Related papers: Transfer operators and topological field theory
This work develops a rigorous mathematical formulation of proton transport by integrating both deterministic and stochastic perspectives. The deterministic framework is based on the Boltzmann-Fokker-Planck equation, formulated as an…
We extend the work of Tanase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We…
We study the statistical mechanics and the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets described by a modified Gross-Pitaevskii equation. To determine the classical partition function thereof, we…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
A procedure is presented for solving the Fokker-Planck equation with constant diffusion but non-stationary drift. It is based on the correspondence between the Fokker-Planck equation and the non-stationary Schr\"odinger equation. The…
Self-oscillation is a phenomenon studied across many scientific disciplines, including the engineering of efficient heat engines and electric generators. We investigate the single electron shuttle, a model nano-scale system that exhibits a…
This paper focuses on the time-changed Q-Wiener process, a Hilbert space-valued sub-diffusion. It is a martingale with respect to an appropriate filtration, hence a stochastic integral with respect to it is definable. For the resulting…
The transfer operator associated to a flow (continuous time dynamical system) is a one-parameter operator semigroup. We consider the operator-valued Laplace transform of this one-parameter semigroup. Estimates on the Laplace transform have…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
We prove strong well-posedness for a class of stochastic evolution equations in Hilbert spaces H when the drift term is Holder continuous. This class includes examples of semilinear stochastic damped wave equations which describe elastic…
Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of…
Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…
Atmospheric regime transitions are highly impactful as drivers of extreme weather events, but pose two formidable modeling challenges: predicting the next event (weather forecasting), and characterizing the statistics of events of a given…
In this paper, enlightened by the asymptotic expansion methodology developed by Li(2013b) and Li and Chen (2016), we propose a Taylor-type approximation for the transition densities of the stochastic differential equations (SDEs) driven by…
In the vicinity of a phase transition, the order parameter starts fluctuating before vanishing at the critical point. The fluctuation regime, i.e. the way the ordered phase disappears, is a characteristics of a transition, and determines…
The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a…
Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete…
The waiting time distribution (WTD) is a common tool for analysing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete,…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
We revisit static, spherically symmetric perfect-fluid stellar models in General Relativity within the framework of the $1+1+2$ semi-tetrad formalism. For locally rotationally symmetric static spacetimes, the Tolman-Oppenheimer-Volkoff…