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We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\log\rho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum…
First we describe briefly an information-action method for the study of stochastic dynamics of hamiltonian systems perturbed by thermal noise and chaotic instability. It is shown that, for the ensemble of possible paths between two…
This thesis is dedicated to the study of stochastic processes; non-deterministic physical phenomena that can be well described by classical physics. The stochastic processes we are interested in are akin to Brownian Motion and can be…
This note provides an introduction to molecular dynamics, the computational implementation of the theory of statistical physics. The discussion is focused on the properties of Langevin dynamics, a degenerate stochastic differential equation…
The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle corresponding, in its simplest form, to the Maximum…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
Estimating the parameters governing the dynamics of a system is a prerequisite for its optimal control. We present a simple but powerful method that we call STEADY, for STochastic Estimation algorithm for DYnamical variables, to estimate…
In this paper we develop a general formalism of a path approach for non-equilibrium statistical mechanics. Firstly, we consider the classical Gibbs approach for states and find that this formalism is ineffective for non-equilibrium…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated.…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…
Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one…
Open quantum systems play a central role in contemporary nanoscale technologies, including molecular electronics, quantum heat engines, quantum computation and information processing. A major theoretical challenge is to construct dynamical…
We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the…
We develop a new master equation as a unified description of the effects of both quantum noise (system-bath interaction) and classical noise on a system's dynamics, using a two-dimensional series expansion method. When quantum and classical…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…