Related papers: Path-integral representation for a stochastic sand…
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many…
In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a…
For any real-valued stochastic process $X$ with c\'rdl\'rg paths we define non-empty family of processes which have locally finite total variation, have jumps of the same order as the process $X$ and uniformly approximate its paths on…
The mathematical models used to represent physical phenomena are generally known to be imperfect representations of reality. Model inadequacies arise for numerous reasons, such as incomplete knowledge of the phenomena or computational…
In this work we introduce a phase-space description based on the positive P representation for bosonic fields interacting with a system of quantum emitters. The formalism is applicable to collective light-matter interactions and open…
A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase…
In this paper, we present a statistical model of spacetime trajectories based on a finite collection of paths organized into a branched manifold. For each configuration of the branched manifold, we define a Shannon entropy. Given the…
A method of path integral construction without gauge fixing in the holomorphic representation is proposed for finite-dimensional gauge models. This path integral determines a manifestly gauge-invariant kernel of the evolution operator.
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a…
Intracellular transport processes driven by molecular motors can be described by stochastic lattice models of self-driven particles. Here we focus on bidirectional transport models excluding the exchange of particles on the same track. We…
A variation to the usual formulation of Grassmann representation path integrals is presented. Time-indexed anticommuting partners are introduced for each Grassmann coherent state variable and a general method for handling the effect of…
The quantum many-body problem in condensed phases is often simplified using a quasiparticle description, such as effective mass theory for electron motion in a periodic solid. These approaches are often the basis for understanding many…
The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on F{\"o}llmer…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven…
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
We perform large-scale simulations of a two-dimensional restricted-height conserved stochastic sandpile, focusing on particle diffusion and mobility, and spatial correlations. Quasistationary (QS) simulations yield the critical particle…
We study the evolution of interacting groups of agents in two-dimensional geometries. We introduce a microscopic stochastic model that includes floor fields modeling the global flow of individual groups as well as local interaction rules.…