General framework of the non-perturbative renormalization group for non-equilibrium steady states

Canet, Léonie; Chaté, Hugues; Delamotte, Bertrand

doi:10.1088/1751-8113/44/49/495001

Cited by 76 publications

(135 citation statements)

References 32 publications

(112 reference statements)

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“…The Functional Renormalization Group (FRG) is a functional realization of the Wilsonian renormalization program and is applied successfully to many problems regarding out of equilibrium systems, for a review see [12] and [13]. In the FRG framework one considers a scale dependent effective action, the Effective Average Action (EAA), which interpolates between the classical action and the standard effective action [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Functional renormalization group approach to the Kraichnan model

Pagani

2015

Phys. Rev. E

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Section: Introductionmentioning

confidence: 99%

Functional renormalization group approach to the Kraichnan model

Pagani

2015

Phys. Rev. E

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“…Nor have I addressed powerful representations through supersymmetric or conformally invariant quantum field theories, Monte Carlo algorithms, or numerical non-perturbative RG approaches, since the latter will be covered elsewhere in this volume; for their applications to non-equilibrium systems, see, e.g., Ref. [30].…”

Section: Discussionmentioning

confidence: 99%

Renormalization Group: Applications in Statistical Physics

Täuber

2012

Nuclear Physics B - Proceedings Supplements

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These notes aim to provide a concise pedagogical introduction to some important applications of the renormalization group in statistical physics. After briefly reviewing the scaling approach and Ginzburg-Landau theory for critical phenomena near continuous phase transitions in thermal equilibrium, Wilson's momentum shell renormalization group method is presented, and the critical exponents for the scalar Φ 4 model are determined to first order in a dimensional expansion about the upper critical dimension d c = 4. Subsequently, the physically equivalent but technically more versatile field-theoretic formulation of the perturbational renormalization group for static critical phenomena is described. It is explained how the emergence of scale invariance connects ultraviolet divergences to infrared singularities, and the renormalization group equation is employed to compute the critical exponents for the O(n)-symmetric Landau-Ginzburg-Wilson theory to lowest non-trivial order in the expansion. The second part of this overview is devoted to field theory representations of non-linear stochastic dynamical systems, and the application of renormalization group tools to critical dynamics. Dynamic critical phenomena in systems near equilibrium are efficiently captured through Langevin stochastic equations of motion, and their mapping onto the Janssen-De Dominicis response functional, as exemplified by the field-theoretic treatment of purely relaxational models with non-conserved (model A) and conserved order parameter (model B). As examples for other universality classes, the Langevin description and scaling exponents for isotropic ferromagnets at the critical point (model J) and for driven diffusive non-equilibrium systems are discussed. Finally, an outlook is presented to scale-invariant phenomena and non-equilibrium phase transitions in interacting particle systems. It is shown how the stochastic master equation associated with chemical reactions or population dynamics models can be mapped onto imaginary-time, non-Hermitian "quantum" mechanics. In the continuum limit, this Doi-Peliti Hamiltonian is in turn represented through a coherent-state path integral action, which allows an efficient and powerful renormalization group analysis of, e.g., diffusion-limited annihilation processes, and of phase transitions from active to inactive, absorbing states.

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“…(273), and a Hamiltonian part S H , which results from the Hamiltonian dynamics in Eqs. (250), (251 In order to determine the correction to the bare action, the logarithm in Eq. (278) is expanded in powers of the fields a * α , a α .…”

Section: Self-consistent Born Approximationmentioning

confidence: 99%

Keldysh field theory for driven open quantum systems

2016

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Recent experimental developments in diverse areas -ranging from cold atomic gases to light-driven semiconductors to microcavity arrays -move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states, as well as their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems. CONTENTS

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General framework of the non-perturbative renormalization group for non-equilibrium steady states

Cited by 76 publications

References 32 publications

Functional renormalization group approach to the Kraichnan model

Functional renormalization group approach to the Kraichnan model

Renormalization Group: Applications in Statistical Physics

Keldysh field theory for driven open quantum systems

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