相关论文: Generalized Continuity Equation and Modified Norma…

The transition from the quantum to the classical is governed by randomizing devices (RD), i.e., dynamical systems that are very sensitive to the environment. We show that, in the presence of RDs, the usual arguments based on the linearity…

Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…

To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making…

We derive a continuum equation for the magnetization of a conducting ferromagnet in the presence of a spin-polarized current. Current effects enter in the form of a topological term in the Landau-Lifshitz equation . In the stationary…

We show that generalizations of classical and quantum dynamics with two times lead to fundamentally constrained evolution. At the level of classical physics, Newton's second law is extended and exactly integrated in $1+2$ dimensional space,…

In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics,…

For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…

The general problem is studied on a simple example. A quantum particle in an infinite one-dimensional well potential is considered. Let the boundaries of well changes in a finite time $T$. The standard methods for calculating probability of…

The degree of entanglement is determined for an arbitrary state of a broad class of PT-symmetric bipartite composite systems. Subsequently we quantify the rate with which entangled states are generated and show that this rate can be…

We show that probability is locally conserved in discrete time quantum walks, corresponding to a particle evolving in discrete space and time. In particular, for a spatial structure represented by an arbitrary directed graph, and any…

In this paper, we introduce the Schrodinger equation with a general kinetic energy operator. The conservation law is proved and the probability continuity equation is deducted in a general sense. Examples with a Hermitian kinetic energy…

We consider a quantum particle under the dynamical confinement caused by PT-symmetric box with a moving wall. The latter is described in terms of the time-dependent Schr\"{o}dinger equation obeying the time-dependent PT-symmetric boundary…

We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the…

PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium…

Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of…

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…

A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass…

In this paper is considered a generalized quantization principle for the gravitational field in canonical quantum gravity, especially with respect to quantum geometrodynamics. This assumption can be interpreted as a transfer from the…

We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…

It is shown that the probability density satisfies a hyperbolic equation of motion with the unique characteristic that in its many-particle form it contains derivatives acting at spatially remote regions. Based on this feature we explore…