Related papers: On the representation of contextual probabilistic …
The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
Radiation hydrodynamics simulations based on the one-fluid two-temperature model may violate the law of energy conservation because the governing equations are expressed in a nonconservative formulation. Here, we maintain the important…
A relativistic collapse model for distinguishable particles is presented. Position and time, for each particle, are the fundamental operators of the theory. The Schr\"odinger equation is of the CSL form, with a Hermitian Hamiltonian and an…
A methodology is proposed for formulating dynamic equations in thermo-piezoelectric and dissipative media from the first principle of energy conservation. The results are in agreement with those from Hamiltonian principle. Our formulations…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
Standard quantum mechanics relies on two distinct dynamical principles: unitary evolution and collapse. A mathematically self-contained variational framework is presented that replaces this dualism with a single principle, in which…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
A geometrical interpretation of Schr\"odinger's kinetic and potential energy operators is proposed, allowing for a covariant momentum space formulation of the dynamics that is relevant for the theories with the deformation of the momentum…
Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov-Maxwell kinetic…
Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart. We use the constraint phase space developed in J. Chem. Phys.…
By the example of a Fourier transform, the possibilities of Hilbert space geometry applications for statistical model construction are analyzed. In accordance with Bohr's complementarity principle, mutually-complementary coordinate and…
The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course,…
Quantum dynamics provides the arguably most fundamental example of hybrid dynamics: As long as no measurement takes place, the system state is governed by the Schr\"odinger-Liouville differential equation, which is however interrupted and…
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our…
In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is…
Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…