Related papers: Madelung Mechanics and Superoscillations
A basic aspect of the recently proposed approach to quantum mechanics is that no use of any axiomatic interpretation of the wave function is made. In particular, the quantum potential turns out to be an intrinsic potential energy of the…
The reinterpretation of quantum mechanical formalism in terms of a classical model with a continuous material "$\Psi$-field" acting upon a point-like particle which is subjected to large friction and random forces is proposed. This model…
The "main road" open by de Broglie's and Schroedinger's discovery of matter waves and of their eigen-functions branched off, as is well known, into different "sub-routes". The most widely accepted one is Standard Quantum Mechanics (SQM),…
Starting from relativistic mass-less Madelung fluid, we shall develop a class of typical wave functions by imposing it to maximize Shannon entropy given its finite average quantum potential. We show that there is a class of solutions in…
p-Adic quantum mechanics is constructed from the Dirac-von Neumann axioms identifying quantum states with square-integrable functions on the N-dimensional p-adic space. This choice is equivalent to the hypothesis of the discreteness of the…
In this note, we first obtain the decomposition of the non-relativistic field velocity into the classical part (i.e., the velocity w=p/m OF the center-of-mass (CM), and the so-called quantum part (i.e., the velocity V of the motion IN the…
It is shown that the Bohmian mechanics and the Madelung quantum hydrodynamics are different theories and the latter is a better ontological interpretation of quantum mechanics. A new stochastic interpretation of quantum mechanics is…
One considers the superfluid (SF) state of a Bose liquid with a strong repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC),…
We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroeodinger Equation $- \epsilon^2 \Delta \psi + V(x) \psi = |\psi|^{p-1} \psi$, on a manifold or in the Euclidean space. Here V represents the potential, p an…
The changes that quantum states undergo during measurement are both probabilistic and nonlocal. These two characteristics complement one another to insure compatibility with relativity and maintain conservation laws. The probabilistic…
The Madelung equations map the non-relativistic time-dependent Schrodinger equation into hydrodynamic equations of a virtual fluid. Here we show that an increase of the Boltzmann entropy of this Madelung fluid is proportional to the…
We develop a many-particle quantum-hydrodynamical model of fermion matter interacting with the external classical electromagnetic and gravitational/inertial and torsion fields. The consistent hydrodynamical formulation is constructed for…
Supersolidity -- a quantum-mechanical phenomenon characterized by the presence of both superfluidity and crystalline order -- was initially envisioned in the context of bulk solid helium, as a possible answer to the question of whether a…
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…
The dynamics of quantized vortices in weakly interacting superfluids are often modeled by a nonlinear Schr\"odinger equation. In contrast, we show that quantized vortices in fact obey a non-Hamiltonian evolution equation, which enhances…
A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
We show an example of benign non-separability in an apparently separable system consisting of $n$ free non-correlated quantum particles, solitonic solutions to the nonlinear phase modification of the Schr\"{o}dinger equation proposed…
Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional…
Order parameters represent a fundamental resource to characterize quantum matter. We show that pair superfluids can be rigorously defined in terms of a nonlocal order parameter, named odd parity, which derivation is experimentally…