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/0502600

Bogoliubov-like mode in the Tonks-Girardeau Gas

Ovchinnikov, Igor V., Daniel Neuhauser

Published Feb 25, 2005• 0 citations
arXivHTMLPDF

Abstract

We reformulate 1D boson-fermion duality in path-integral terms. The result is a 1D counterpart of the boson-fermion duality in the 2D Chern-Simons gauge theory. The theory is consistent and enables, using standard resummation techniques, to obtain the long-wave-length asymptotics of the collective mode in 1D boson systems at the Tonks-Girardeau regime. The collective mode has the dispersion of Bogoliubov phonons: $ω(q)=q \sqrt{\barρU(q)/m}$, where $\barρ$ is the bosons density and $U(q)$ is a Fourier component of the two-body potential.

DOI
10.48550/arxiv.cond-mat/0502600

Related papers

1D composite fermions: Bogoliubov-like mode in the Tonks-Girardeau gas

I. V Ovchinnikov, Daniel Neuhauser

We reformulate 1D boson-fermion duality in path-integral terms. The result is a 1D counterpart of the boson-fermion duality in the 2D Chern-Simons gauge theory. The theory is consistent and enables, using standard resummation techniques, to obtain the long-wavelength asymptotics of the collective mode in 1D boson systems at the Tonks-Girardeau regime. The collective mode has the dispersion of Bogoliubov phonons: ω( q ) = q ( U ( q )/ m ) 1/2 , where is the bosons density and U ( q ) is a Fourier component of the two-body potential.

Europhysics Letters (EPL)•May 4, 2006•0 citations

Anyons in a tight wave-guide and the Tonks-Girardeau gas

Nicolas Rougerie, Qiyun Yang

We consider a many-body system of 2D anyons, free quantum particles with general statistics parameter \alpha ∈ ]0,2[ α ∈ ] 0 , 2 [ . In the magnetic gauge picture they are described as bosons attached to Aharonov-Bohm fluxes of intensity 2\pi \alpha 2 π α , generating long-range magnetic forces. A dimensional reduction to 1D is obtained by imposing a strongly anisotropic trapping potential. This freezes the motion in the direction of strong trapping, leading to 1D physics along the weak direction. The latter is governed to leading order by the Tonks-Girardeau model of impenetrable bosons, independently of \alpha α .

arXiv:2302.05220•SciPost Physics Core•Nov 15, 2023•4 citations

Super-Tonks-Girardeau regime in trapped one-dimensional dipolar gases

G. E. Astrakharchik, Yu. E. Lozovik

Possible signatures are discussed of a super-Tonks-Girardeau gas in bosonic systems of trapped quasi-one-dimensional dipoles at zero temperature. We provide an estimation of the frequency of the lowest compressional mode and compare it to analytical results derived using the harmonic approach in the high-density regime. We construct an exact mapping of the ground-state wave function of a one-dimensional dipolar system of bosons, fermions, and a Bose-Fermi mixture and conclude that the local properties and energy are the same at zero temperature. The question as to what extent the dipolar potential can be treated as long or short range is discussed.

arXiv:0709.4609•Physical Review A•Jan 11, 2008•52 citations

Fermionization of a strongly interacting Bose-Fermi mixture in a one-dimensional harmonic trap

Bess Fang, Patrizia Vignolo, Christian Miniatura +1 more

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

arXiv:0809.4419•Physical Review A•Feb 26, 2009•20 citations

Collective mode damping and viscosity in a 1D unitary Fermi gas

M Punk, W. Zwerger

We calculate the damping of the Bogoliubov–Anderson mode in a one-dimensional (1D) two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther–Emery liquid of weakly bound pairs to a Lieb–Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks–Girardeau gas with a universal constant α ζ = 0.38 in the viscosity ζ = α ζ ℏ n for T = 0. For the trapped case, we calculate the Q-factor of the breathing mode and show that the damping provides a sensitive measure of temperature in 1D Fermi gases.

