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Following the experimental observation of bright matter-wave solitons [L. Khaykovich et al., Science v. 296, 1290 (2002); K. E. Strecker et al., Nature (London) v. 417, 150 (2002)], we develop a semi-phenomenological theory for soliton thermodynamics and find the condensation temperature. Under a modified thermodynamic limit, the condensate occupation at the critical temperature undergoes a sudden jump to a nonzero value, indicating a discontinuous phase transition. Treating the condensation as a diffusion over a barrier shows that the condensation time is exponentially long as one approaches the thermodynamic limit, and the longest near the critical temperature.
We present a new theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles
Soliton hydrodynamics is an appealing tool to describe strong turbulence in low-dimensional systems. Strong turbulence in quasi-one dimensional spuerfluids, such as Bose-Einstein condensates, involves the dynamics of dark solitons and, therefore, the
We study the ground state of a one-dimensional (1D) trapped Bose gas with two mobile impurity particles. To investigate this set-up, we develop a variational procedure in which the coordinates of the impurity particles are slow-like variables. We val
For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the in
Most experimental observations of solitons are limited to one-dimensional (1D) situations, where they are naturally stable. For instance, in 1D cold Bose gases, they exist for any attractive interaction strength $g$ and particle number $N$. By contra