Path integral approach to birth-death processes on a lattice

Peliti, Luca

doi:10.1051/jphys:019850046090146900

Cited by 572 publications

(743 citation statements)

References 33 publications

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“…In a first step, the process is mapped onto a field theory by a Fock space formalism, an approach devised by several authors [8,[28][29][30][31]; for a review see [32]. In our case of diffusing particles which coagulate upon contact, the action of the path integral can be split up as…”

Section: A the Field-theoretic Actionmentioning

confidence: 99%

Long-range and many-body effects in coagulation processes

Winkler

Frey

2013

Phys. Rev. E

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We study the problem of diffusing particles which coalesce upon contact. With the aid of a nonperturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violating this classical law. It originates in long-range and many-particle fluctuations and is a simple, universal function of the macroscopic decay rate.

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Section: A the Field-theoretic Actionmentioning

confidence: 99%

Long-range and many-body effects in coagulation processes

Winkler

Frey

2013

Phys. Rev. E

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“…Following the formalism developed in Refs. [18,19,20], the state of the system is described by the state vector |P (t) = {σ} P ({σ}, t) |{σ} , whose time evolution is governed by the master equation ∂ t |P (t) =L|P (t) . HereL is the generator of the Markov process that contains the transition rates between the different microstates of the system, |{σ} .…”

mentioning

confidence: 99%

Contact process in heterogeneous and weakly disordered systems

2006

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The critical behavior of the contact process (CP) in heterogeneous periodic and weakly-disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents β (from series expansion) and η (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the directed percolation (DP) universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents.

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“…The Legendre transform Γ of log Z is then analogous to the Gibbs free energy and is the generator of the 1PI correlation functions. There are two main means to build field theories in out of equilibrium statistical mechanics: either from a Langevin formulation of the problem or from a more microscopic approach -if it exists -à la Doi-Peliti [38,39], that is from a master equation.…”

Section: The Out Of Equilibrium Casementioning

confidence: 99%

What can be learnt from the nonperturbative renormalization group?

Delamotte¹,

Canet²

2005

Condens. Matter Phys.

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We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non-perturbative renormalization group formalism is a promising candidate to overcome some of them. We present some results recently obtained in the literature that substantiate our claims. We finally list some open issues for which this formalism could be useful and also review some of its drawbacks.

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Path integral approach to birth-death processes on a lattice

Abstract: Résumé. 2014 On donne une formulation par intégrales de

Cited by 572 publications

References 33 publications

Long-range and many-body effects in coagulation processes

Long-range and many-body effects in coagulation processes

Contact process in heterogeneous and weakly disordered systems

What can be learnt from the nonperturbative renormalization group?

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