scholarly journals Nonequilibrium physics in integrable systems and spin-flip non-invariant conserved quantities

2020 ◽  
Vol 53 (13) ◽  
pp. 134001
Author(s):  
Chihiro Matsui
Keyword(s):  
Integrable Systems ◽  
Conserved Quantities ◽  
Spin Flip ◽  
Nonequilibrium Physics

ATTEMPTS TO DEFINE QUASI-INTEGRABILITY

2012 ◽  
Vol 09 (06) ◽  
pp. 1261004 ◽  
Author(s):  
LUIZ A. FERREIRA ◽  
WOJTEK J. ZAKRZEWSKI
Keyword(s):  
Field Theory ◽  
Integrable Systems ◽  
Integrable Model ◽  
Conserved Quantities ◽  
Preliminary Results ◽  
Sine Gordon Model

In this paper we discuss some ideas on how to define the concept of quasi-integrability. Our ideas stem from the observation that many field theory models are "almost" integrable; i.e. they possess a large number of "almost" conserved quantities. Most of our discussion will involve a certain class of models which generalize the sine-Gordon model in (1 + 1) dimensions. As will be mentioned many field configurations of these models look like those of the integrable systems and so appear to be close to those in integrable model. We will then attempt to quantify these claims looking in particular, both analytically and numerically, at field configurations with scattering solitons. We will also discuss some preliminary results obtained in other models.

scholarly journals Observation of dynamical fermionization

Science ◽  
2020 ◽  
Vol 367 (6485) ◽  
pp. 1461-1464 ◽  
Author(s):  
Joshua M. Wilson ◽  
Neel Malvania ◽  
Yuan Le ◽  
Yicheng Zhang ◽  
Marcos Rigol ◽  
...  
Keyword(s):  
Wave Function ◽  
Momentum Distribution ◽  
Integrable Systems ◽  
Trap Depth ◽  
Fermi Gas ◽  
One Dimension ◽  
Conserved Quantities ◽  
Many Body ◽  
Absolute Value ◽  
Momentum Distributions

The wave function of a Tonks-Girardeau (T-G) gas of strongly interacting bosons in one dimension maps onto the absolute value of the wave function of a noninteracting Fermi gas. Although this fermionization makes many aspects of the two gases identical, their equilibrium momentum distributions are quite different. We observed dynamical fermionization, where the momentum distribution of a T-G gas evolves from bosonic to fermionic after its axial confinement is removed. The asymptotic momentum distribution after expansion in one dimension is the distribution of rapidities, which are the conserved quantities associated with many-body integrable systems. Our measurements agree well with T-G gas theory. We also studied momentum evolution after the trap depth is suddenly changed to a new nonzero value, and we observed the theoretically predicted bosonic-fermionic oscillations.

scholarly journals NONTRIVIAL SOLITON SCATTERING IN PLANAR INTEGRABLE SYSTEMS

2003 ◽  
Vol 18 (27) ◽  
pp. 4975-4998 ◽  
Author(s):  
THEODORA IOANNIDOU
Keyword(s):  
Infinite Number ◽  
Integrable Systems ◽  
The Self ◽  
Conserved Quantities ◽  
Yang Mills ◽  
Change Of Direction ◽  
Extended Review

The behavior of solitons in integrable theories is strongly constrained by the integrability of the theory, that is by the existence of an infinite number of conserved quantities that these theories are known to possess. As a result, the soliton scattering of such theories is expected to be trivial (with no change of direction, velocity or shape). In this paper we present an extended review on soliton scattering of two spatial dimensional integrable systems which have been derived as dimensional reductions of the self-dual Yang–Mills equations and whose scattering properties are highly nontrivial.

scholarly journals Conserved Quantities of Q-systems from Dimer Integrable Systems

10.37236/6994 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Panupong Vichitkunakorn
Keyword(s):  
Urban Renewal ◽  
Integrable Systems ◽  
Homology Class ◽  
Weighted Graph ◽  
Type A ◽  
Partition Functions ◽  
Conserved Quantities ◽  
Type B ◽  
Hard Particles ◽  
Poisson Commute

We study a discrete dynamic on weighted bipartite graphs on a torus, analogous to dimer integrable systems in Goncharov-Kenyon 2013. The dynamic on the graph is an urban renewal together with shrinking all 2-valent vertices, while it is a cluster transformation on the weight. The graph is not necessary obtained from an integral polygon. We define the Hamiltonians of a weighted graph as partition functions of all weighted perfect matchings with a common homology class, then show that they are invariant under a move on the weighted graph. This move coincides with a cluster mutation, analog to Y-seed mutation in dimer integrable systems. We construct graphs for Q-systems of type A and B and show that the Hamiltonians are conserved quantities of the systems. This reproves the results of Di Francesco-Kedem 2010 and Galashin-Pylyavskyy 2016 for the Q-systems of type A, and gives new results for that of type B. Similar to the results in Di Francesco-Kedem 2010, the conserved quantities for Q-systems of type B can also be written as partition functions of hard particles on a certain graph. For type A, we show that the conserved quantities Poisson commute under a nondegenerate Poisson bracket.

scholarly journals Identifying Local and Quasilocal Conserved Quantities in Integrable Systems

2015 ◽  
Vol 114 (14) ◽  
Author(s):  
Marcin Mierzejewski ◽  
Peter Prelovšek ◽  
Tomaž Prosen
Keyword(s):  
Integrable Systems ◽  
Conserved Quantities

scholarly journals INTEGRABLE SYSTEMS ON FLAG MANIFOLD AND COHERENT STATE PATH-INTEGRAL

1995 ◽  
Vol 10 (25) ◽  
pp. 1847-1855 ◽  
Author(s):  
MYUNG-HO KIM ◽  
PHILLIAL OH
Keyword(s):  
Coherent State ◽  
Path Integral ◽  
Integrable Systems ◽  
Symplectic Structure ◽  
Flag Manifold ◽  
Exact Expression ◽  
Integrable Models ◽  
Conserved Quantities ◽  
Special Cases ◽  
State Path

We construct integrable models on flag manifold by using the symplectic structure explicitly given in the Bruhat coordinatization of flag manifold. They are noncommutative integrable and some of the conserved quantities are given by the Casimir invariants. We quantize the systems using the coherent state path-integral technique and find the exact expression for the propagator for some special cases.

scholarly journals Solitons: Conservation laws and dressing methods

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1930003
Author(s):  
Anastasia Doikou ◽  
Iain Findlay
Keyword(s):  
Conservation Laws ◽  
Riccati Equation ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Soliton Solutions ◽  
Toda Chain ◽  
Lax Pair ◽  
Conserved Quantities ◽  
Nonlinear Schrödinger ◽  
Marchenko Equation

We review some of the fundamental notions associated with the theory of solitons. More precisely, we focus on the issue of conservation laws via the existence of the Lax pair and also on methods that provide solutions to partial or ordinary differential equations that are associated to discrete or continuous integrable systems. The Riccati equation associated to a given continuous integrable system is also solved and hence suitable conserved quantities are derived. The notion of the Darboux–Bäcklund transformation is introduced and employed in order to obtain soliton solutions for specific examples of integrable equations. The Zakharov–Shabat dressing scheme and the Gelfand–Levitan–Marchenko equation are also introduced. Via this method, generic solutions are produced and integrable hierarchies are explicitly derived. Various discrete and continuous integrable models are employed as examples such as the Toda chain, the discrete nonlinear Schrödinger model, the Korteweg–de Vries and nonlinear Schrödinger equations as well as the sine-Gordon and Liouville models.

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

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