Related papers: Induced osmotic vorticity in the quantum hydrodyna…
We review the derivation of quantum theory as an application of entropic methods of inference. The new contribution in this paper is a streamlined derivation of the Schr\"odinger equation based on a different choice of microstates and…
Mermin's "shut up and calculate!" somehow summarizes the most widely accepted view on quantum mechanics. This conception has led to a rather constraining way to think and understand the quantum world. Nonetheless, a closer look at the…
The Schroedinger equation with the nonlinear term is derived by the natural generalization of the hydrodynamical model of quantum mechanics. The nonlinear term appears to be logically necessary because it enables explanation of the…
We provide a comprehensive picture for the formulation of the perfect fluid in the modern effective field theory formalism at both the classical and quantum level. Due to the necessity of decomposing the hydrodynamical variables $(\rho, p,…
It is common practice to approximate a weakly nonlinear wave equation through a kinetic transport equation, thus raising the issue of controlling the validity of the kinetic limit for a suitable choice of the random initial data. While for…
The linear Schr\"{o}dinger equation does not predict that macroscopic bodies should be located at one place only. Quantum mechanics textbooks generally solve the problem by introducing the projection postulate, which forces definite values…
The quantum hydrodynamic analogy (QHA) equivalent to the Schrodinger equation is generalized to its stochastic version by a systematic technique. On large scale, the quantum stochastic hydrodynamic analogy (QSHA) shows dynamics that under…
In this paper, we show that the Kirchhoff equations are derived from the Schr\"odinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of $n$ point vortices in…
Using the linear local induction approximation, we investigated the self-induced motion of a vortex line that corresponds to the motion of a particle in quantum mechanics. Concerning Kelvin waves, the effective Schr\"odinger equation,…
The framework of anisotropic hydrodynamics is generalized to include finite particle masses. Two schemes are introduced and their predictions compared with exact solutions of the kinetic equation in the relaxation time approximation. The…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
Modified uncertainty principle and non-commutative variables may phenomenologically account for quantum gravity effects, independently of the considered theory of quantum gravity. We show that quantum fluids enable experimental analogs and…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum…
This paper investigates the collisionless quantum hydrodynamic, or quantum Euler, system in \(\mathbb{T}^3\) with the linear pressure law \(P(\rho)=\rho\). Since this pressure is associated with the logarithmic internal energy…
In the present paper a simple dynamical model for computing the osmotically driven fluid flow in a variety of complex, non equilibrium situations is derived from first principles. Using the Oberbeck-Boussinesq approximation, the basic…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…
Micellar aqueous solutions of ionic surfactants have been observed to exhibit proton delocalization (the nuclear quantum effect) and to oscillate between a low density (LDL) and a high density (HDL) state of water state at a fixed…
The quantum master equation obtained from two different thermodynamic arguments is seriously nonlinear. We argue that, for quantum systems, nonlinearity occurs naturally in the step from reversible to irreversible equations and we analyze…