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Title: Quantum–classical transition in the Caldeira–Leggett model

Abstract

The quantum–classical transition in the Caldeira–Leggett model is investigated in the framework of the functional renormalization group method. It is shown that a divergent quadratic term arises in the action due to the heat bath in the model. By removing the divergence with a frequency cutoff we considered the critical behavior of the model. The critical exponents belonging to the susceptibility and the correlation length are determined and their independence of the frequency cutoff and the renormalization scheme is shown.

Authors:
 [1];  [2];  [3];  [1];  [1]
  1. Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen (Hungary)
  2. (Hungary)
  3. Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen (Hungary)
Publication Date:
OSTI Identifier:
22617455
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 376; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLASSICAL MECHANICS; QUANTUM SYSTEMS; RENORMALIZATION

Citation Formats

Kovács, J., Institute of Nuclear Research, P.O. Box 51, H-4001 Debrecen, Fazekas, B., Nagy, S., E-mail: nagys@phys.unideb.hu, and Sailer, K.. Quantum–classical transition in the Caldeira–Leggett model. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2016.12.010.
Kovács, J., Institute of Nuclear Research, P.O. Box 51, H-4001 Debrecen, Fazekas, B., Nagy, S., E-mail: nagys@phys.unideb.hu, & Sailer, K.. Quantum–classical transition in the Caldeira–Leggett model. United States. doi:10.1016/J.AOP.2016.12.010.
Kovács, J., Institute of Nuclear Research, P.O. Box 51, H-4001 Debrecen, Fazekas, B., Nagy, S., E-mail: nagys@phys.unideb.hu, and Sailer, K.. Sun . "Quantum–classical transition in the Caldeira–Leggett model". United States. doi:10.1016/J.AOP.2016.12.010.
@article{osti_22617455,
title = {Quantum–classical transition in the Caldeira–Leggett model},
author = {Kovács, J. and Institute of Nuclear Research, P.O. Box 51, H-4001 Debrecen and Fazekas, B. and Nagy, S., E-mail: nagys@phys.unideb.hu and Sailer, K.},
abstractNote = {The quantum–classical transition in the Caldeira–Leggett model is investigated in the framework of the functional renormalization group method. It is shown that a divergent quadratic term arises in the action due to the heat bath in the model. By removing the divergence with a frequency cutoff we considered the critical behavior of the model. The critical exponents belonging to the susceptibility and the correlation length are determined and their independence of the frequency cutoff and the renormalization scheme is shown.},
doi = {10.1016/J.AOP.2016.12.010},
journal = {Annals of Physics},
number = ,
volume = 376,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2017},
month = {Sun Jan 15 00:00:00 EST 2017}
}
  • Highlights: > Classical Brownian motion described by a non-Markovian Fokker-Planck equation. > Quantization process. > Quantum Brownian motion described by a non-Markovian Caldeira-Leggett equation. > A non-equilibrium quantum thermal force is predicted. - Abstract: We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker-Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett master equation on the basis of which we work out the conceptmore » of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of a free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.« less
  • There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira–Leggett and Ambegaokar–Eckern–Schön approaches. Here, we recall the differences between them and explain the consequences of applying each to a zero-dimensional spin (having an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).
  • Interaction between system and reservoir is considered to be linear in the coordinates of heat bath but nonlinear in the system coordinate and velocity. The reduced partition function of the system is presented and the corresponding effective classical potential is calculated by using the path-integral Monte Carlo method. In the presence of the nonlinear coupling, a dissipative threshold is observed at finite temperatures, and the decay rate of a particle in a metastable potential can be hindered by inhomogeneous dissipation above twice the crossover temperature.
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  • The Caldeira-Leggett (CL) model, which describes a system bi-linearly coupled to a harmonic bath, has enjoyed popularity in condensed phase spectroscopy owing to its utmost simplicity. However, the applicability of the model to cases with anharmonic system potentials, as it is required for the description of realistic systems in solution, is questionable due to the presence of the invertibility problem [F. Gottwald et al., J. Phys. Chem. Lett. 6, 2722 (2015)] unless the system itself resembles the CL model form. This might well be the case at surfaces or in the solid regime, which we here confirm for a particularmore » example of an iodine molecule in the atomic argon environment under high pressure. For this purpose we extend the recently proposed Fourier method for parameterizing linear generalized Langevin dynamics [F. Gottwald et al., J. Chem. Phys. 142, 244110 (2015)] to the non-linear case based on the CL model and perform an extensive error analysis. In order to judge on the applicability of this model in advance, we give practical empirical criteria and discuss the effect of the potential renormalization term. The obtained results provide evidence that the CL model can be used for describing a potentially broad class of systems.« less