We calculate the dynamic polarizability of a one-dimensional Bose gas confined into a parabolic trap near the Tonks–Girardeau limit. We use the duality between the one-dimensional Bose gas with δ-interaction and the one-dimensional Fermi gas with δ''-interaction to map the strong interaction regime of the first into the weak one of the latter. The quantities which depend only on the modulus of the wavefunction can be calculated with either of the two theories; therefore, we have used the random-phase approximation in the weak coupling regime of the fermionic system to access dynamic properties in the strong coupling regime of the bosonic one.We calculate the dynamic polarizability of a one-dimensional Bose gas confined into a parabolic trap near the Tonks–Girardeau limit. We use the duality between the one-dimensional Bose gas with δ-interaction and the one-dimensional Fermi gas with δ''-interaction to map the strong interaction regime of the first into the weak one of the latter. The quantities which depend only on the modulus of the wavefunction can be calculated with either of the two theories; therefore, we have used the random-phase approximation in the weak coupling regime of the fermionic system to access dynamic properties in the strong coupling regime of the bosonic one.

Journal of Physics B Atomic Molecular and Optical PhysicsMay 2, 20066 citations

Introduction to One-Dimensional Bose Gases

Tim Langen

Springer thesesJan 1, 20150 citations

Critical Temperature Shift in Weakly Interacting Bose Gas

V. А. Kashurnikov, Nikolay V. Prokof'ev, Boris V. Svistunov

With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional $|\ensuremath{\psi}{|}^{4}$ theory (which includes quantum Bose gas). In terms of critical density, ${n}_{c}$ , mass, $m$ , interaction, $U$ , and temperature, $T$ , this shift is universal: $\ensuremath{\Delta}{n}_{c}(T){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}Cm}^{3}{T}^{2}U$, the constant $C$ found to be equal to $0.0140\ifmmode\pm\else\textpm\fi{}0.0005$. For quantum Bose gas with the scattering length $a$ this implies $\ensuremath{\Delta}{T}_{c}{/T}_{c}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}C}_{0}{\mathrm{an}}^{1/3}$, with ${C}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.29\ifmmode\pm\else\textpm\fi{}0.05$.With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional $|\ensuremath{\psi}{|}^{4}$ theory (which includes quantum Bose gas). In terms of critical density, ${n}_{c}$, mass, $m$, interaction, $U$, and temperature, $T$, this shift is universal: $\ensuremath{\Delta}{n}_{c}(T){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}Cm}^{3}{T}^{2}U$, the constant $C$ found to be equal to $0.0140\ifmmode\pm\else\textpm\fi{}0.0005$. For quantum Bose gas with the scattering length $a$ this implies $\ensuremath{\Delta}{T}_{c}{/T}_{c}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}C}_{0}{\mathrm{an}}^{1/3}$, with ${C}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.29\ifmmode\pm\else\textpm\fi{}0.05$.

Physical Review LettersAug 28, 2001223 citations

Universality of the one-dimensional Bose gas with delta interaction

Luigi Amico A, V. E. Korepin

arXiv:cond-mat/0405155Annals of PhysicsSep 21, 200428 citations

{n}_{c}

, mass,

m

, interaction,

U

, and temperature,

T

, this shift is universal: $\ensuremath{\Delta}{n}_{c}(T){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}Cm}^{3}{T}^{2}U$, the constant

C

found to be equal to $0.0140\ifmmode\pm\else\textpm\fi{}0.0005$. For quantum Bose gas with the scattering length

a

this implies $\ensuremath{\Delta}{T}_{c}{/T}_{c}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}C}_{0}{\mathrm{an}}^{1/3}$, with ${C}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.29\ifmmode\pm\else\textpm\fi{}0.05$.