardly be distinguished from their overall scaling of the ETF result at unitarity.

DOI
10.1088/0953-4075/41/11/115301

Related papers

Cold atoms at unitarity and semiclassical ground state of a Fermi gas for Haldane-Wu exclusion statistics

Jérôme Roccia

We investigate finite particle systems of cold atoms bound in a local potential V(r). We derive the ground state energy and the particle density using a recently developed semiclassical theory (2008 Phys. Rev. Lett. 100 200408), and assuming the particles are described by the Haldane-Wu fractional exclusion statistics (FES) at unitarity. This approach is applied to atoms trapped into a three dimensional harmonic oscillator. We show that the parameter-free FES semiclassical theory yields results that are consistent with numerical simulations by Chang and Bertsch [2007 Phys. Rev A 76 021603(R)] and Bulgac (2007 Phys. Rev. A 76 040502).

arXiv:1002.3270•Feb 17, 2010•0 citations

Fermions at unitarity and Haldane exclusion statistics

R K Bhaduri, M V N Murthy, M K Srivastava

We consider a gas of neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate the variation of the chemical potential and the energy per particle as a function of temperature by assuming the system to be an ideal gas obeying the Haldane–Wu fractional exclusion statistics. Our results for the untrapped gas compare favourably with the recently published Monte Carlo calculations of two groups. For a harmonically trapped gas, the results agree with the experiment, and also with other published works.

arXiv:cond-mat/0606117•Journal of Physics B Atomic Molecular and Optical Physics•Apr 30, 2007•13 citations

Fermions at unitarity and Haldane exclusion statistics

R. K. Bhaduri, M. V. N. Murthy, M. K. Srivastava

PACS. 05.30.-d – Quantum statistical mechanics. Abstract. – We consider a gas of neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate, the variation of the chemical potential and the energy per particle as a function of temperature by assuming the system to be an ideal gas obeying the Haldane-Wu fractional exclusion statistics. Our results for the untrapped gas compare favourably with the recently published Monte Carlo calculations of two groups. For a harmonically trapped gas, the results agree with experiment, and also with other published work. Consider a dilute gas of neutral fermionic atoms at a low temperature. In general, the low-energy properties of the gas are determined by the scattering length a, the number density n, and the temperature T of the gas ( the effective range r0 is small, so that r0/|a | → 0 as a becomes large). When the attractive interaction between the atoms is increased continuously by magnetic tuning from weak to strong, the scattering length a goes from a small negative to a small positive value. In between, there is a zero-energy two-body bound state, and |a|

•Jan 1, 2006•6 citations

Interacting fermions in a two-dimensional trap and fractional exclusion statistics

M. K. Srivastava, R. K. Bhaduri, J. Law +1 more

We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a self-consistent Hartree-Fock calculation. The two results are shown to agree even for a small number of particles. We next use the finite-temperature Thomas-Fermi method to demonstrate that in the local density approximation, these interacting fermions are equivalent to a system of noninteracting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto a system of N noninteracting quasiparticles enables us to predict the energies of the ground and excited states of the N-body system. PACS Nos.: 05.30-d, 73.20Dx

Canadian Journal of Physics•Jan 1, 2000•7 citations

A two-dimensional interacting system obeying Fractional Exclusion Statistics

M. K. Srivastava, R. K. Bhaduri, J. Law +1 more

We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a self-consistent Hartree-Fock calculation. The two results are shown to agree even for a small number of particles. We next use the finite temperature Thomas-Fermi method to demonstrate that in the local density approximation, these interacting fermions are equivalent to a system of noninteracting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto to a system of N noninteracting quasi-particles enables us to predict the energies of the excited states of the N-body system.

arXiv:cond-mat/9902158•Feb 11, 1999•0 citations

Numerical study of unitary fermions in one spatial dimension

Michael G. Endres

I perform lattice Monte Carlo studies of universal four-component fermion systems in one spatial dimension. Continuum few-body observables (i.e., ground-state energies and integrated contact densities) are determined for both unpolarized and polarized systems of up to eight fermions confined to a harmonic trap. Estimates of the continuum energies for four and five trapped fermions show agreement with exact analytic calculations to within approximately one percent statistical uncertainties. Continuum many-body observables are determined for unpolarized systems of up to 88 fermions confined to a finite box, and 56 fermions confined to a harmonic trap. Results are reported for universal quantities such as the Bertsch parameter, defined as the energy of the untrapped many-body system in units of the corresponding free-gas energy, and its subleading correction at large but finite scattering length. Two independent estimates of these quantities are obtained from thermodynamic limit extrapolations of continuum extrapolated observables. A third estimate of the Bertsch parameter is obtained by combining estimates of the untrapped and trapped integrated contact densities with additional theoretical input from a calculation based on Thomas-Fermi theory. All estimates of the Bertsch parameter and its subleading correction are found to be consistent to within approximately one percent statistical uncertainties. Finally, the continuum restoration of virial theorems is verified for both few- and many-body systems confined to a trap.

