Path integral methods for the dynamics of stochastic and disordered systems

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Path integral methods for the dynamics of stochastic and disordered systems. / Hertz, John A.; Roudi, Yasser; Sollich, Peter.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 50, No. 3, 033001, 20.01.2017.

Research output: Contribution to journal › Review › Research › peer-review

Harvard

Hertz, JA, Roudi, Y & Sollich, P 2017, 'Path integral methods for the dynamics of stochastic and disordered systems', Journal of Physics A: Mathematical and Theoretical, vol. 50, no. 3, 033001. https://doi.org/10.1088/1751-8121/50/3/033001

APA

Hertz, J. A., Roudi, Y., & Sollich, P. (2017). Path integral methods for the dynamics of stochastic and disordered systems. Journal of Physics A: Mathematical and Theoretical, 50(3), [033001]. https://doi.org/10.1088/1751-8121/50/3/033001

Vancouver

Hertz JA, Roudi Y, Sollich P. Path integral methods for the dynamics of stochastic and disordered systems. Journal of Physics A: Mathematical and Theoretical. 2017 Jan 20;50(3). 033001. https://doi.org/10.1088/1751-8121/50/3/033001

Author

Hertz, John A. ; Roudi, Yasser ; Sollich, Peter. / Path integral methods for the dynamics of stochastic and disordered systems. In: Journal of Physics A: Mathematical and Theoretical. 2017 ; Vol. 50, No. 3.

Bibtex

@article{b8be65b8d9e1416ea3c1e2fe7d58c57a,
title = "Path integral methods for the dynamics of stochastic and disordered systems",
abstract = "We review some of the techniques used to study the dynamics of disorderedsystems subject to both quenched and fast (thermal) noise. Starting from theMartin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism fora single variable stochastic dynamics, we provide a pedagogical survey of theperturbative, i.e. diagrammatic, approach to dynamics and how this formalismcan be used for studying soft spin models. We review the supersymmetricformulation of the Langevin dynamics of these models and discuss the physicalimplications of the supersymmetry. We also describe the key stepsinvolved in studying the disorder-averaged dynamics. Finally, we discuss thepath integral approach for the case of hard Ising spins and review some recentdevelopments in the dynamics of such kinetic Ising models.",
keywords = "path integral methods, disordered systems, spin glasses, dynamics",
author = "Hertz, {John A.} and Yasser Roudi and Peter Sollich",
year = "2017",
month = jan,
day = "20",
doi = "10.1088/1751-8121/50/3/033001",
language = "English",
volume = "50",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "Institute of Physics Publishing Ltd",
number = "3",

}

RIS

TY - JOUR

T1 - Path integral methods for the dynamics of stochastic and disordered systems

AU - Hertz, John A.

AU - Roudi, Yasser

AU - Sollich, Peter

PY - 2017/1/20

Y1 - 2017/1/20

N2 - We review some of the techniques used to study the dynamics of disorderedsystems subject to both quenched and fast (thermal) noise. Starting from theMartin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism fora single variable stochastic dynamics, we provide a pedagogical survey of theperturbative, i.e. diagrammatic, approach to dynamics and how this formalismcan be used for studying soft spin models. We review the supersymmetricformulation of the Langevin dynamics of these models and discuss the physicalimplications of the supersymmetry. We also describe the key stepsinvolved in studying the disorder-averaged dynamics. Finally, we discuss thepath integral approach for the case of hard Ising spins and review some recentdevelopments in the dynamics of such kinetic Ising models.

AB - We review some of the techniques used to study the dynamics of disorderedsystems subject to both quenched and fast (thermal) noise. Starting from theMartin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism fora single variable stochastic dynamics, we provide a pedagogical survey of theperturbative, i.e. diagrammatic, approach to dynamics and how this formalismcan be used for studying soft spin models. We review the supersymmetricformulation of the Langevin dynamics of these models and discuss the physicalimplications of the supersymmetry. We also describe the key stepsinvolved in studying the disorder-averaged dynamics. Finally, we discuss thepath integral approach for the case of hard Ising spins and review some recentdevelopments in the dynamics of such kinetic Ising models.

KW - path integral methods

KW - disordered systems

KW - spin glasses

KW - dynamics

U2 - 10.1088/1751-8121/50/3/033001

DO - 10.1088/1751-8121/50/3/033001

M3 - Review

VL - 50

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 3

M1 - 033001

ER -

ID: 172472689