ON CONDENSATION IN NON-IDEAL BOSE GAS

1989 ◽  
Vol 03 (06) ◽  
pp. 471-478
Author(s):  
D.P. SANKOVICH
Keyword(s):  
Critical Temperature ◽  
Low Temperature ◽  
Upper Bound ◽  
Bose Gas ◽  
The One ◽  
Ideal Bose Gas

A model of the non-ideal Bose gas is considered. We prove the existence of condensate in the model at sufficiently low temperature. The method of majorizing estimates for the Duhamel Two Point Functions is used. The equation for the critical temperature and the upper bound for the one-particle excitations energy are obtained.

ON THE LOW-TEMPERATURE BEHAVIOR OF THE INFINITE-VOLUME IDEAL BOSE GAS

2010 ◽  
Vol 13 (01) ◽  
pp. 39-63
Author(s):  
KARL-HEINZ FICHTNER ◽  
KEI INOUE ◽  
MASANORI OHYA
Keyword(s):  
Low Temperature ◽  
Numerical Simulations ◽  
Bose Gas ◽  
Temperature Behavior ◽  
Infinite Volume ◽  
Position Distribution ◽  
Bounded Volume ◽  
Ideal Bose Gas ◽  
The Ideal

In Ref. 11 clustering representations of the position distribution of the ideal Bose gas were considered. In principle that gives rise to possibilities concerning simulations of the system of positions of the particles. But one has to take into account that in case of low temperature the clusters are very large and their origins are far from a fixed bounded volume. For that reason we will consider some estimations of the influence of these clusters on the behavior of the subsystem of particles located in a fixed bounded volume. All points in the fixed bounded volume come from a bigger volume which the estimation (5.2) in Theorem 5.2 gives on average. Several numerical simulations in dimension two are shown in Sec. 5.

scholarly journals Free energy asymptotics of the quantum Heisenberg spin chain

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Marcin Napiórkowski ◽  
Robert Seiringer
Keyword(s):  
Free Energy ◽  
Low Temperature ◽  
Upper And Lower Bounds ◽  
One Dimension ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Analogous Estimate ◽  
Spatial Dimensions ◽  
The One ◽  
Ideal Bose Gas

AbstractWe consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin $$S\ge 1/2$$ S ≥ 1 / 2 . We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.

scholarly journals The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Isabelle Bouchoule ◽  
Benjamin Doyon ◽  
Jerome Dubail
Keyword(s):  
Loss Rate ◽  
Time Derivative ◽  
Numerical Procedure ◽  
Hard Core ◽  
Bose Gas ◽  
Rapidity Distribution ◽  
One Dimensional ◽  
Non Local ◽  
The One ◽  
Ideal Bose Gas

We theoretically investigate the effect of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of KK-body losses (K=1,2,3,\dotsK=1,2,3,…) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion – where the gas behaves like an ideal Bose gas – and hard-core repulsion – where the gas is mapped to a non-interacting Fermi gas –, we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.

CBED study of low-temperature InP grown by gas source MBE

1993 ◽  
Vol 51 ◽  
pp. 810-811
Author(s):  
R. Rajesh ◽  
M.J. Kim ◽  
J.S. Bow ◽  
R.W. Carpenter ◽  
G.N. Maracas
Keyword(s):  
Low Temperature ◽  
Second Phase ◽  
Material System ◽  
Ion Milling ◽  
Electrical Measurements ◽  
Gas Source ◽  
Structural And Electrical Properties ◽  
The One ◽  
Lt Inp ◽  
Gas Source Mbe

In our previous work on MBE grown low temperature (LT) InP, attempts had been made to understand the relationships between the structural and electrical properties of this material system. Electrical measurements had established an enhancement of the resistivity of the phosphorus-rich LT InP layers with annealing under a P2 flux, which was directly correlated with the presence of second-phase particles. Further investigations, however, have revealed the presence of two fundamentally different types of precipitates. The first type are the surface particles, essentially an artefact of argon ion milling and containing mostly pure indium. The second type and the one more important to the study are the dense precipitates in the bulk of the annealed layers. These are phosphorus-rich and are believed to contribute to the improvement in the resistivity of the material.The observation of metallic indium islands solely in the annealed LT layers warranted further study in order to better understand the exact reasons for their formation.

Particle number fluctuations in an ideal Bose gas

1997 ◽  
Vol 44 (10) ◽  
pp. 1801-1814 ◽  
Author(s):  
MARTIN WILKENS and CHRISTOPH WEISS
Keyword(s):  
Particle Number ◽  
Bose Gas ◽  
Ideal Bose Gas

scholarly journals Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Phan Thành Nam ◽  
Marcin Napiórkowski
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Mean Field ◽  
Interaction Strength ◽  
Bose Gas ◽  
Body Density ◽  
The Mean ◽  
The One ◽  
Mean Field Regime ◽  
Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

scholarly journals A BOUND FOR THE INDEX OF A QUADRATIC FORM AFTER SCALAR EXTENSION TO THE FUNCTION FIELD OF A QUADRIC

2018 ◽  
Vol 19 (2) ◽  
pp. 421-450 ◽  
Author(s):  
Stephen Scully
Keyword(s):  
Quadratic Form ◽  
Upper Bound ◽  
Function Field ◽  
The Other ◽  
Direct Generalization ◽  
Other Hand ◽  
General Field ◽  
The One ◽  
Anisotropic Quadratic Form

Let $q$ be an anisotropic quadratic form defined over a general field $F$. In this article, we formulate a new upper bound for the isotropy index of $q$ after scalar extension to the function field of an arbitrary quadric. On the one hand, this bound offers a refinement of an important bound established in earlier work of Karpenko–Merkurjev and Totaro; on the other hand, it is a direct generalization of Karpenko’s theorem on the possible values of the first higher isotropy index. We prove its validity in two key cases: (i) the case where $\text{char}(F)\neq 2$, and (ii) the case where $\text{char}(F)=2$ and $q$ is quasilinear (i.e., diagonalizable). The two cases are treated separately using completely different approaches, the first being algebraic–geometric, and the second being purely algebraic.

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