Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit

• URL: http://arxiv.org/abs/2007.12683v1
• Date: Fri, 24 Jul 2020 17:55:00 GMT
• Title: Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit
• Authors: Spyros Sotiriadis
• Abstract summary: We focus on the Tonks-Girardeau or hard-core boson limit of the Lieb-Liniger model. We develop an analytical method for the derivation of the Non-Equilibrium Steady States.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Aiming at studying the emergence of Non-Equilibrium Steady States (NESS) in quantum integrable models by means of an exact analytical method, we focus on the Tonks-Girardeau or hard-core boson limit of the Lieb-Liniger model. We consider the abrupt expansion of a gas from one half to the entire confining box, a prototypical case of inhomogeneous quench, also known as "geometric quench". Based on the exact calculation of quench overlaps, we develop an analytical method for the derivation of the NESS by rigorously treating the thermodynamic and large time and distance limit. Our method is based on complex analysis tools for the derivation of the asymptotics of the many-body wavefunction, does not make essential use of the effectively non-interacting character of the hard-core boson gas and is sufficiently robust for generalisation to the genuinely interacting case.

Related papers

• Analytic thermodynamic properties of the Lieb-Liniger gas [0.0]
  We present a review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the 1D Bose gas. This paradigmatic model of quantum many-body-theory plays an important role in many areas of physics.
  arXiv  Detail & Related papers  (2024-04-09T07:50:05Z)
• Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence [65.63201894457404]
  We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear differential equations. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations.
  arXiv  Detail & Related papers  (2023-05-24T20:43:47Z)
• Universal features of entanglement entropy in the honeycomb Hubbard model [44.99833362998488]
  This paper introduces a new method to compute the R'enyi entanglement entropy in auxiliary-field quantum Monte Carlo simulations. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two dimensional model of interacting fermions.
  arXiv  Detail & Related papers  (2022-11-08T15:52:16Z)
• Sampling with Mollified Interaction Energy Descent [57.00583139477843]
  We present a new optimization-based method for sampling called mollified interaction energy descent (MIED) MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs) We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD.
  arXiv  Detail & Related papers  (2022-10-24T16:54:18Z)
• Global Convergence of Over-parameterized Deep Equilibrium Models [52.65330015267245]
  A deep equilibrium model (DEQ) is implicitly defined through an equilibrium point of an infinite-depth weight-tied model with an input-injection. Instead of infinite computations, it solves an equilibrium point directly with root-finding and computes gradients with implicit differentiation. We propose a novel probabilistic framework to overcome the technical difficulty in the non-asymptotic analysis of infinite-depth weight-tied models.
  arXiv  Detail & Related papers  (2022-05-27T08:00:13Z)
• Lindbladian dissipation of strongly-correlated quantum matter [0.9290757451344674]
  The Sachdev-Ye-Kitaev Lindbladian is a paradigmatic solvable model of dissipative many-body quantum chaos. Analytical progress is possible by developing a mean-field theory for the Liouvillian time evolution on the Keldysh contour.
  arXiv  Detail & Related papers  (2021-12-22T18:17:52Z)
• Normalizing flows for atomic solids [67.70049117614325]
  We present a machine-learning approach, based on normalizing flows, for modelling atomic solids. We report Helmholtz free energy estimates for cubic and hexagonal ice modelled as monatomic water as well as for a truncated and shifted Lennard-Jones system. Our results thus demonstrate that normalizing flows can provide high-quality samples and free energy estimates of solids, without the need for multi-staging or for imposing restrictions on the crystal geometry.
  arXiv  Detail & Related papers  (2021-11-16T18:54:49Z)
• Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results [68.8204255655161]
  We show that the proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates.
  arXiv  Detail & Related papers  (2021-05-11T14:08:02Z)
• A general approach to model counterpropagating continuous variable entangled states in a lossy CROW [0.0]
  We present a general approach to model an integrated source of counterpropagating continuous-variable entangled states based on a coupled-resonator optical waveguide.
  arXiv  Detail & Related papers  (2020-12-01T01:35:33Z)
• Many-body density and coherence of trapped cold bosons [0.0]
  Many-body densities and correlation functions are of paramount importance for understanding quantum many-body physics. We analyze quasi-one-dimensional harmonically-trapped bosons with weak to strong contact interaction strength up to the Tonks-Girardeau limit. We find that the higher-order correlation functions and densities resemble those in the Tonks-Girardeau limit for way smaller interactions than anticipated from just the one-body density.
  arXiv  Detail & Related papers  (2020-06-18T18:00:00Z)
• Bosonic representation of a Lipkin-Meshkov-Glick model with Markovian dissipation [0.0]
  We study the dynamics of a Lipkin-Meshkov-Glick model in the presence of Markovian dissipation. We use degenerate perturbation theory in the weak-dissipation limit to analytically obtain the eigenvalues and eigenvectors of the Liouvillian superoperator.
  arXiv  Detail & Related papers  (2020-04-05T15:31:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.