Contribution to the problem of the entropy increase of quantum mechanical many-body systems

1965 ◽  
Vol 18 (2) ◽  
pp. 145-148 ◽  
Author(s):  
J. I. Horváth
Keyword(s):  
Quantum Mechanical ◽  
Many Body ◽  
Entropy Increase ◽  
Many Body Systems

scholarly journals A REMARK ON ONE-DIMENSIONAL MANY-BODY PROBLEMS WITH POINT INTERACTIONS

2000 ◽  
Vol 14 (07) ◽  
pp. 721-727 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
LUDWIK DABROWSKI ◽  
SHAO-MING FEI
Keyword(s):  
Singular Point ◽  
Bound States ◽  
Quantum Mechanical ◽  
Contact Interactions ◽  
Many Body ◽  
Point Interactions ◽  
One Dimensional ◽  
Integrable Quantum ◽  
Scattering Matrices ◽  
Many Body Systems

The integrability of one-dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) δ-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.

scholarly journals The Correlation Production in Thermodynamics

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 111 ◽  
Author(s):  
Sheng-Wen Li
Keyword(s):  
Open System ◽  
Open Systems ◽  
Boltzmann Distribution ◽  
Ideal Gas ◽  
Many Body ◽  
Particle Collisions ◽  
Von Neumann ◽  
Entropy Increase ◽  
Many Body Systems ◽  
The Many

Macroscopic many-body systems always exhibit irreversible behaviors. However, in principle, the underlying microscopic dynamics of the many-body system, either the (quantum) von Neumann or (classical) Liouville equation, guarantees that the entropy of an isolated system does not change with time, which is quite confusing compared with the macroscopic irreversibility. We notice that indeed the macroscopic entropy increase in standard thermodynamics is associated with the correlation production inside the full ensemble state of the whole system. In open systems, the irreversible entropy production of the open system can be proved to be equivalent with the correlation production between the open system and its environment. During the free diffusion of an isolated ideal gas, the correlation between the spatial and momentum distributions is increasing monotonically, and it could well reproduce the entropy increase result in standard thermodynamics. In the presence of particle collisions, the single-particle distribution always approaches the Maxwell-Boltzmann distribution as its steady state, and its entropy increase indeed indicates the correlation production between the particles. In all these examples, the total entropy of the whole isolated system keeps constant, while the correlation production reproduces the irreversible entropy increase in the standard macroscopic thermodynamics. In this sense, the macroscopic irreversibility and the microscopic reversibility no longer contradict with each other.

scholarly journals On the Dynamical Nature of Nonlinear Coupling of Logarithmic Quantum Wave Equation, Everett-Hirschman Entropy and Temperature

2018 ◽  
Vol 73 (7) ◽  
pp. 619-628 ◽  
Author(s):  
Konstantin G. Zloshchastiev
Keyword(s):  
Wave Equation ◽  
Dynamical Behavior ◽  
Quantum Mechanical ◽  
Nonlinear Coupling ◽  
Many Body ◽  
Quantum Wave ◽  
Many Body Systems ◽  
Quantum Mechanical Systems ◽  
Logarithmic Equation ◽  
Quantum Wave Equation

AbstractWe study the dynamical behavior of the nonlinear coupling of a logarithmic quantum wave equation. Using the statistical mechanical arguments for a large class of many-body systems, this coupling is shown to be related to temperature, which is a thermodynamic conjugate to the Everett-Hirschman’s quantum information entropy. A combined quantum-mechanical and field-theoretical model is proposed, which leads to a logarithmic equation with variable nonlinear coupling. We study its properties and present arguments regarding its nature and interpretation, including the connection to Landauer’s principle. We also demonstrate that our model is able to describe linear quantum-mechanical systems with shape-changing external potentials.

Some U(n1 + n2) ⊃U(n1) ⊗U(n2) isoscalar factors

2017 ◽  
Vol 26 (09) ◽  
pp. 1750057 ◽  
Author(s):  
H. G. Ganev
Keyword(s):  
Mechanical Treatment ◽  
Quantum Mechanical ◽  
Many Body ◽  
Type Formula ◽  
Quantum Mechanical Treatment ◽  
Two Component ◽  
Many Body Systems

Some of the [Formula: see text] isoscalar factors (IFs), involving the [Formula: see text] couplings of the type [Formula: see text], are obtained using the building-up procedure. It is shown that such type of IFs are relevant to the quantum-mechanical treatment of the two-component many-body systems.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

scholarly journals Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

2021 ◽  
Vol 126 (11) ◽  
Author(s):  
Benjamin Geiger ◽  
Juan Diego Urbina ◽  
Klaus Richter
Keyword(s):  
Many Body ◽  
Many Body Systems

scholarly journals Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems

2020 ◽  
Vol 125 (26) ◽  
Author(s):  
Norifumi Matsumoto ◽  
Kohei Kawabata ◽  
Yuto Ashida ◽  
Shunsuke Furukawa ◽  
Masahito Ueda
Keyword(s):  
Phase Transition ◽  
Continuous Phase ◽  
Many Body ◽  
Continuous Phase Transition ◽  
Many Body Systems ◽  
Gap Closing
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