Conditional probabilities in multiplicative noise processes

Moreno, Miguel V.; Barci, Daniel G.; Arenas, Zochil González

doi:10.1103/physreve.99.032125

Cited by 12 publications

(18 citation statements)

References 53 publications

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“…In classical terms, an interaction that is everywhere finite can stabilize cluster crystals at low temperature and high density [21][22][23][24][25], based on purely energetic considerations [26]: for example, when repulsion is "fatter" than Gaussian, it is more convenient to form isolated blobs of particles than having them distributed homogeneously in space. Such an arrangement ensures a large mobility to atoms, which can freely hop from one site to another [27]. Cluster-crystal order also occurs in weakly-repulsive bosons at high pressure, with the additional bonus of supersolid behavior (i.e., crystalline order coexisting with superfluid behavior) near the melting point [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Freezing of soft-core bosons at zero temperature: A variational theory

2018

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The properties of a macroscopic assembly of weakly-repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits a quantum transition from superfluid to cluster supersolid as a function of pressure. We develop a thermodynamically rigorous treatment of the different phases of the system by adopting a variational formulation of the condensate wave function -represented as a sum of Gaussiansthat is amenable to exact manipulations. Not only is this description quantitatively accurate, but it is also capable to predict the order (and sometimes even the location) of the transition. We consider a number of crystal structures in two and three dimensions and determine the phase diagram.Depending on the lattice, the transition from fluid to solid can be first-order or continuous, a lower coordination entailing a milder transition. In two dimensions, crystallization would occur at the same pressure on three distinct lattices (square, honeycomb, and stripes), all providing metastable phases with respect to the triangular crystal. A similar scenario holds in three dimensions, where the simple-cubic and diamond crystals also share a common melting point; however, the stable crystal at low pressure is typically fcc. Upon compression and depending on the shape of the potential, the fcc crystal may transform into hcp. We conclude by sketching a theory of the solid-fluid interface and of quantum nucleation of the solid from the fluid.

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Section: Introductionmentioning

confidence: 99%

Freezing of soft-core bosons at zero temperature: A variational theory

2018

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“…5, making the path integral become the conditional probability. The conditional probability is written in as a path integral [39,40]…”

Section: Ultra-relativistic Regimementioning

confidence: 99%

“…We use the variational formula for the Fokker-Planck [36,37], and we integrate it numerically. We also use the Path integral formalism [38][39][40][41] to deal with the ultra-relativistic case. The results are compared with numerical simulations of the stochastic process and are found in agreement.…”

Section: Introductionmentioning

confidence: 99%

Heat Distribution of Relativistic Brownian Motion

Paraguassú,

Morgado

2021

Preprint

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Understanding the statistical behavior of the heat in stochastic systems gives us insight about the thermodynamics of such systems. Using the recently proposed Relativistic Stochastic Thermodynamics, we investigate the statistics of the heat of a Relativistic Ornstein-Uhlenbeck particle, comparing with the classical cases. The results are exact through numerical integration of the Fokker-Planck of the joint distribution, and are validated by numerical simulations.

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“…[40]. More recently, we have presented a useful path integral technique to compute weak noise expansions [44]. The integration over fluctuations in the multiplicative case is not trivial.…”

Section: Introductionmentioning

confidence: 99%

“…The reason is that the diffusion function produces an integration measure that resembles a curved time axis [45]. We have provided a local time reparametrization in order to integrate fluctuations [44]. In this paper, we compute the conditional probability of finding a particle in a well at large times t/2, provided it was in the same or the other well at −t/2.…”

Section: Introductionmentioning

confidence: 99%

State dependent diffusion in a bistable potential: conditional probabilities and escape rates

Moreno,

Barci,

Arenas

2019

Preprint

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We consider a simple model of a bistable system under the influence of multiplicative noise. We provide a path integral representation of the overdamped Langevin dynamics and compute conditional probabilities and escape rates in the weak noise approximation. The saddle-point solution of the functional integral is given by a diluted gas of instantons and anti-instantons, similarly to the additive noise problem. However, in this case, the integration over fluctuations is more involved. We introduce a local time reparametrization that allows its computation in the form of usual Gaussian integrals. We found corrections to the Kramers escape rate produced by the diffusion function which governs the state dependent diffusion for arbitrary values of the stochastic prescription parameter.

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Conditional probabilities in multiplicative noise processes

Cited by 12 publications

References 53 publications

Freezing of soft-core bosons at zero temperature: A variational theory

Freezing of soft-core bosons at zero temperature: A variational theory

Heat Distribution of Relativistic Brownian Motion

State dependent diffusion in a bistable potential: conditional probabilities and escape rates

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