相关论文: Quantum Potential and Random Phase - Space Dynamic…

A nonlinear wave mechanical equation is proposed by inserting an imaginary quantum potential into the Schr\"{o}dinger equation. An explicit expression for its solution is given under certain assumptions and it is shown that it entails…

We propose new equations of motion under the theory of the Brownian motion to connect the states of quantum, diffusion, soliton, and periodic localization. The new equations are nothing but the classical equations of motion with two…

Current dynamical control based on the bang-bang control mechanism involving various types of pulse sequences is essentially a perturbative theory. This paper presents a non-perturbative dynamical control approach based on the exact…

A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary non-exponential distribution of the residence times, is developed. The formally exact expression…

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…

As examples of models having interesting constraint structures, we derive a quantum mechanical model from the spatial freezing of a well known relativistic field theory - the chiral Schwinger model. We apply the Hamiltonian constraint…

Energy absorption by driven chaotic systems, the theory of energy spreading and quantal Brownian motion are considered. In particular we discuss the theory of a classical particle that interacts with quantal chaotic degrees of freedom, and…

This paper's aim is threefold. First, using Feynman's path approach to the derivation of theclassical Schr{\"o}dinger's equation in [6] and by introducing a slight path (or wave) dependency ofthe action, we derive a new class of equations…

The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian…

Despite the prevalent view that quantum mechanics is irrelevant to macroscopic biological systems because of inherent noise and decoherence, this paper demonstrates that the electrical noise (Brownian motion) in neuron membranes gives rise…

We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an…

This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…

We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…

Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…

We derive the exact action for a damped mechanical system ( and the special case of the linear oscillator) from the path integral formulation of the quantum Brownian motion problem developed by Schwinger and by Feynman and Vernon. The…

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov--Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The…

It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…

In this paper, we show how the motion of physical fields, in particular the electromagnetic potential, is connected with the choice of a space and time decomposition of the background spacetime manifold. The relation of the field dynamics…

These short notes present to the reader (students, in particular) a concise approach to the derivation of the propagator of Hamiltonians with position-dependent kinetic energy. The formalism is applied to the von Roos Hamiltonian with…

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…