Statistical mechanics of stochastic growth phenomena

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Statistical mechanics of stochastic growth phenomena. / Alekseev, Oleg; Mineev-Weinstein, Mark.

In: Physical Review E, Vol. 96, No. 1, 010103, 20.07.2017.

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

Author

Alekseev, Oleg ; Mineev-Weinstein, Mark. / Statistical mechanics of stochastic growth phenomena. In: Physical Review E. 2017 ; Vol. 96, No. 1.

BibTeX

@article{1954d9e098954c739df9b8f7de3fc8a9,

title = "Statistical mechanics of stochastic growth phenomena",

abstract = "We develop statistical mechanics for stochastic growth processes and apply it to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and describes adiabatic (quasistatic) thermodynamic processes in the two-dimensional Dyson gas. By using Einstein's theory of thermodynamic fluctuations we consider transitional probabilities between thermodynamic states, which are in a one-to-one correspondence with simply connected domains occupied by gas. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with a free-particle propagator on an infinite-dimensional complex manifold with a K{\"a}hler metric.",

author = "Oleg Alekseev and Mark Mineev-Weinstein",

year = "2017",

month = jul,

day = "20",

doi = "10.1103/PhysRevE.96.010103",

language = "English",

volume = "96",

journal = "Physical Review E",

issn = "1539-3755",

publisher = "American Physical Society",

number = "1",

}

RIS

TY - JOUR

T1 - Statistical mechanics of stochastic growth phenomena

AU - Alekseev, Oleg

AU - Mineev-Weinstein, Mark

PY - 2017/7/20

Y1 - 2017/7/20

N2 - We develop statistical mechanics for stochastic growth processes and apply it to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and describes adiabatic (quasistatic) thermodynamic processes in the two-dimensional Dyson gas. By using Einstein's theory of thermodynamic fluctuations we consider transitional probabilities between thermodynamic states, which are in a one-to-one correspondence with simply connected domains occupied by gas. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with a free-particle propagator on an infinite-dimensional complex manifold with a Kähler metric.

AB - We develop statistical mechanics for stochastic growth processes and apply it to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and describes adiabatic (quasistatic) thermodynamic processes in the two-dimensional Dyson gas. By using Einstein's theory of thermodynamic fluctuations we consider transitional probabilities between thermodynamic states, which are in a one-to-one correspondence with simply connected domains occupied by gas. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with a free-particle propagator on an infinite-dimensional complex manifold with a Kähler metric.

UR - http://www.scopus.com/inward/record.url?scp=85025631526&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.96.010103

DO - 10.1103/PhysRevE.96.010103

M3 - Article

AN - SCOPUS:85025631526

VL - 96

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

M1 - 010103

ER -

ID: 36351758