Upon Generating Discrete Expanding Integrable Models of the Toda Lattice Systems and Infinite Conservation Laws

2017 ◽  
Vol 72 (1) ◽  
pp. 77-86 ◽  
Author(s):  
Yufeng Zhang ◽  
Xiangzhi Zhang ◽  
Yan Wang ◽  
Jiangen Liu
Keyword(s):  
Conservation Laws ◽  
Statistical Physics ◽  
Quantum Physics ◽  
Toda Lattice ◽  
Lattice System ◽  
Integrable Models ◽  
Matrix Approach ◽  
Lattice Systems ◽  
Lax Pairs ◽  
Dimensional Lattice

AbstractWith the help ofR-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula byR-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.

scholarly journals SL(2)k WZNW MODELS, PERTURBATIONS AND INTEGRABLE MODELS

1991 ◽  
Vol 06 (09) ◽  
pp. 1617-1639 ◽  
Author(s):  
L. BONORA ◽  
Y.-Z. ZHANG ◽  
M. MARTELLINI
Keyword(s):  
Conservation Laws ◽  
Linear Systems ◽  
Equations Of Motion ◽  
Integrable Models ◽  
Lax Pairs ◽  
R Matrix ◽  
Zero Curvature ◽  
Perturbed Systems ◽  
Wznw Model

Perturbations of the SL(2)kC WZNW model by relevant operators are studied. Nontrivial off-critical conservation laws in these perturbed systems are constructed. For the rational level k, one of the perturbations is shown to be an analogue of the (1, 2j+1) operator in the WZNW model. Linear systems (Lax pairs) are defined whose zero curvature conditions give rise to the classical versions of the perturbed equations of motion. The classical r-matrix for these linear systems is found.

Random exponential attractor for second-order nonautonomous stochastic lattice systems with multiplicative white noise

2019 ◽  
Vol 19 (06) ◽  
pp. 1950044
Author(s):  
Haijuan Su ◽  
Shengfan Zhou ◽  
Luyao Wu
Keyword(s):  
White Noise ◽  
Weighted Space ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lattice System ◽  
Exponential Attractor ◽  
Lattice Systems ◽  
Random System ◽  
Multiplicative White Noise ◽  
Infinite Sequences

We studied the existence of a random exponential attractor in the weighted space of infinite sequences for second-order nonautonomous stochastic lattice system with linear multiplicative white noise. Firstly, we present some sufficient conditions for the existence of a random exponential attractor for a continuous cocycle defined on a weighted space of infinite sequences. Secondly, we transferred the second-order stochastic lattice system with multiplicative white noise into a random lattice system without noise through the Ornstein–Uhlenbeck process, whose solutions generate a continuous cocycle on a weighted space of infinite sequences. Thirdly, we estimated the bound and tail of solutions for the random system. Fourthly, we verified the Lipschitz continuity of the continuous cocycle and decomposed the difference between two solutions into a sum of two parts, and carefully estimated the bound of the norm of each part and the expectations of some random variables. Finally, we obtained the existence of a random exponential attractor for the considered system.

Notes on “infinite number of conservation laws and Darboux transformations for a 6-field integrable lattice system [Int. J. Mod. Phys. B 33 (2019) 1950147]

2021 ◽  
pp. 2150141
Author(s):  
Ning Zhang ◽  
Xi-Xiang Xu
Keyword(s):  
Conservation Laws ◽  
Darboux Transformation ◽  
Infinite Number ◽  
Lattice System ◽  
Darboux Transformations ◽  
Integrable Lattice

We show that the Darboux transformation in “Infinite number of conservation laws and Darboux transformations for a 6-field integrable lattice system” [Int. J. Mod. Phys. B 33 (2019) 1950147] is incorrect, and construct a correct Darboux transformation.

scholarly journals Automatic contraction of unstructured tensor networks

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Adam Jermyn
Keyword(s):  
Partition Function ◽  
Statistical Physics ◽  
Discrete Models ◽  
Correlation Structure ◽  
Central Problem ◽  
Partition Functions ◽  
Lattice Systems ◽  
Tensor Networks ◽  
Tensor Network

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.

Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities

2021 ◽  
Vol 71 (6) ◽  
pp. 1459-1470
Author(s):  
Kun Li ◽  
Yanli He
Keyword(s):  
Traveling Wave ◽  
Solution Method ◽  
Traveling Wave Solutions ◽  
Lower Solution ◽  
Cooperative System ◽  
Lattice Systems ◽  
Dimensional Lattice ◽  
Wave Solutions ◽  
Higher Dimensional ◽  
Lower Solution Method

Abstract In this paper, we are concerned with the existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities. By using the upper and lower solution method and Schauder’s fixed point theorem, we establish the existence of traveling wave solutions. To illustrate our results, the existence of traveling wave solutions for a nonlocal delayed higher-dimensional lattice cooperative system with two species are considered.

Exact solutions and aysmptotic state analysis of a modified Toda lattice system with a perturbation parameter

2021 ◽  
Author(s):  
Meng-Li Qin ◽  
Xiao-Yong Wen ◽  
Cui-Lian Yuan
Keyword(s):  
Asymptotic Analysis ◽  
Exact Solutions ◽  
Toda Lattice ◽  
Soliton Solutions ◽  
Perturbation Parameter ◽  
Lattice System ◽  
Rational Solutions ◽  
Limit States ◽  
Mixed Solutions ◽  
Analysis Technique

Under consideration is a modified Toda lattice system with a perturbation parameter, which may describe the particle motion in a lattice. With the aid of symbolic computation Maple, the discrete generalized [Formula: see text]-fold Darboux transformation (DT) of this system is constructed for the first time. Different types of exact solutions are derived by applying the resulting DT through choosing different [Formula: see text]. Specifically, standard soliton solutions, rational solutions and their mixed solutions are given via the [Formula: see text]-fold DT, [Formula: see text]-fold DT and [Formula: see text]-fold DT, respectively. Limit states of various exact solutions are analyzed via the asymptotic analysis technique. Compared with the known results, we find that the asymptotic states of mixed solutions of standard soliton and rational solutions are consistent with the asymptotic analysis results of solitons and rational solutions alone. Soliton interaction and propagation phenomena are shown graphically. Numerical simulations are used to explore relevant soliton dynamical behaviors. These results and properties might be helpful for understanding lattice dynamics.

scholarly journals Quantum mechanism of condensation and high Tc superconductivity

2019 ◽  
Vol 33 (14) ◽  
pp. 1950139
Author(s):  
Tian Ma ◽  
Shouhong Wang
Keyword(s):  
Statistical Physics ◽  
Quantum Physics ◽  
Average Energy ◽  
Physics First ◽  
Electron Pairs ◽  
High Tc ◽  
Quantum Mechanism ◽  
Recent Developments ◽  
The Common ◽  
New Interpretation

The main objective of this paper is to introduce a new quantum mechanism of condensates and superconductivity based on a new interpretation of quantum mechanical wavefunctions, and on recent developments in quantum physics and statistical physics. First, we postulate that the wavefunction [Formula: see text]e[Formula: see text] is the common wavefunction for all particles in the same class determined by the external potential V(x), [Formula: see text](x)[Formula: see text] represents the distribution density of the particles, and [Formula: see text] is the velocity field of the particles. Although the new interpretation does not alter the basic theories of quantum mechanics, it is an entirely different interpretation from the classical Bohr interpretation, removes all absurdities and offers new insights for quantum physics and for condensed matter physics. Second, we show that the key for condensation of bosonic particles is that their interaction is sufficiently weak to ensure that a large collection of boson particles are in a state governed by the same condensation wavefunction field [Formula: see text] under the same bounding potential V. For superconductivity, the formation of superconductivity comes down to conditions for the formation of electron pairs, and for the electron pairs to share a common wavefunction. Thanks to the recently developed principle of interaction dynamics (PID) interaction potential of electrons and the average-energy level formula of temperature, these conditions for superconductivity are explicitly derived. Furthermore, we obtain both microscopic and macroscopic formulas for the critical temperature. The field and topological phase transition equations for condensates are also derived.

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