Operator orderings and functional formulations of quantum and stochastic dynamics

Leschke, Hajo; Schmutz, M.

doi:10.1007/bf01315509

Cited by 55 publications

(21 citation statements)

References 25 publications

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“…This approach has been first developed for cases with an additive noise [45,46,47,48,49,50]. It was later generalised to cases with a multiplicative noise [6] and extended to various discretization schemes and to higher dimensions [7,8]. Below, we recall the construction of such a path-integral representation on the case of the multiplicative-noise equation (2.1) by following a procedureà la MartinSiggia-Rose-Janssen-deDominicis (MSRJD).…”

Section: The Path-integral Formulationmentioning

confidence: 99%

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Dynamical symmetries of Markov processes with multiplicative white noise

Aron¹,

Barci²,

Cugliandolo³

et al. 2016

J. Stat. Mech.

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We analyse various properties of stochastic Markov processes with multiplicative white noise. We take a single-variable problem as a simple example, and we later extend the analysis to the LandauLifshitz-Gilbert equation for the stochastic dynamics of a magnetic moment. In particular, we focus on the non-equilibrium transfer of angular momentum to the magnetization from a spin-polarised current of electrons, a technique which is widely used in the context of spintronics to manipulate magnetic moments. We unveil two hidden dynamical symmetries of the generating functionals of these Markovian multiplicative white-noise processes. One symmetry only holds in equilibrium and we use it to prove generic relations such as the fluctuation-dissipation theorems. Out of equilibrium, we take profit of the symmetry-breaking terms to prove fluctuation theorems. The other symmetry yields strong dynamical relations between correlation and response functions which can notably simplify the numerical analysis of these problems. Our construction allows us to clarify some misconceptions on multiplicative white-noise stochastic processes that can be found in the literature. In particular, we show that a first-order differential equation with multiplicative white noise can be transformed into an additive-noise equation, but that the latter keeps a non-trivial memory of the discretisation prescription used to define the former.

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Section: The Path-integral Formulationmentioning

confidence: 99%

“…2.3 we recall the path-integral generating-functional formalism for stochastic Langevin processes with multiplicative white noise [6,7,8,9,10,11]. We explain the apparent differences with the path integrals used in Ref.…”

Section: Contents 1 Introductionmentioning

confidence: 99%

Dynamical symmetries of Markov processes with multiplicative white noise

Aron¹,

Barci²,

Cugliandolo³

et al. 2016

J. Stat. Mech.

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“…где V e (t) берется в картине евклидова взаимодействия (6). Для оператора эволюции U (t i , t f ) из-за наличия упорядоченных по времени аргументов (t f > t i ) представле-ние, полученное с использованием антихронологически упорядоченной экспоненты, имеет вид…”

Section: зависящие от времени функции грина при конечной температуреunclassified

“…Кроме обычных квантово-механических задач, важные стохастические задачи можно сформулировать в терминах полевых операторов, аналогичных операторам квантовой теории поля [5], [6], которые порождают функции Грина, определенные по аналогии с (1). Основное отличие от функций Грина квантовой теории поля со-стоит в виде оператора плотности, который в случае стохастических задач построен существенно отличающимся от (2) или (3) путем.…”

Section: Introductionunclassified

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Контурно Упорядоченные Функции Грина В Стохастической Теории Поля

Хонконен¹,

Honkonen²

2013

ТМФ

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Effective descriptions of complex quantum systems: path integrals and operator ordering problems

Eckern¹,

Gruber²,

Schwab³

2005

Ann. Phys.

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Key words Effective quantum theories, operator ordering, coordinate-dependent mass. PACS 05.30.-d, 05.40.-a, 31.15.Kb Dedicated to Bernhard Mühlschlegel on the occasion of his 80th birthdayWe study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard Feynman-Vernon Caldeira-Leggett model to include a non-linear coupling between "particle" and environment, and considering a particular spectral density of the coupling, a coordinatedependent mass (or velocity-dependent potential) is obtained. The related effective quantum theory, which depends on the proper discretisation of the path integral, is derived and discussed. As a result, we find that in general a simple effective low-energy Hamiltonian, in which only the coordinate-dependent mass enters, cannot be formulated. The quantum theory of weakly coupled superconductors and the quantum dynamics of vortices in Josephson junction arrays are physical examples where these considerations, in principle, are of relevance.

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Operator orderings and functional formulations of quantum and stochastic dynamics

Cited by 55 publications

References 25 publications

Dynamical symmetries of Markov processes with multiplicative white noise

Dynamical symmetries of Markov processes with multiplicative white noise

Контурно Упорядоченные Функции Грина В Стохастической Теории Поля

Effective descriptions of complex quantum systems: path integrals and operator ordering problems

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