Related papers: Madelung Mechanics and Superoscillations
The hydrodynamic interpretation of quantum mechanics treats a system of particles in an effective manner. In this work, we investigate squeezed coherent states within the hydrodynamic interpretation. The Hamiltonian operator in question is…
Special relativity combined with the stochastic vacuum flux impact model lead to an explicit interpretation of many of the phenomena of elementary quantum mechanics. We examine characteristics of a repetitively impacted submicroscopic…
We present a microscopic theory for superfluidity in an interacting many-particle Bose system (such as liquid $^4$He). We show that, similar to superconductivity in superconductors, superfluidity in a Bose system arises from pairing of…
We analyze the Schr\"{o}dinger dynamics and the Schr\"{o}dinger function (or the so-called wavefunction) in the following four aspects. (1) The Schr\"{o}dinger equation is reconstructed from scratch in the real field only, without referring…
In this paper we pose two fundamental ideas on the motion of an elementary particle supporting the internal "spin motion" or $\textit{Zitterbewegung}$ and a particle as concentrated energy. First, the particle moves randomly in a limited…
In the first part (Sections 1 and 2) of this paper --starting from the Pauli current, in the ordinary tensorial language-- we obtain the decomposition of the non-relativistic field velocity into two orthogonal parts: (i) the "classical…
The existence of precise particle trajectories in any quantum state is accounted for in a consistent way by allowing delocalization of the particle charge. The relativistic mass of the particle remains within a small volume surrounding a…
Under the assumption of two fluid kinematics of a nonrelativistic Bose liquid in the presence of a local velocity field $v(x)$, local Galilei transformations are used to derive formulas for the spatial distribution of superfluidity. The…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
We name strongly localized quantum crystalline state (SLQCS) a determinantal wave-function of the single-particle wave-functions obtained by crystalline translations of a wave-function different from zero only within a primitive cell of the…
A weakly nonlocal extension of ideal fluid dynamics is derived from the Second Law of thermodynamics. It is proved that in the reversible limit the additional pressure term can be derived from a potential. The requirement of the additivity…
The present contribution is based on the assumption that the probabilistic character of quantum mechanics does not originate from uncertainties caused by the process of measurement or observation, but rather reflects the presence of…
We consider the one-dimensional Schroedinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, confined to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the…
Existence, uniqueness and stability of solutions is studied for a set of nonlinear fixed point equations which define self-consistent hydrostatic equilibria of a classical continuum fluid that is confined inside a container and in contact…
By identifying the Schr\"{o}dinger equation with the hydrodynamic equations in superfluid ${^3}$He, the effective potential is introduced in the Schr\"{o}dinger equation to solve the quantum pressure in steady state. The pure gauge velocity…
We prove the existence of global in time, finite energy, weak solutions to a quantum magnetohydrodynamic system (QMHD) with large data, modeling a charged quantum fluid interacting with a self-generated electromagnetic field. The analysis…
We study the discrete nonlinear Schr\"odinger equation (DNLS) in an annular geometry with on-site defects. The dynamics of a traveling plane-wave maps onto an effective ''non-rigid pendulum'' Hamiltonian. The different regimes include the…
We study the mean-field and semiclassical limit of the quantum many-body dynamics with a repulsive $\delta$-type potential $N^{3\beta}V(N^{\beta}x)$ and a Coulomb potential, which leads to a macroscopic fluid equation, the Euler-Poisson…
We consider the case of a cubic nonlinear Schr\"{o}dinger equation with an additional chaotic potential, in the sense that such a potential produces chaotic dynamics in classical mechanics. We derive and describe an appropriate…
Much of modern condensed matter physics is understood in terms of elementary excitations, or quasiparticles - fundamental quanta of energy and momentum. Various strongly-interacting atomic systems are successfully treated as a collection of…