Related papers: Forward-Time Equivalent of a "Retrocausal" Diffusi…
We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the…
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…
Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used…
This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, similar to that of the Pauli matrices, and…
I present a technical report indicating that the two methods used for calculating characteristic functions for the work distribution in weakly driven quantum master equations are equivalent. One involves applying the notion of quantum jump…
We extend the classical forbidden-interval theorems for a stochastic-resonance noise benefit in a nonlinear system to a quantum-optical communication model and a continuous-variable quantum key distribution model. Each quantum…
We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
We suggest a new approach for describing quantum dissipation in a small systems for which the system-plus-reservoir approach is not relevant. We first analyze the fact that equilibrium thermodynamics may reveal the existence of an…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from statistical point of view as a particular example of the Kramers-Moyal expansion. Quantum mechanics is extended to…
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…
We show in detail how to determine the time-reversed representation of a stationary hidden stochastic process from linear combinations of its forward-time $\epsilon$-machine causal states. This also gives a check for the $k$-cryptic…
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…
In this article, we introduce a novel backward method to model stochastic gene expression and protein level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation…
Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most…
We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining…
Continuum mechanics with dislocations, with the Cattaneo type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov type system of the first order, symmetric…
We consider a multidimensional time-homogeneous dynamical system and add a randomly perturbed time-dependent deterministic signal to some of its components, giving rise to a high-dimensional system of stochastic differential equations,…