Bose gases confined in highly elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1D model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1D Bose gas become independent of the actual value of the 3D scattering length a(3D). In this unitary regime, the energy of the system is well described by a hard-rod equation of state. We investigate the stability of quasi-1D Bose gases with positive and negative a(3D).Bose gases confined in highly elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1D model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1D Bose gas become independent of the actual value of the 3D scattering length a(3D). In this unitary regime, the energy of the system is well described by a hard-rod equation of state. We investigate the stability of quasi-1D Bose gases with positive and negative a(3D).

arXiv:cond-mat/0308585Physical Review LettersJan 22, 200481 citations

Weakly Interacting Bose Gas

WORLD SCIENTIFIC eBooksJul 1, 20100 citations

Exact 1∕N and optimized perturbative evaluation of μc for homogeneous interacting Bose gases

Jean-Loı̈c Kneur, Marcus Benghi Pinto

In the framework of the $\mathrm{O}(N)$ three-dimensional effective scalar field model for homogeneous dilute weakly interacting Bose gases we use the $1∕N$ expansion, within the large- $N$ limit, to evaluate the parameter ${r}_{c}$ which is directly related to the critical chemical potential ${\ensuremath{\mu}}_{c}$. This quantity enters the order- ${a}^{2}{n}^{2∕3}$ coefficient contributing to the critical temperature shift $\ensuremath{\Delta}{T}_{c}$ where $a$ represents the $s$ -wave scattering length and $n$ represents the density. Compared to the recent precise numerical lattice simulation results, our calculation suggests that the large- $N$ approximation performs rather well even for the physical case $N=2$ . We then calculate the same quantity but using different forms of the optimized perturbative (variational) method, showing that these produce excellent results for both the finite- $N$ and large- $N$ cases.In the framework of the $\mathrm{O}(N)$ three-dimensional effective scalar field model for homogeneous dilute weakly interacting Bose gases we use the $1∕N$ expansion, within the large-$N$ limit, to evaluate the parameter ${r}_{c}$ which is directly related to the critical chemical potential ${\ensuremath{\mu}}_{c}$. This quantity enters the order-${a}^{2}{n}^{2∕3}$ coefficient contributing to the critical temperature shift $\ensuremath{\Delta}{T}_{c}$ where $a$ represents the $s$-wave scattering length and $n$ represents the density. Compared to the recent precise numerical lattice simulation results, our calculation suggests that the large-$N$ approximation performs rather well even for the physical case $N=2$. We then calculate the same quantity but using different forms of the optimized perturbative (variational) method, showing that these produce excellent results for both the finite-$N$ and large-$N$ cases.

arXiv:cond-mat/0408538Physical Review AMar 9, 200518 citations

In the framework of the

\mathrm{O}(N)

three-dimensional effective scalar field model for homogeneous dilute weakly interacting Bose gases we use the

1∕N

expansion, within the large-

N

limit, to evaluate the parameter

{r}_{c}

which is directly related to the critical chemical potential ${\ensuremath{\mu}}_{c}$. This quantity enters the order-

{a}^{2}{n}^{2∕3}

coefficient contributing to the critical temperature shift $\ensuremath{\Delta}{T}_{c}$ where

a

represents the

s

-wave scattering length and

n

represents the density. Compared to the recent precise numerical lattice simulation results, our calculation suggests that the large-

N

approximation performs rather well even for the physical case

N=2

. We then calculate the same quantity but using different forms of the optimized perturbative (variational) method, showing that these produce excellent results for both the finite-

N

and large-

N

cases.