Related papers: Generalized quantum potentials in scale relativity
The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum…
Universal scaling near phase transitions is one of the central ideas of physics, linking the growth of spatial correlations to the slowing down of dynamics. So far, direct experimental access to this critical behavior has remained largely…
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…
In this paper we consider a nonlinear stochastic approach to the description of quantum systems. It is shown that a possibility to derive quantum properties - spectrum quantization, zero point positive energy and uncertainty relations,…
New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the…
We propose a unified diffusion-mobility relation which quantifies both quantum and classical levels of understanding on electron dynamics in ordered and disordered materials. This attempt overcomes the inability of classical Einstein…
In this work, surface diffusion is studied with a different perspective by showing how the corresponding open dynamics is transformed when passing, in a continuous and smooth way, from a pure quantum regime to a full classical regime; the…
Rotating turbulence is ubiquitous in nature. Previous works suggest that such turbulence could be described as an ensemble of interacting inertial waves across a wide range of length scales. For turbulence in macroscopic quantum…
We expose the Schr\"odinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schr\"odinger, Pauli and Dirac equations, as well as…
An analogy between non-relativistic quantum mechanics in the Madelung formulation and quantum geometrodynamics in the case of the maximally symmetric space is drawn. The equations equivalent to the continuity equation and the hydrodynamic…
The quantum potential is shown to result from the presence of a subtle thermal vacuum energy distributed across the whole domain of an experimental setup. Explicitly, its form is demonstrated to be exactly identical to the heat distribution…
We introduce non-trivial contributions to diffusion constant in generic many-body systems arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in…
We develop a neutral vortex fluid theory on closed surfaces with zero genus. The theory describes collective dynamics of many well-separated quantum vortices in a superfluid confined on a closed surface. Comparing to the case on a plane,…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
The new uncertainty relation is derived in the context of the canonical quantum theory with gravity for the case of the maximally symmetric space. This relation establishes a connection between fluctuations of the quantities which determine…
In the paper, we discuss the studies of mathematical models of diffusion scattering of waves in the phase space, and relation of these models with quantum mechanics. In the previous works it is shown that in these models of classical…
If the presence of a gravitational field breaks the Lorentz symmetry valid for special relativity, an "absolute motion" might be detectable. We summarize a scalar theory of gravity with a such "ether", which starts from a tentative…
Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub-diffusive law. It is shown…
We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…