scholarly journals A kinetic beam scheme for ideal quantum gas dynamics

2006 ◽  
Vol 462 (2069) ◽  
pp. 1553-1572 ◽  
Author(s):  
Jaw-Yen Yang ◽  
Yu-Hsin Shi
Keyword(s):  
Excited States ◽  
Gas Dynamics ◽  
Local Thermodynamic Equilibrium ◽  
Spatial Dimension ◽  
Quantum Gas ◽  
Quantum Distribution ◽  
Spatial Dimensions ◽  
Ideal Quantum ◽  
Bose Einstein ◽  
The Ideal

A novel kinetic beam scheme for the ideal quantum gas is presented for the computation of quantum gas dynamical flows. The quantum Boltzmann equation approach is adopted and the local thermodynamic equilibrium quantum distribution is assumed. Both Bose–Einstein and Fermi–Dirac gases are considered. Formulae for one spatial dimension is first derived and the resulting beam scheme is tested for shock tube flows. Implementation of high-order methods is also outlined. We only consider the system in the normal phase consisting of particles in excited states and both the classical limit and the nearly degenerate limit are computed. The flow structures can all be accurately captured by the present beam scheme. Formulations for multiple spatial dimensions are also included.

scholarly journals Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

Atoms ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Hiroyuki Tajima ◽  
Junichi Takahashi ◽  
Simeon Mistakidis ◽  
Eiji Nakano ◽  
Kei Iida
Keyword(s):  
Spectral Function ◽  
Einstein Condensate ◽  
Three Dimensions ◽  
Quantum Gas ◽  
Many Body ◽  
Bose Einstein Condensate ◽  
Spatial Dimensions ◽  
Three Body ◽  
Bose Einstein ◽  
The Impact

The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.

The Ideal Quantum Gas

2001 ◽  
pp. 141-159
Author(s):  
Ragnar Ekholm ◽  
Leonard D. Kohn ◽  
Seymour H. Wollman
Keyword(s):  
Quantum Gas ◽  
Ideal Quantum ◽  
The Ideal

Kinetic Flux Vector Splitting Schemes for Ideal Quantum Gas Dynamics

2007 ◽  
Vol 29 (1) ◽  
pp. 221-244 ◽  
Author(s):  
Jaw‐Yen Yang ◽  
Tse‐Yang Hsieh ◽  
Yu‐Hsin Shi
Keyword(s):  
Gas Dynamics ◽  
Quantum Gas ◽  
Flux Vector ◽  
Splitting Schemes ◽  
Flux Vector Splitting ◽  
Ideal Quantum

ν-DIMENSIONAL IDEAL QUANTUM q-GAS: BOSE-EINSTEIN CONDENSATION AND λ-POINT TRANSITION

1994 ◽  
Vol 08 (23) ◽  
pp. 3281-3298 ◽  
Author(s):  
M. R-MONTEIRO ◽  
ITZHAK RODITI ◽  
LIGIA M.C.S. RODRIGUES
Keyword(s):  
Critical Temperature ◽  
Chemical Potential ◽  
Ideal Gas ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Spatial Dimensions ◽  
Quantum Symmetries ◽  
Ideal Quantum ◽  
Bose Einstein ◽  
Λ Point

We consider an ideal quantum q-gas in ν spatial dimensions and energy spectrum ωiα pα Departing from the Hamiltonian H=ω[N], we study the effect of the deformation on thermodynamic functions and equation of state of that system. The virial expansion is obtained for the high temperature (or low density) regime. The critical temperature is higher than in non-deformed ideal gases. We show that Bose-Einstein condensation always exists (unless when ν/α=1) for finite q but not for q=∞. Employing numerical calculations and selecting for v/α the values 3/2, 2 and 3, we show the critical temperature as a function of q, the specific heat CV and the chemical potential µ as functions of [Formula: see text] for q=1.05 and q=4.5. CV exhibits a λ-point discontinuity in all cases, instead of the cusp singularity found in the usual ideal gas. Our results indicate that physical systems which have quantum symmetries can exhibit Bose-Einstein condensation phenomenon, the critical temperature being favored by the deformation parameter.

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