arXiv:1302.6694•Physical Review A•Jun 19, 2013•4 citations
We consider a few-particle system of trapped neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate the energies and the spatial densities of the few-body systems using a generalization of the extended Thomas–Fermi (ETF) method, and assuming the particles obey the Haldane–Wu fractional exclusion statistics (FES) at unitarity. This method is different from the scaled ETF version given by Chang and Bertsch (2007 Phys. Rev. A 76 021603). Our semiclassical FES results are consistent with the Monte Carlo calculations of the above authors, but can hardly be distinguished from their overall scaling of the ETF result at unitarity.
We investigate finite particle systems of cold atoms bound in a local potential V(r). We derive the ground state energy and the particle density using a recently developed semiclassical theory (2008 Phys. Rev. Lett. 100 200408), and assuming the particles are described by the Haldane-Wu fractional exclusion statistics (FES) at unitarity. This approach is applied to atoms trapped into a three dimensional harmonic oscillator. We show that the parameter-free FES semiclassical theory yields results that are consistent with numerical simulations by Chang and Bertsch [2007 Phys. Rev A 76 021603(R)] and Bulgac (2007 Phys. Rev. A 76 040502).
We consider a gas of neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate the variation of the chemical potential and the energy per particle as a function of temperature by assuming the system to be an ideal gas obeying the Haldane–Wu fractional exclusion statistics. Our results for the untrapped gas compare favourably with the recently published Monte Carlo calculations of two groups. For a harmonically trapped gas, the results agree with the experiment, and also with other published works.
PACS. 05.30.-d – Quantum statistical mechanics. Abstract. – We consider a gas of neutral fermionic atoms at ultra-low temperatures, with the attractive interaction tuned to Feshbach resonance. We calculate, the variation of the chemical potential and the energy per particle as a function of temperature by assuming the system to be an ideal gas obeying the Haldane-Wu fractional exclusion statistics. Our results for the untrapped gas compare favourably with the recently published Monte Carlo calculations of two groups. For a harmonically trapped gas, the results agree with experiment, and also with other published work. Consider a dilute gas of neutral fermionic atoms at a low temperature. In general, the low-energy properties of the gas are determined by the scattering length a, the number density n, and the temperature T of the gas ( the effective range r0 is small, so that r0/|a | → 0 as a becomes large). When the attractive interaction between the atoms is increased continuously by magnetic tuning from weak to strong, the scattering length a goes from a small negative to a small positive value. In between, there is a zero-energy two-body bound state, and |a|
We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a self-consistent Hartree-Fock calculation. The two results are shown to agree even for a small number of particles. We next use the finite-temperature Thomas-Fermi method to demonstrate that in the local density approximation, these interacting fermions are equivalent to a system of noninteracting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto a system of N noninteracting quasiparticles enables us to predict the energies of the ground and excited states of the N-body system. PACS Nos.: 05.30-d, 73.20Dx
We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a self-consistent Hartree-Fock calculation. The two results are shown to agree even for a small number of particles. We next use the finite temperature Thomas-Fermi method to demonstrate that in the local density approximation, these interacting fermions are equivalent to a system of noninteracting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto to a system of N noninteracting quasi-particles enables us to predict the energies of the excited states of the N-body system.
I perform lattice Monte Carlo studies of universal four-component fermion systems in one spatial dimension. Continuum few-body observables (i.e., ground-state energies and integrated contact densities) are determined for both unpolarized and polarized systems of up to eight fermions confined to a harmonic trap. Estimates of the continuum energies for four and five trapped fermions show agreement with exact analytic calculations to within approximately one percent statistical uncertainties. Continuum many-body observables are determined for unpolarized systems of up to 88 fermions confined to a finite box, and 56 fermions confined to a harmonic trap. Results are reported for universal quantities such as the Bertsch parameter, defined as the energy of the untrapped many-body system in units of the corresponding free-gas energy, and its subleading correction at large but finite scattering length. Two independent estimates of these quantities are obtained from thermodynamic limit extrapolations of continuum extrapolated observables. A third estimate of the Bertsch parameter is obtained by combining estimates of the untrapped and trapped integrated contact densities with additional theoretical input from a calculation based on Thomas-Fermi theory. All estimates of the Bertsch parameter and its subleading correction are found to be consistent to within approximately one percent statistical uncertainties. Finally, the continuum restoration of virial theorems is verified for both few- and many-body systems confined to a trap.