arXiv subjects

Valeriy I. Sbitnev

Publications and source records attributed to Valeriy I. Sbitnev.

14 recordsLinked to original sources

arXiv2019

Quaternion algebra on 4D superfluid quantum space-time. Gravitomagnetism

Gravitomagnetic equations result from applying quaternionic differential operators to the energy-momentum tensor. These equations are similar to the Maxwell's EM equations. Both sets of the equations are isomorphic after changing orientation of either the gravitomagnetic orbital force or the magnetic induction. The gravitomagnetic equations turn out to be parent equations generating the following set of equations: (a) the vorticity equation giving solutions of vortices with nonzero vortex cores and with infinite lifetime; (b) the Hamilton-Jacobi equation loaded by the quantum potential. This equation in pair with the continuity equation leads to getting the \Schrodinger equation describing a state of the superfluid quantum medium (a modern version of the old ether); (c) gravitomagnetic wave equations loaded by forces acting on the outer space. These waves obey to the Planck's law of radiation.

gr-qc↗

arXiv2017

Hydrodynamics of Superfluid Quantum Space: particle of spin-1/2 in a magnetic field

The modified Navier-Stokes equation describing the velocity field in the superfluid quantum space is loaded by the external Lorentz force introducing electromagnetic fields. In order to open the path for getting the \Schrodinger-Pauli equation describing the behavior of a particle with spin-1/2 in the magnetic field we need to extend the continuity equation to take into account conservation of spin flows on the 3D sphere. This extension includes conservation of the density distribution function in 6D space, that is a multiplication of the 3D Euclidean space by the 3D sphere of unit radius. The special unitary group SU(2) underlies the rotations of the spin on this sphere. This group is isomorphic to the group of quaternions containing the real 4x4 matrices of norm 1. Transition to the quaternion group opens up the way to the possibility of describing the spin-1/2 behavior in a magnetic field as a motion of a spin flag on the 2D sphere. Maxwell's electromagnetic field theory manifests itself in the quaternion group basis by the natural manner.

quant-ph↗

arXiv2017

Hydrodynamics of Superfluid Quantum Space: de Broglie interpretation of the quantum mechanics

The ubiquitous ether coming from the ancient times up to middle of the twenty century is replaced by a superfluid quantum space. It represents by itself a Bose-Einstein condensate consisting of enormous amount of virtual particle-antiparticle pairs emerging and disappearing in an infinitely ongoing dance. Flowing of this medium in the non-relativistic limit is described by the modified Navier-Stokes equation along with the continuity equation. The first equation admits the splitting on to two coupled equations. They are the quantum Hamilton-Jacobi equation and the equation for vorticity. The quantum Hamilton-Jacoby equation paired with the continuity equation can be reduced to the \Schrodinger equation. These two equations representing the kernel of the Bohmian mechanics give finding bundle of the Bohmian trajectories. Whereas the vorticity equation gives solutions for vortices moving along such trajectories. As the result we come to the de Broglie's interpretation of quantum mechanics according to which there is a pilot-wave guiding the particle (in our case it is a vortex clot) from a source up to its detection along an optimal path that is the Bohmian trajectory.

quant-ph↗

arXiv2016

Physical vacuum is a special superfluid medium

The Navier-Stokes equation contains two terms which have been subjected to slight modification: (a) the viscosity term depends of time (the viscosity in average on time is zero, but its variance is non-zero), (b) the pressure gradient contains an added term describing the quantum entropy gradient multiplied by the pressure. Owing to these modifications, the Navier-Stokes equation can be reduced to the Schrödinger equation describing behavior of a particle into the vacuum being as a superfluid medium. Vortex structures arising in this medium show infinitely long life owing to zeroth average viscosity. The non-zero variance describes exchange of the vortex energy with zero-point energy of the vacuum. Radius of the vortex trembles around some average value. This observation sheds the light to the Zitterbewegung phenomenon. The long-lived vortex has a non-zero core where the vortex velocity vanishes.

