Stability of logarithmic Bose–Einstein condensate in harmonic trap

Bouharia, B.

doi:10.1142/s0217984914502601

Cited by 22 publications

(21 citation statements)

References 32 publications

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“…It was also demonstrated, using different methods, that logarithmic quantum fluids are stable against small perturbations [9,13]. This stability is an important ingredient for justifying an actual physical existence of such fluids.…”

Section: Introductionmentioning

confidence: 93%

Singularity-free model of electrically charged fermionic particles and gauged Q -balls

Dzhunushaliev

Makhmudov²,

Zloshchastiev

2016

Phys. Rev. D

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We propose a model of an electrically charged fermion as a regular localized solution of electromagnetic and spinor fields interacting with a physical vacuum, which is phenomenologically described as a logarithmic superfluid. We analytically study the asymptotic behavior of the solution, while obtaining its form by numerical methods. The solution has physically plausible properties, such as finite size, self-energy, total charge and mass. In the case of spherical symmetry, its electric field obeys the Coulomb asymptotics at large distances from its core. It is shown that the observable rest mass of the fermion arises as a result of interaction of the fields with the physical vacuum. The spinor and scalar field components of the solution decay exponentially outside the core; therefore they can be regarded as internal degrees of freedom which can only be probed at sufficiently large scales of energy and momentum. Apart from conventional Fermi particles, our model can find applications in a theory of exotic localized objects, such as U (1) gauged Q-balls with half-integer spin.

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Section: Introductionmentioning

confidence: 93%

Singularity-free model of electrically charged fermionic particles and gauged Q -balls

Dzhunushaliev

Makhmudov²,

Zloshchastiev

2016

Phys. Rev. D

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“…One of the best known examples is provided by [16,17] in which the toy models are considered in the form of the nonlinear logarithmic Schrödinger Equation (5) with the wave-function solutions ψ ∈ L 2 ( d ) studied in an interval of time t ∈ (t 0 , t 1 ). This equation, along with its relativistic analogue, finds multiple applications in the physics of quantum fields and particles [49][50][51][52][53][54][55], extensions of quantum mechanics [16,56], optics and transport or diffusion phenomena [57][58][59][60], nuclear physics [61,62], the theory of dissipative systems and quantum information [63][64][65][66][67][68], the theory of superfluidity [69][70][71][72] and the effective models of the physical vacuum and classical and quantum gravity [73][74][75][76], where one can utilize the well-known fluid/gravity analogy between inviscid fluids and pseudo-Riemannian manifolds [77][78][79][80][81]. The relativistic analogue of Equation (5) is obtained by replacing the derivative part with the d'Alembert operator and is not considered here.…”

Section: Broader Context In Physicsmentioning

confidence: 99%

“…Firstly, although the experimental tests as performed for conserved systems in atomic physics excluded any quantitatively predictive implementation of the "effective nonlinearity" hypothesis of the logarithmic type, the reality-mimicking situation appeared perceivably more encouraging in nuclear-physics phenomenology where the spatial separation of the individual fermions may be expected to be reduced [61,62], as well as in a theory of superfluidity, where many-body interactions become strongly nonlinear with an increase of density [69][70][71][72]. The appealing possibility of making quantum theory slightly nonlinear survived as a challenging theoretical option.…”

Section: Roots In Phenomenologymentioning

confidence: 99%

Schrödinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

2017

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Schrödinger equations with non-Hermitian, but P T -symmetric quantum potentials V(x) found, recently, a new field of applicability in classical optics. The potential acquired there a new physical role of an "anomalous" refraction index. This turned attention to the nonlinear Schrödinger equations in which the interaction term becomes state-dependent, V(x) → W(ψ(x), x). Here, the state-dependence in W(ψ(x), x) is assumed logarithmic, and some of the necessary mathematical assumptions, as well as some of the potential phenomenological consequences of this choice are described. Firstly, an elementary single-channel version of the nonlinear logarithmic model is outlined in which the complex self-interaction W(ψ(x), x) is regularized via a deformation of the real line of x into a self-consistently constructed complex contour C. The new role played by P T -symmetry is revealed. Secondly, the regularization is sought for a multiplet of equations, coupled via the same nonlinear self-interaction coupling of channels. The resulting mathematical structures are shown to extend the existing range of physics covered by the logarithmic Schrödinger equations.

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“…Wave equations with logarithmic nonlinearity began to gain a considerable interest among physicists since works by Rosen (1968) and Bialynicki-Birula and Mycielski (1976). The corresponding models have been proven to be instrumental in dealing with physics of quantum fields and particles (Rosen, 1968;Rosen, 1969;Bialynicki-Birula and Mycielski, 1979;Zloshchastiev, 2010;Zloshchastiev, 2011) nonlinear generalizations of quantum mechanics (Bialynicki-Birula and Mycielski, 1976) optics and transport or diffusion phenomena, nuclear physics, theory of dissipative systems and quantum information (Yasue, 1978;Brasher, 1991;Znojil et al, 2017, Zloshchastiev, 2018a, theory of quantum liquids and superfluidity (Zloshchastiev, 2011;Avdeenkov and Zloshchastiev, 2011;Zloshchastiev, 2012;Bouharia, 2015;Zloshchastiev, 2017) and theory of physical vacuum and classical and quantum gravity. (Zloshchastiev, 2010;Zloshchastiev, 2011;Scott et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

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

Zloshchastiev¹

2019

Journal of Theoretical and Applied Mechanics

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We formulate the mapping between a large class of nonlinear wave equations and flow equations for barotropic fluid with internal surface tension and capillary effects. Motivated by statistical mechanics and multi-channel physics arguments, we focus on wave equations with logarithmic nonlinearity, and further generalize them to matrix equations. We map the resulting equation to flow equations of multi-channel or multi-component Korteweg-type materials. For some special cases, we analytically derive Gaussian-type matrix solutions and study them in the context of fluid mechanics.

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Stability of logarithmic Bose–Einstein condensate in harmonic trap

Cited by 22 publications

References 32 publications

Singularity-free model of electrically charged fermionic particles and gauged Q -balls

Singularity-free model of electrically charged fermionic particles and gauged Q -balls

Schrödinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

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

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