Related papers: A First Principles Derivation of Classical and Qua…
The longstanding question of how stochastic behaviour arises from deterministic Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable of describing this transition. In this review, we introduce the…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Classical mechanics admits multiple equivalent formulations, from Newton's equations to the variational Lagrange-Hamilton framework and the scalar Hamilton-Jacobi (HJ) theory. In the HJ formulation, classical ensembles evolve through the…
A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…
Stochastic field theories are often constructed phenomenologically, without a systematic assessment of thermodynamic consistency or local detailed balance. This may hinder a physical description of irreversibility at the field-theoretic…
Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
This paper is concerned with a quantum memory system for storing quantum information in the form of its initial dynamic variables in the presence of environmental noise. In order to compensate for the deviation from the initial conditions,…
Suppose the observations of Lagrangian trajectories for fluid flow in some physical situation can be modelled sufficiently accurately by a spatially correlated It\^o stochastic process (with zero mean) obtained from data which is taken in…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the…
The theories of stochastic quantum mechanics and stochastic electrodynamics bring to light important aspects of the quantum dynamics that are concealed in the standard formalism. Here we take further previous work regarding the connection…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the Cameron-Martin-Girsanov theorem. More precisely, the notion…
Nelson's stochastic mechanics links quantum mechanics to an underlying Brownian motion with the identification $\hbar = m\sigma$. Ghose's interpolating equation introduces a continuous parameter $\lambda$ that suppresses the quantum…
This paper aims to explore the relationship between maximum principle and dynamic programming principle for stochastic recursive control problem with random coefficients. Under certain regular conditions for the coefficients, the…