quant-ph↗

arXiv2016

Hydrodynamics of the Physical Vacuum: I. Scalar quantum sector

Physical vacuum is a special superfluid medium. Its motion is described by the Navier-Stokes equation having two slightly modified terms that relate to internal forces. They are the pressure gradient and the dissipation force because of viscosity. The modifications are as follows: (a) the pressure gradient contains an added term describing the pressure multiplied by the entropy gradient; (b) time-averaged viscosity is zero, but its variance is not zero. Owing to these modifications, the Navier-Stokes equation can be reduced to the Schrodinger equation describing behavior of a particle into the vacuum, which looks like a superfluid medium populated by enormous amount of virtual particle-antiparticle pairs.

quant-ph↗

arXiv2016

Dark matter is a manifestation of the vacuum Bose-Einstein condensate

The vorticity equation stemming from the modified Navier-Stokes equation gives a solution for a flat profile of the orbital speed of spiral galaxies. Solutions disclose existence of the Gaussian vortex clouds, the coherent vortices with infinite life-time, what can be a manifestation of the dark matter. The solutions also disclose what we might call a breathing of the galaxies - due to an exchange of the vortex energy with zero-point fluctuations in the vacuum. .

physics.gen-ph↗

arXiv2016

Quantum consciousness in warm, wet, and noisy brain

The emergence of quantum consciousness stems from dynamic flows of hydrogen ions in brain liquid. This liquid contains vast areas of the fourth phase of water with hexagonal packing of its molecules, the so-called exclusion zone (EZ) of water. The hydrogen ion motion on such hexagonal lattices shows as the hopping of the ions forward and the holes (vacant places) backward, caused by the Grotthuss mechanism. By supporting this motion using external infrasound sources, one may achieve the appearance of the superfluid state of the EZ water. Flows of the hydrogen ions are described by the modified Navier-Stokes equation. It, along with the continuity equation, yields the nonlinear Schrodinger equation, which describes the quantum effects of these flows, such as the tunneling at long distances or the interference on gap junctions.

q-bio.NC↗

arXiv2016

Hydrodynamics of the Physical Vacuum: II. Vorticity dynamics

Physical vacuum is a special superfluid medium populated by enormous amount of virtual particle-antiparticle pairs. Its motion is described by the modified Navier-Stokes equation: (a)~the pressure gradient divided by the mass density is replaced by the gradient from the quantum potential; (b)~time-averaged the viscosity vanishes, but its variance is not zero. Vortex structures arising in this medium show infinitely long lifetime owing to zero average viscosity. The nonzero variance is conditioned by exchanging the vortex energy with zero-point vacuum fluctuations. The vortex has a non-zero core where the orbital speed vanishes. The speed reaches a maximal value on the core wall and further it decreases monotonically. The vortex trembles around some average value and possesses by infinite life time. The vortex ball resulting from topological transformation of the vortex ring is considered as a model of a particle with spin. Anomalous magnetic moment of electron is computed.

quant-ph↗

arXiv2015

Hydrodynamics of the physical vacuum: dark matter is an illusion

The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schrödinger equation in the non-relativistic limit). In both cases it is required to get the quantum potential, which follows from pressure gradients within a superfluid vacuum medium. This special fluid, endowed with viscosity allows to describe emergence of the flat orbital speeds of spiral galaxies. The viscosity averaged on time vanishes, but its variance is different from zero. It is a function fluctuating about zero. Therefore the flattening is the result of the energy exchange of the torque with zero-point fluctuations of the physical vacuum on the ultra-low frequencies.

physics.gen-ph↗

arXiv2014

From the Newton's laws to motions of the fluid and superfluid vacuum: vortex tubes, rings, and others

