scholarly journals High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph

2020 ◽  
pp. 2050035
Author(s):  
Zied Ammari ◽  
Antsa Ratsimanetrimanana
Keyword(s):  
High Temperature ◽  
Fundamental Property ◽  
Quantum Statistical Mechanics ◽  
Finite Graph ◽  
Quantum Systems ◽  
Semiclassical Analysis ◽  
Equilibrium Measures ◽  
Bogoliubov Inequality ◽  
Kms Condition ◽  
Quantum Condition

The Kubo–Martin–Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and Verboven, proposed an analogue to the KMS condition for infinite classical mechanical systems and highlighted its relationship with the Kirkwood–Salzburg equations and with the Gibbs equilibrium measures. In this paper, we prove that in a certain limiting regime of high temperature the classical KMS condition can be derived from the quantum condition in the simple case of the Bose–Hubbard dynamical system on a finite graph. The main ingredients of the proof are Golden–Thompson inequality, Bogoliubov inequality and semiclassical analysis.

scholarly journals Experimentally Accessible Witnesses of Many-Body Localization

2019 ◽  
Vol 1 (1) ◽  
pp. 50-62 ◽  
Author(s):  
Marcel Goihl ◽  
Mathis Friesdorf ◽  
Albert H. Werner ◽  
Winton Brown ◽  
Jens Eisert
Keyword(s):  
Statistical Physics ◽  
Optical Lattices ◽  
Cold Atoms ◽  
Quantum Statistical Mechanics ◽  
Quantum Systems ◽  
Many Body ◽  
Physical Systems ◽  
Tensor Network ◽  
Distinct Features ◽  
Flight Measurements

The phenomenon of many-body localized (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalize, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localized systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density–density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models.

QUASI-MODULAR SYMMETRY AND QUASI-HYPERGEOMETRIC FUNCTIONS IN QUANTUM STATISTICAL MECHANICS OF FRACTIONAL EXCLUSION STATISTICS

1999 ◽  
Vol 13 (29n30) ◽  
pp. 1039-1046 ◽  
Author(s):  
KAZUMOTO IGUCHI ◽  
KAZUHIKO AOMOTO
Keyword(s):  
Statistical Mechanics ◽  
Modular Group ◽  
Hypergeometric Functions ◽  
Chemical Potential ◽  
Quantum Statistical Mechanics ◽  
Quantum Systems ◽  
Quantum Statistical ◽  
Physical Quantities

We investigate a novel symmetry in dualities of Wu's equation: wg(1+w)1-g=eβ(ε-μ) for a degenerate g-on gas with fractional exclusion statistics of g, where β=1/k B T, ∊ the energy, and μ the chemical potential of the system. We find that the particle–hole duality between g and 1/g and the supersymmetric duality between g and 1-g form a novel quasi-modular group of order six for Wu's equation. And we show that many physical quantities in quantum systems with the fractional exclusion statistics can be represented in terms of quasi-hypergeometric functions and that the quasi-modular symmetry acts on these functions.

scholarly journals High-temperature criticality in strongly constrained quantum systems

2006 ◽  
Vol 73 (14) ◽  
Author(s):  
Claudio Castelnovo ◽  
Claudio Chamon ◽  
Christopher Mudry ◽  
Pierre Pujol
Keyword(s):  
High Temperature ◽  
Quantum Systems

q-Deformed Tamm–Dancoff oscillators: Coherent state and thermostatistics

2014 ◽  
Vol 28 (21) ◽  
pp. 1450130 ◽  
Author(s):  
Won Sang Chung ◽  
Abdullah Algin
Keyword(s):  
High Temperature ◽  
Equation Of State ◽  
Coherent State ◽  
Specific Heat ◽  
High Temperatures ◽  
Deformation Parameter ◽  
Quantum Systems ◽  
Oscillator Algebra ◽  
Many Body ◽  
The Real

The q-deformed bosonic Tamm–Dancoff oscillator algebra is considered. The coherent state of the q-deformed bosonic Tamm–Dancoff oscillator algebra is first constructed in detail. Second, the high-temperature thermostatistical properties of a gas of the Tamm–Dancoff oscillators are investigated. For high temperatures, the specific heat, the entropy and the equation of state for the system are derived in terms of the real deformation parameter q. The results obtained by the effects of Tamm–Dancoff type q-deformation show that they could be useful for further researches on understanding of mutual interactions between bosons and fermions in many-body quantum systems.

scholarly journals Semiclassical analysis of constrained quantum systems

2004 ◽  
Vol 37 (21) ◽  
pp. 5605-5624 ◽  
Author(s):  
G F Dell'Antonio ◽  
L Tenuta
Keyword(s):  
Quantum Systems ◽  
Semiclassical Analysis

QUANTIZATION OF CLASSICAL CONSTANTS OF MOTION AND EQUILIBRIUM DISTRIBUTIONS IN QUANTUM MECHANICS

1996 ◽  
Vol 10 (15) ◽  
pp. 723-730
Author(s):  
Z. HABA
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Quantum Statistical Mechanics ◽  
Quantum Systems ◽  
Quantization Procedure ◽  
Constant Of Motion ◽  
Additional Constant ◽  
Constants Of Motion ◽  
Equilibrium Distributions ◽  
Quantum Statistical

We distinguish a class of quantum systems (trigonometric and hyperbolic potentials) with an additional constant of motion unrelated to any symmetry. The various quantum constants of motion result from non-uniqueness of the quantization procedure. We discuss equilibrium distributions in quantum statistical mechanics determined by the constants of motion.

scholarly journals Reworking Zubarev’s Approach to Nonequilibrium Quantum Statistical Mechanics

Particles ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 197-207 ◽  
Author(s):  
Francesco Becattini ◽  
Matteo Buzzegoli ◽  
Eduardo Grossi
Keyword(s):  
Local Thermodynamic Equilibrium ◽  
Quantum Statistical Mechanics ◽  
Gluon Plasma ◽  
Quantum Systems ◽  
Kubo Formula ◽  
Operator Approach ◽  
Nuclear Collisions ◽  
Quantum Statistical ◽  
Relativistic Nuclear Collisions ◽  
Nonequilibrium Quantum Statistical Mechanics

In this work, the nonequilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at a local thermodynamic equilibrium is revisited. This method, which was used to obtain the first “Kubo” formula of shear viscosity, is especially suitable to describe quantum effects in fluids. This feature makes it a viable tool to describe the physics of Quark–Gluon Plasma in relativistic nuclear collisions.

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