ﻻ يوجد ملخص باللغة العربية
We present a detailed beyond-mean-field analysis of a weakly interacting Bose gas in the crossover from three to low dimensions. We find an analytical solution for the energy and provide a clear qualitative picture of the crossover in the case of a box potential with periodic boundary conditions. We show that the leading contribution of the confinement-induced resonance is of beyond-mean-field order and calculate the leading corrections in the three- and low-dimensional limits. We also characterize the crossover for harmonic potentials in a model system with particularly chosen short- and long-range interactions and show the limitations of the local-density approximation. Our analysis is applicable to Bose-Bose mixtures and gives a starting point for developing the beyond-mean-field theory in inhomogeneous systems with long-range interactions such as dipolar particles or Rydberg-dressed atoms.
We present a novel approach to modeling dynamics of trapped, degenerate, weakly interacting Bose gases beyond the mean field limit. We transform a many-body problem to the interaction representation with respect to a suitably chosen part of the Hamil
Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate-like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dim
In quantum gases with contact repulsion, the distribution of momenta of the atoms typically decays as $sim 1/|p|^4$ at large momentum $p$. Tans relation connects the amplitude of that $1/|p|^4$ tail to the adiabatic derivative of the energy with resp
Recent experiments with ultracold lanthanide atoms which are characterized by a large magnetic moment have revealed the crucial importance of beyond-mean-field corrections in understanding the dynamics of the gas. We study how the presence of an exte
The mean-field dynamics of a Bose gas is shown to break down at time $tau_h = (c_1/gamma) ln N$ where $gamma$ is the Lyapunov exponent of the mean-field theory, $N$ is the number of bosons, and $c_1$ is a system-dependent constant. The breakdown time