Linear response and modified fluctuation-dissipation relation in random potential

© 2015 American Physical Society. In this work, a physical system described by the Hamiltonian Hω=H0+Vω(t) consisting of a solvable model H0 and external random and time-dependent potential Vω(t) is investigated. Under the conditions in which, for each realization, the potential changes smoothly so...

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Main Authors: Fattah Sakuldee, Sujin Suwanna
Other Authors: Mahidol University
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Published: 2018
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Online Access:https://repository.li.mahidol.ac.th/handle/123456789/36197
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spelling th-mahidol.361972018-11-23T17:26:21Z Linear response and modified fluctuation-dissipation relation in random potential Fattah Sakuldee Sujin Suwanna Mahidol University Mathematics © 2015 American Physical Society. In this work, a physical system described by the Hamiltonian Hω=H0+Vω(t) consisting of a solvable model H0 and external random and time-dependent potential Vω(t) is investigated. Under the conditions in which, for each realization, the potential changes smoothly so that the evolution of the system follows the Schrödinger dynamics, and that the average external potential with respect to all realizations is constant in time, an adjusted equilibrium state can be defined as a reference state and the mean dynamics can be derived from taking the average of the equation with respect to the configuration parameter ω. It provides extra contributions from the deviations of the Hamiltonian and evolves the state along the time by the Heisenberg and Liouville-von Neumann equations. Consequently, the Kubo formula and the fluctuation-dissipation relation (FDR) are modified in the sense that the contribution from the information of randomness and memory effects from the time dependence is also present. The modified Kubo formula now has a contribution from two terms. The first term is an antisymmetric cross correlation between two observables measured by a probe as expected, and the latter term is an accumulation of the propagation of the effects from the randomness. When the considered system is in the adjusted equilibrium state at the time the measurement probe interacts, the latter contribution vanishes, and the standard FDR is recovered. 2018-11-23T10:26:21Z 2018-11-23T10:26:21Z 2015-11-16 Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Vol.92, No.5 (2015) 10.1103/PhysRevE.92.052118 15502376 15393755 2-s2.0-84949207371 https://repository.li.mahidol.ac.th/handle/123456789/36197 Mahidol University SCOPUS https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84949207371&origin=inward
institution Mahidol University
building Mahidol University Library
continent Asia
country Thailand
Thailand
content_provider Mahidol University Library
collection Mahidol University Institutional Repository
topic Mathematics
spellingShingle Mathematics
Fattah Sakuldee
Sujin Suwanna
Linear response and modified fluctuation-dissipation relation in random potential
description © 2015 American Physical Society. In this work, a physical system described by the Hamiltonian Hω=H0+Vω(t) consisting of a solvable model H0 and external random and time-dependent potential Vω(t) is investigated. Under the conditions in which, for each realization, the potential changes smoothly so that the evolution of the system follows the Schrödinger dynamics, and that the average external potential with respect to all realizations is constant in time, an adjusted equilibrium state can be defined as a reference state and the mean dynamics can be derived from taking the average of the equation with respect to the configuration parameter ω. It provides extra contributions from the deviations of the Hamiltonian and evolves the state along the time by the Heisenberg and Liouville-von Neumann equations. Consequently, the Kubo formula and the fluctuation-dissipation relation (FDR) are modified in the sense that the contribution from the information of randomness and memory effects from the time dependence is also present. The modified Kubo formula now has a contribution from two terms. The first term is an antisymmetric cross correlation between two observables measured by a probe as expected, and the latter term is an accumulation of the propagation of the effects from the randomness. When the considered system is in the adjusted equilibrium state at the time the measurement probe interacts, the latter contribution vanishes, and the standard FDR is recovered.
author2 Mahidol University
author_facet Mahidol University
Fattah Sakuldee
Sujin Suwanna
format Article
author Fattah Sakuldee
Sujin Suwanna
author_sort Fattah Sakuldee
title Linear response and modified fluctuation-dissipation relation in random potential
title_short Linear response and modified fluctuation-dissipation relation in random potential
title_full Linear response and modified fluctuation-dissipation relation in random potential
title_fullStr Linear response and modified fluctuation-dissipation relation in random potential
title_full_unstemmed Linear response and modified fluctuation-dissipation relation in random potential
title_sort linear response and modified fluctuation-dissipation relation in random potential
publishDate 2018
url https://repository.li.mahidol.ac.th/handle/123456789/36197
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