Uniqueness of the limit Gibbs distribution in one-dimensional classical systems

1975 ◽  
Vol 24 (1) ◽  
pp. 697-703 ◽  
Author(s):  
R. A. Minlos ◽  
G. M. Natapov
Keyword(s):  
Gibbs Distribution ◽  
One Dimensional ◽  
Classical Systems

scholarly journals One-Dimensional Coulomb Multiparticle Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
V. A. Malyshev ◽  
A. A. Zamyatin
Keyword(s):  
Coulomb Interaction ◽  
Short Review ◽  
Gibbs Distribution ◽  
Complete Picture ◽  
Nearest Neighbour ◽  
Zero Temperature ◽  
One Dimensional ◽  
System Of Particles ◽  
Local Properties ◽  
Multiparticle Systems

We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero temperature case there is sufficiently complete picture and we give a short review. For Gibbs distribution the situation is more difficult and we present two related results.

scholarly journals On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
J. Hutchinson ◽  
J. P. Keating ◽  
F. Mezzadri
Keyword(s):  
Classical System ◽  
Companion Paper ◽  
Quantum Systems ◽  
Spin Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
One Dimensional ◽  
Classical Systems ◽  
Long Range Interactions ◽  
Quantum Hamiltonian

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified.

scholarly journals QUANTUM CORNER — TRANSFER MATRIX DMRG

2008 ◽  
Vol 19 (08) ◽  
pp. 1145-1161 ◽  
Author(s):  
ERIK BARTEL ◽  
ANDREAS SCHADSCHNEIDER
Keyword(s):  
Thermal Properties ◽  
Transfer Matrix ◽  
Heisenberg Model ◽  
Quantum Systems ◽  
Test Cases ◽  
The Novel ◽  
Simple Test ◽  
Ising Chain ◽  
One Dimensional ◽  
Classical Systems

We propose a new method for the calculation of thermodynamic properties of one-dimensional quantum systems by combining the TMRG approach with the corner transfer-matrix method. The corner transfer-matrix DMRG method brings reasonable advantage over TMRG for classical systems. We have modified the concept for the calculation of thermal properties of one-dimensional quantum systems. The novel QCTMRG algorithm is implemented and used to study two simple test cases, the classical Ising chain and the isotropic Heisenberg model. In a discussion, the advantages and challenges are illuminated.

scholarly journals Factorizations of one-dimensional classical systems

2008 ◽  
Vol 323 (2) ◽  
pp. 413-431 ◽  
Author(s):  
Şengül Kuru ◽  
Javier Negro
Keyword(s):  
One Dimensional ◽  
Classical Systems

KOLMOGOROV SYSTEMS AND ANOSOV SYSTEMS IN QUANTUM THEORY

2001 ◽  
Vol 04 (01) ◽  
pp. 85-119 ◽  
Author(s):  
H. NARNHOFER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Quantum Field ◽  
Modular Systems ◽  
One Dimensional ◽  
Classical Systems ◽  
Anosov Systems

In analogy to classical systems, quantum K-systems and quantum Anosov systems are defined. Their relation especially for modular systems is discussed as well as the consequences on clustering properties. Examples for such systems in the framework of quantum field theory and one-dimensional theories are offered.

Complex Dynamical Invariants for One-Dimensional Classical Systems

2003 ◽  
Vol 67 (3) ◽  
pp. 181-185 ◽  
Author(s):  
Shweta Singh ◽  
R S Kaushal
Keyword(s):  
One Dimensional ◽  
Classical Systems ◽  
Dynamical Invariants
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