Matrix logarithmic wave equation and multi-channel systems in fluid mechanics

Zloshchastiev, Konstantin G.

doi:10.15632/jtam-pl/112063

Cited by 9 publications

(9 citation statements)

References 28 publications

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“…In this picture, massless excitations, such as photons, are analogous to acoustic waves propagating with velocity c s ∝ |p (ρ)|, where fluid pressure p = p(ρ) is determined via the equation of state. For the system (2), both the equation of state and speed of sound can be derived using the fluid-Schrödinger analogy, which was established for a special case in [14], and generalized for an arbitrary F(ρ) in works [7,15]. In a leading-order approximation with respect to the Planck constant, we obtain…”

Section: Logarithmic Superfluid Vacuummentioning

confidence: 99%

“…For the system (2), both the equation of state and speed of sound can be derived using the fluid-Schrödinger analogy, which was established for a special case in Ref. [14], and generalized for an arbitrary F (ρ) in works [7,15]. In a leading-order approximation with respect to the Planck constant, we obtain…”

Section: Logarithmic Superfluid Vacuummentioning

confidence: 99%

“…while higher-order corrections would induce Korteweg-type effects, thus significantly complicating the subject matter [15]. Furthermore, it is natural to require that superfluid vacuum theory must recover Einstein's theory of relativity at a certain limit.…”

Section: Logarithmic Superfluid Vacuummentioning

confidence: 99%

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An Alternative to Dark Matter and Dark Energy: Scale-Dependent Gravity in Superfluid Vacuum Theory

Zloshchastiev

2020

Universe

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We derive an effective gravitational potential, induced by the quantum wavefunction of a physical vacuum of a self-gravitating configuration, while the vacuum itself is viewed as the superfluid described by the logarithmic quantum wave equation. We determine that gravity has a multiple-scale pattern, to such an extent that one can distinguish sub-Newtonian, Newtonian, galactic, extragalactic and cosmological terms. The last of these dominates at the largest length scale of the model, where superfluid vacuum induces an asymptotically Friedmann–Lemaître–Robertson–Walker-type spacetime, which provides an explanation for the accelerating expansion of the Universe. The model describes different types of expansion mechanisms, which could explain the discrepancy between measurements of the Hubble constant using different methods. On a galactic scale, our model explains the non-Keplerian behaviour of galactic rotation curves, and also why their profiles can vary depending on the galaxy. It also makes a number of predictions about the behaviour of gravity at larger galactic and extragalactic scales. We demonstrate how the behaviour of rotation curves varies with distance from a gravitating center, growing from an inner galactic scale towards a metagalactic scale: A squared orbital velocity’s profile crosses over from Keplerian to flat, and then to non-flat. The asymptotic non-flat regime is thus expected to be seen in the outer regions of large spiral galaxies.

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Section: Logarithmic Superfluid Vacuummentioning

confidence: 99%

Section: Logarithmic Superfluid Vacuummentioning

confidence: 99%

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An Alternative to Dark Matter and Dark Energy: Scale-Dependent Gravity in Superfluid Vacuum Theory

Zloshchastiev

2020

Universe

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“…where P 0 is an arbitrary constant, and the approximation symbol means that we keep only the leading-order terms with respect to the Planck constant; a detailed derivation of these formulae can be found, e.g., in Sec. 3.1 of [43].…”

Section: Modelmentioning

confidence: 98%

Resolving the puzzle of sound propagation in liquid helium at low temperatures

Scott

Zloshchastiev

2019

Low Temperature Physics

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Experimental data suggests that, at temperatures below 1 K, the pressure in liquid helium has a cubic dependence on density. Thus the speed of sound scales as a cubic root of pressure. Near a critical pressure point, this speed approaches zero whereby the critical pressure is negative, thus indicating a cavitation instability regime. We demonstrate that to explain this dependence, one has to view liquid helium as a mixture of three quantum Bose liquids: dilute (Gross-Pitaevskii-type) Bose-Einstein condensate, Ginzburg-Sobyanin-type fluid, and logarithmic superfluid. Therefore, the dynamics of such a mixture is described by a quantum wave equation, which contains not only the polynomial (Gross-Pitaevskii and Ginzburg-Sobyanin) nonlinearities with respect to a condensate wavefunction, but also a non-polynomial logarithmic nonlinearity. We derive an equation of state and speed of sound in our model, and show their agreement with experiment.

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“…Furthermore, in the Madelung representation, the wave equation ( 2) can be written in hydrodynamic form; from which one can deduce the equation of state and related values [23]. If we assume that b does not contain the Planck constant in higher than the first power; then in the leading order approximation with respect to this constant, we can neglect the second derivatives of density.…”

Section: The Modelmentioning

confidence: 99%

Acoustic oscillations in cigar-shaped logarithmic Bose-Einstein condensate in the Thomas-Fermi approximation

Zloshchastiev

2022

Preprint

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We consider the dynamical properties of density fluctuations in the cigar-shaped Bose-Einstein condensate described by the logarithmic wave equation with a constant nonlinear coupling by using the Thomas-Fermi and linear approximations. It is shown that the propagation of small density fluctuations along the long axis of a condensed lump in a strongly anisotropic trap is essentially onedimensional, while the trapping potential can be disregarded in the linear regime. Depending on the sign of nonlinear coupling, the fluctuations either take the form of translationally symmetric pulses and standing waves, or become oscillations with varying amplitudes. We also study the condensate in an axial harmonic trap, by using elasticity theory's notions. Linear particle density and energy also behave differently depending on the nonlinear coupling's value. If it is negative, the density monotonously grows along with lump's radius, while energy is a monotonous function of density. For the positive coupling, the density is bound from above, whereas energy grows monotonously as a function of density until it reaches its global maximum.

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Matrix logarithmic wave equation and multi-channel systems in fluid mechanics

Cited by 9 publications

References 28 publications

An Alternative to Dark Matter and Dark Energy: Scale-Dependent Gravity in Superfluid Vacuum Theory

An Alternative to Dark Matter and Dark Energy: Scale-Dependent Gravity in Superfluid Vacuum Theory

Resolving the puzzle of sound propagation in liquid helium at low temperatures

Acoustic oscillations in cigar-shaped logarithmic Bose-Einstein condensate in the Thomas-Fermi approximation

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