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Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
The time evolution of the thermally activated decay rates is considered. This evolution is of particular importance for the recent nanoscale experiments discussed in the literature, where the potential barrier is relatively low (or the…
We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…
We study the dynamics of atoms interacting periodically with a dissipative optical cavity and employ Floquet theory to analyze their low-frequency behavior. By means of an effective atom-only master equation, valid in the bad cavity regime,…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
The thermodynamic properties of time-delayed dynamics remain largely unexplored, especially for systems that exhibit asymptotically non-stationary behavior. Here, we investigate heat dissipation in two classes of marginally stable linear…
We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an…
The quantum dynamics of a damped and forced harmonic oscillator is investigated in terms of a Lindblad master equation. Elementary algebraic techniques are employed allowing for example to analyze the long time behavior, i.e. the quantum…
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory numbers statistics for the model of nonlinear dissipative oscillator. It is shown by numerical simulation of an ensemble of quantum trajectories…
We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
There are numerous examples of natural and artificial processes that represent stochastic sequences of events followed by an absolute refractory period during which the occurrence of a subsequent event is impossible. In the simplest case of…
We study the probability distribution and the escape rate in systems with delayed dissipation that comes from the coupling to a thermal bath. To logarithmic accuracy in the fluctuation intensity, the problem is reduced to a variational…
An adiabatic transition between two equilibrium states corresponding to different stiffnesses in an infinite chain of particles is studied. Initially, the chain particles have random displacements and random velocities corresponding to a…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
We investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence (delayed random walk). The characteristic feature of such a model is the oscillatory behavior of…
We present an investigation of stochastic evolution in which a family of evolution equations in $L^1$ are driven by continuous-time Markov processes. These are examples of so-called piecewise deterministic Markov processes (PDMP's) on the…