Owing to three conditions (namely: (a) the velocity is represented by sum of irrotational and solenoidal components; (b) the fluid is barotropic; (c) a bath with the fluid undergoes vertical vibrations) the Navier-Stokes equation admits reduction to the modified Hamilton-Jacobi equation. The modification term is the Bohmian(quantum) potential. This reduction opens possibility to define a complex-valued function, named the wave function, which is a solution of the Schrödinger equation. The solenoidal component being added to the momentum operator poses itself as a vector potential by analogy with the magnetic vector potential. The vector potential is represented by the solenoidal velocity multiplied by mass of the fluid element. Vortex tubes, rings, and balls along with the wave function guiding these objects are solutions of this equation. Motion of the vortex balls along the Bohmian trajectories gives a model of droplets moving on the fluid surface. A peculiar fluid is the superfluid physical vacuum. It contains Bose particle-antiparticle pairs. Vortex lines presented by electron-positron pairs are main torque objects. Bundles of the vortex lines can transmit a torque from one rotating disk to other unmoved disk.

physics.flu-dyn↗

arXiv2013

Droplets moving on a fluid surface: interference pattern from two slits

The Feynman path integral approach for solving the motion of a droplet along a silicon oil surface is developed by replacing the Planck constant by a surrogate parameter. The latter is proportional to the surface tension of the silicon oil multiplied by the area of the thin air film, separating the droplet from the oil, and by the half-period of the Faraday oscillations. It is shown that the Navier-Stokes equation together with the mass conservation equation can be reduced to the Schrödinger equation when the surrogate parameter replaces the Planck constant. The Feynman path integral underlying the Schrödinger equation is used then to calculate a wave function that plays the role of the de Broglie pilot-wave.

physics.flu-dyn↗

arXiv2010

Matter waves in the Talbot-Lau interferometry

Paths of particles, emitted from distributed sources and passing out through slits of two gratings, $G_{0}$ and $G_{1}$, up to detectors, have been computed in details by the path integral method. The slits are represented by Gaussian functions that simulate fuzzy edges of the slits. Waves of matter be computed by this method show perfect interference patterns both between the gratings and behind the second grating. Coherent and noncoherent the distributed particle sources reproducing the interference patterns are discussed in details. Paraxial approximation stems from the wave function when removing the distributed sources onto infinity. The more hard-edged slits of the grating $G_{1}$ are examined by simulating those slits by a superposition of more hard the Gaussian functions. As for the particles here we consider fullerene molecules. De Broglie wavelength of the molecules is adopted equal to 5 pm.

quant-ph↗

arXiv2009

N-Slit Interference: Fractals in Near-Field Region, Bohmian Trajectories

Scattering cold particles on an $N$-slit grating is shown to reproduce an interference pattern, that manifests itself in the near-field region as the fractal Talbot carpet. In the far-field region the pattern is transformed to an ordinary diffraction, where principal beams are partitioned from each other by ($N-2$) weak ones. A probability density plot of the wave function, to be represented by a gaussian wavepacket, is calculated both in the near-field region and in the far-field one. Bohmian (geodesic) trajectories, to be calculated by a guidance equation, are superimposed on the probability density plot well enough. It means, that a particle, moving from a source to a detector, passes across the grating along a single bohmian trajectory through-passing one and only one slit. Keywords: Gaussian wavepacket, neutron scattering, guidance equation, bohmian trajectory, near-field interference, far-field diffraction, Talbot carpet, fractal

quant-ph↗

arXiv2008

Bohmian trajectories and the Path Integral Paradigm. Complexified Lagrangian Mechanics

David Bohm shown that the Schr{ö}dinger equation, that is a "visiting card" of quantum mechanics, can be decomposed onto two equations for real functions - action and probability density. The first equation is the Hamilton-Jacobi (HJ) equation, a "visiting card" of classical mechanics, to be modified by the Bohmian quantum potential. And the second is the continuity equation. The latter can be transformed to the entropy balance equation. The Bohmian quantum potential is transformed to two Bohmian quantum correctors. The first corrector modifies kinetic energy term of the HJ equation, and the second one modifies potential energy term. Unification of the quantum HJ equation and the entropy balance equation gives complexified HJ equation containing complex kinetic and potential terms. Imaginary parts of these terms have order of smallness about the Planck constant. The Bohmian quantum corrector is indispensable term modifying the Feynman's path integral by expanding coordinates and momenta to imaginary sector.

quant-ph↗