arXiv:cond-mat/0605413•New Journal of Physics•Aug 30, 2006•20 citations

Observation of a One-Dimensional Tonks-Girardeau Gas

Toshiya Kinoshita, Trevor Wenger, David S. Weiss

We report the observation of a one-dimensional (1D) Tonks-Girardeau (TG) gas of bosons moving freely in 1D. Although TG gas bosons are strongly interacting, they behave very much like noninteracting fermions. We enter the TG regime with cold rubidium-87 atoms by trapping them with a combination of two light traps. By changing the trap intensities, and hence the atomic interaction strength, the atoms can be made to act either like a Bose-Einstein condensate or like a TG gas. We measure the total 1D energy and the length of the gas. With no free parameters and over a wide range of coupling strengths, our data fit the exact solution for the ground state of a 1D Bose gas.

Science•Jul 29, 2004•1,413 citations
We reformulate 1D boson-fermion duality in path-integral terms. The result is a 1D counterpart of the boson-fermion duality in the 2D Chern-Simons gauge theory. The theory is consistent and enables, using standard resummation techniques, to obtain the long-wave-length asymptotics of the collective mode in 1D boson systems at the Tonks-Girardeau regime. The collective mode has the dispersion of Bogoliubov phonons: ω(q)=qρˉU(q)/mω(q)=q \sqrt{\barρU(q)/m}ω(q)=qρˉ​U(q)/m​, where ρˉ\barρρˉ​ is the bosons density and U(q)U(q)U(q) is a Fourier component of the two-body potential.
We reformulate 1D boson-fermion duality in path-integral terms. The result is a 1D counterpart of the boson-fermion duality in the 2D Chern-Simons gauge theory. The theory is consistent and enables, using standard resummation techniques, to obtain the long-wavelength asymptotics of the collective mode in 1D boson systems at the Tonks-Girardeau regime. The collective mode has the dispersion of Bogoliubov phonons: ω( q ) = q ( U ( q )/ m ) 1/2 , where is the bosons density and U ( q ) is a Fourier component of the two-body potential.
We consider a many-body system of 2D anyons, free quantum particles with general statistics parameter \alpha ∈ ]0,2[ α ∈ ] 0 , 2 [ . In the magnetic gauge picture they are described as bosons attached to Aharonov-Bohm fluxes of intensity 2\pi \alpha 2 π α , generating long-range magnetic forces. A dimensional reduction to 1D is obtained by imposing a strongly anisotropic trapping potential. This freezes the motion in the direction of strong trapping, leading to 1D physics along the weak direction. The latter is governed to leading order by the Tonks-Girardeau model of impenetrable bosons, independently of \alpha α .
Possible signatures are discussed of a super-Tonks-Girardeau gas in bosonic systems of trapped quasi-one-dimensional dipoles at zero temperature. We provide an estimation of the frequency of the lowest compressional mode and compare it to analytical results derived using the harmonic approach in the high-density regime. We construct an exact mapping of the ground-state wave function of a one-dimensional dipolar system of bosons, fermions, and a Bose-Fermi mixture and conclude that the local properties and energy are the same at zero temperature. The question as to what extent the dipolar potential can be treated as long or short range is discussed.
We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient CCC is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.
We calculate the damping of the Bogoliubov–Anderson mode in a one-dimensional (1D) two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther–Emery liquid of weakly bound pairs to a Lieb–Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks–Girardeau gas with a universal constant α ζ = 0.38 in the viscosity ζ = α ζ ℏ n for T = 0. For the trapped case, we calculate the Q-factor of the breathing mode and show that the damping provides a sensitive measure of temperature in 1D Fermi gases.
We report the observation of a one-dimensional (1D) Tonks-Girardeau (TG) gas of bosons moving freely in 1D. Although TG gas bosons are strongly interacting, they behave very much like noninteracting fermions. We enter the TG regime with cold rubidium-87 atoms by trapping them with a combination of two light traps. By changing the trap intensities, and hence the atomic interaction strength, the atoms can be made to act either like a Bose-Einstein condensate or like a TG gas. We measure the total 1D energy and the length of the gas. With no free parameters and over a wide range of coupling strengths, our data fit the exact solution for the ground state of a 1D Bose gas.