Related papers: Uniform formalism for description of dynamic quant…
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…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
The approximation of quantum unitary dynamics of a particle by a swarm of point wise classical samples of this particle is proposed. Quantum mechanism of speedup rests on the creation and annihilation of absolutely rigid bons, which join…
Here it is shown that the unitary dynamics of a quantum object may be obtained as the conditional expectation of a counting process of object-clock interactions. Such a stochastic process arises from the quantization of the clock, and this…
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…
The decoherent (consistent) histories formalism has been proposed as a means of eliminating measurements as a fundamental concept in quantum mechanics. In this formalism, probabilities can be assigned to any description which satisfies a…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
We propose a general stochastic formalism for describing the evolution of chemical reactions involving a finite number of molecules. This approach is consistent with the statistical analysis based on the Chemical Master Equation, and…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
It is argued that the conventional formulation of quantum mechanics is inadequate: the usual interpretation of the mathematical formalism in terms of the results of measurements cannot be applied to situations in which discontinuous…
Every open-system dynamics can be associated to infinitely many stochastic pictures, called unravelings, which have proved to be extremely useful in several contexts, both from the conceptual and the practical point of view. Here, focusing…
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general…
A new class of stochastic variables, governed by a specifice set of rules, is introduced. These rules force them to loose some properties usually assumed for this kind of variables. We demonstrate that stochastic processes driven by these…