Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schrödinger model
type: Item
instance of: scholarly article
title: Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schrödinger model
zbMATH Open document ID: 1315.81037
author: K. K. Kozlowski
published in: Annales Henri Poincaré
publication date: 2015-02-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1101.1626
full work available at URL: https://bib-pubdb1.desy.de/record/89341
review text: Nature at the most fundamental level is best understood via the studies inter alia involving the quantum theory and various related practical approaches. In this effort the role played by Erwin Schrödinger's equation including its nonlinear form as well as the different models built around the basic quantum theme are quite well known. There are very specific problems in this connection being investigated at length by many reputed author researchers so far. Work continues. The paper under review here is an authoritative contribution relating to the large-distance (LD) and long-time (LT) asymptotic behavior of the reduced density matrix (RDM) in the nonlinear Schrödinger model (NLSM). Here we see the continuation and consolidation of the author's earlier contribution in this area for the past several years. Indeed, the current presentation is pleasantly lucid and exhaustive enough. There are 5 sections altogether inclusive of the conclusion. The first section of the article is a detailed introduction. The second part presents the NLSM with two sub-sections. The third section with 2 sub-sections covers the concrete method adopted and the main, crucial results. The fourth section with 7 sub-sections is essentially on the form factor series. There are 84 equations, a conjecture, definitions, 2 figures and 4 appendices with 188 equations within the 98 page work. On the whole, the review work by a well-known researcher on an extremely significant topic is surely of great value with a comprehensive bibliography of 85 references also.
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 81S22
zbMATH DE Number: 6405739
zbMATH Keywords: quantum theory
zbMATH Keywords: nonlinear Schrödinger model
MaRDI profile type: Publication
OpenAlex ID: W2963023213
arXiv ID: 1101.1626
cites work: Q3136728
cites work: Hidden Grassmann structure in the \(XXZ\) model. II: Creation operators
cites work: Algebraic representation of correlation functions in integrable spin chains
cites work: Hidden Grassmann structure in the \(XXZ\) model
cites work: Q4793354
cites work: Density matrices for finite segments of Heisenberg chains of arbitrary length
cites work: Erratum to: Form factors of integrable higher-spin XXZ chains and the affine quantum-group symmetry.
cites work: Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method
cites work: A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
cites work: New thermodynamic Bethe ansatz equations without strings
cites work: Unified approach to thermodynamic Bethe ansatz and finite size corrections for lattice models and field theories.
cites work: Orthogonality and completeness of the Bethe Ansatz eigenstates of the nonlinear Schrödinger model
cites work: Q4251395
cites work: Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
cites work: Integral representations for correlation functions of theXXZchain at finite temperature
cites work: Long-distance asymptotics of temperature correlators of the impenetrable Bose gas
cites work: DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS
cites work: Large time and distance asymptotics of field correlation function of impenetrable bosons at finite temperature
cites work: The quantum inverse scattering method approach to correlation functions.
cites work: Correlation functions for the Heisenberg \(XXZ\)-antiferromagnet.
cites work: \(XXZ\) chain with a boundary
cites work: Quantum KZ equation with |q| = 1 and correlation functions of theXXZmodel in the gapless regime
cites work: Hidden Grassmann structure in the XXZ model. V: Sine-Gordon model
cites work: Q3001072
cites work: Form factor approach to dynamical correlation functions in critical models
cites work: On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
cites work: Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
cites work: Emptiness formation probability of theXXZspin- Heisenberg chain at
cites work: Spin-spin correlation functions of the \(XXZ-1/2\) Heisenberg chain in a magnetic field
cites work: Dynamical correlation functions of the \(XXZ\) spin-1/2 chain
cites work: Exact results for the σztwo-point function of theXXZchain at Δ = 1/2
cites work: Master equation for spin-spin correlation functions of the \(XXZ\) chain
cites work: Correlation functions of the \(XXZ\) Heisenberg spin-\({1\over 2}\) chain in a magnetic field
cites work: Large distance asymptotic behaviour of the emptiness formation probability of theXXZspin-1/2 Heisenberg chain
cites work: Central charges of the 6- and 19-vertex models with twisted boundary conditions
cites work: Conformal spectrum of the six-vertex model
cites work: Determinant representation for dynamical correlation functions of the quantum nonlinear Schrödinger equation
cites work: Correlation function of fields in one-dimensional Bose-gas
cites work: Dual field formulation of quantum integrable models
cites work: The time dependent correlation function of an impenetrable Bose gas as a Fredholm minor. I
cites work: FORM FACTORS IN THE FINITE VOLUME
cites work: Riemann-Hilbert approach to the time-dependent generalized sine kernel
cites work: On form factors of the conjugated field in the nonlinear Schrödinger model
cites work: Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
cites work: Q5485625
cites work: Quantum projectors and local operators in lattice integrable models
cites work: Notes on infinite determinants of Hilbert space operators
cites work: Quantum version of the method of inverse scattering problem
cites work: A nonlinear identity for the scattering phase of integrable models
cites work: Integral equations for correlation functions of a quantum one-dimensional Bose gas
cites work: Q3998750
cites work: A general formula for soliton form factors in the quantum sine-Gordon model
cites work: Thermodynamics of a One-Dimensional System of Bosons with Repulsive Delta-Function Interaction
DOI: 10.1007/S00023-014-0327-3
description: scientific article