Related papers: Probabilistic whereabouts of the "quantum potentia…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
We consider the motion of an underdamped Brownian particle in a tilted periodic potential in a wide temperature range. Based on the previous data [1] and the new simulation results we show that the underdamped motion of particles in…
The dynamics of a freely diffusing particle in a two-dimensional channel with cross sectional area $A(x)$, can be effectively described by a one-dimensional diffusion equation under the action of a potential of mean force $U(x)=-k_BT\ln…
The present paper deals with some kind of quantum ``velocity'' which is introduced by the method of hydrodynamical analogy. It is found that this ``velocity'' is in general irrotational, namely, a vorticity vanishes, and then a velocity…
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…
Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we discuss how the propagator of a reacting molecule pair can be represented as a product of three factors in the Laplace…
In this paper the computational aspects of probability calculations for dynamical partial sum expressions are discussed. Such dynamical partial sum expressions have many important applications, and examples are provided in the fields of…
We give a convenient expression for the appearance probability P(nu_mu -> nu_e) describing neutrino oscillations in matter of constant density, derived using textbook quantum mechanics stratagems. Our formulation retains the clarity of an…
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated "trial" distribution. A particularly interesting case is when a driven system (e.g., active matter) is…
As the dimensions of physical systems approach the nanoscale, the laws of thermodynamics must be reconsidered due to the increased importance of fluctuations and quantum effects. While the statistical mechanics of small classical systems is…
In this paper, we deal with fluid motion in terms of quantum mechanics. Mechanism accounting for the appearance of quantum behavior is discussed.
We survey various origins and expressions for the quantum potential with some new observations.
We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for…
We present a probabilistic argument supporting the application of polar duality, as discussed in our previous work, to express the indeterminacy principle of quantum mechanics. Our approach combines the properties of the Mahler volume of a…
We present a completely new approach to the problem of interacting fluids, which we believe may provide important insights into microscopic mechanisms that lead to the occurrence of phase transitions. The approach exploits enumerative…
The relationship between the refractive index decrement, $\delta$, and the real part of the atomic form factor, $f^\prime$, is used to derive a simple polynomial functional form for $\delta(E)$ far from the K-edge of the element. The…
This paper investigates quantum diffusion of matter waves in two-dimensional random potentials, focussing on expanding Bose-Einstein condensates in spatially correlated optical speckle potentials. Special care is taken to describe the…