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Title: Solutions to Master equations of quantum Brownian motion in a general environment with external force

Abstract

We revisit the model of a system made up of a Brownian quantum oscillator linearly coupled to an environment made up of many quantum oscillators at finite temperature. We show that the HPZ master equation for the reduced density matrix derived earlier [B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)] has incorrectly specified coefficients for the case of nonlocal dissipation. We rederive the QBM master equation, correctly specifying all coefficients, and determine the position uncertainty to be free of excessive cutoff sensitivity. Our coefficients and solutions are reduced entirely to contour integration for analytic spectra at arbitrary temperature, coupling strength, and cut-off. As an illustration we calculate the master equation coefficients and solve the master equation for ohmic coupling (with finite cutoff) and example supra-ohmic and sub-ohmic spectral densities. We determine the effect of an external force on the quantum oscillator and also show that our representation of the master equation and solutions naturally extends to a system of multiple oscillators bilinearly coupled to themselves and the bath in arbitrary fashion. This produces a formula for investigating the standard quantum limit which is central to addressing many theoretical issues in macroscopic quantum phenomena and experimental concernsmore » related to low temperature precision measurements. We find that in a dissipative environment, all initial states settle down to a Gaussian density matrix whose covariance is determined by the thermal reservoir and whose mean is determined by the external force. We specify the thermal covariance for the spectral densities we explore.« less

Authors:
 [1];  [2];  [2]
  1. Los Alamos National Laboratory
  2. UNIV OF MARYLAND
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
962282
Report Number(s):
LA-UR-08-07176; LA-UR-08-7176
Journal ID: ISSN 1550-7998; PRVDAQ; TRN: US200919%%46
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D; Journal ID: ISSN 1550-7998
Country of Publication:
United States
Language:
English
Subject:
71; ACCURACY; DENSITY MATRIX; OSCILLATORS; SENSITIVITY; SPECTRA

Citation Formats

Roura, Albert, Fleming, C H, and Hu, B L. Solutions to Master equations of quantum Brownian motion in a general environment with external force. United States: N. p., 2008. Web.
Roura, Albert, Fleming, C H, & Hu, B L. Solutions to Master equations of quantum Brownian motion in a general environment with external force. United States.
Roura, Albert, Fleming, C H, and Hu, B L. Tue . "Solutions to Master equations of quantum Brownian motion in a general environment with external force". United States. https://www.osti.gov/servlets/purl/962282.
@article{osti_962282,
title = {Solutions to Master equations of quantum Brownian motion in a general environment with external force},
author = {Roura, Albert and Fleming, C H and Hu, B L},
abstractNote = {We revisit the model of a system made up of a Brownian quantum oscillator linearly coupled to an environment made up of many quantum oscillators at finite temperature. We show that the HPZ master equation for the reduced density matrix derived earlier [B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)] has incorrectly specified coefficients for the case of nonlocal dissipation. We rederive the QBM master equation, correctly specifying all coefficients, and determine the position uncertainty to be free of excessive cutoff sensitivity. Our coefficients and solutions are reduced entirely to contour integration for analytic spectra at arbitrary temperature, coupling strength, and cut-off. As an illustration we calculate the master equation coefficients and solve the master equation for ohmic coupling (with finite cutoff) and example supra-ohmic and sub-ohmic spectral densities. We determine the effect of an external force on the quantum oscillator and also show that our representation of the master equation and solutions naturally extends to a system of multiple oscillators bilinearly coupled to themselves and the bath in arbitrary fashion. This produces a formula for investigating the standard quantum limit which is central to addressing many theoretical issues in macroscopic quantum phenomena and experimental concerns related to low temperature precision measurements. We find that in a dissipative environment, all initial states settle down to a Gaussian density matrix whose covariance is determined by the thermal reservoir and whose mean is determined by the external force. We specify the thermal covariance for the spectral densities we explore.},
doi = {},
url = {https://www.osti.gov/biblio/962282}, journal = {Physical Review D},
issn = {1550-7998},
number = ,
volume = ,
place = {United States},
year = {2008},
month = {1}
}