Quantum Bose liquids with logarithmic nonlinearity: self-sustainability and emergence of spatial extent

@article{Avdeenkov2011QuantumBL,
  title={Quantum Bose liquids with logarithmic nonlinearity: self-sustainability and emergence of spatial extent},
  author={Alexander V. Avdeenkov and Konstantin G. Zloshchastiev},
  journal={Journal of Physics B},
  year={2011},
  volume={44},
  pages={195303}
}
The Gross–Pitaevskii (GP) equation is a long-wavelength approach widely used to describe the dilute Bose–Einstein condensates (BEC). However, in many physical situations, such as higher densities, it is unlikely that this approximation suffices; hence, one might need models which would account for long-range correlations and multi-body interactions. We show that the Bose liquid described by the logarithmic wave equation has a number of drastic differences from the GP one. It possesses the self… Expand

Figures from this paper

Temperature-driven dynamics of quantum liquids: Logarithmic nonlinearity, phase structure and rising force
We study a large class of strongly interacting condensate-like materials, which can be characterized by a normalizable complex-valued function. A quantum wave equation with logarithmic nonlinearityExpand
Stability and Metastability of Trapless Bose-Einstein Condensates and Quantum Liquids
Abstract Various kinds of Bose-Einstein condensates are considered, which evolve without any geometric constraints or external trap potentials including gravitational. For studies of their collectiveExpand
Stability of Logarithmic Bose-Einstein Condensate in Harmonic Trap
In this paper we investigate the stability of a recently introduced Bose-Einstein condensate (BEC) which involves logarithmic interaction between atoms. The Gaussian variational approach is employedExpand
Freezing of soft-core bosons at zero temperature: A variational theory
The properties of a macroscopic assembly of weakly-repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits aExpand
Time-varying Bose–Einstein condensates
Bose–Einstein condensates (BECs), a state of matter formed when a low-density gas of bosons is cooled to near absolute zero, continue to motivate novel work in theoretical and experimental physics.Expand
Schrödinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels
TLDR
Two elementary single-channel versions of the nonlinear logarithmic Schrodinger model are 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, and the new role played by PT -symmetry is revealed. Expand
Nonlinear Quantum Search
Author(s): Wong, Thomas Giechaung | Abstract: Although quantum mechanics is linear, there are nevertheless quantum systems with multiple interacting particles in which the effective evolution of aExpand
Modeling and computation of Bose-Einstein condensates: stationary states, nucleation, dynamics, stochasticity
The aim of this chapter is first to give an introduction to the derivation of the Gross-Pitaevskii Equations (GPEs) that arise in the modeling of Bose-Einstein Condensates (BECs). In particular, weExpand
Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systems
We compare two approaches to open quantum systems, namely, the non-Hermitian dynamics and the Lindblad master equation. In order to deal with more general dissipative phenomena, we propose theExpand
Resolving cosmological singularity problem in logarithmic superfluid theory of physical vacuum
Recently proposed statistical mechanics arguments [1] and previously known Madelung hydrodynamical presentation of condensate functions [2] have revealed that the quantum liquids with logarithmicExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 64 REFERENCES
Analogue gravity from Bose-Einstein condensates
We analyse prospects for the use of Bose–Einstein condensates as condensedmatter systems suitable for generating a generic ‘effective metric’, and for mimicking kinematic aspects of generalExpand
Low-dimensional bose liquids: beyond the gross-pitaevskii approximation
The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that forExpand
Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory
Our primary task is to demonstrate that the logarithmic nonlinearity in the quantum wave equation can cause the spontaneous symmetry breaking and mass generation phenomena on its own, at least inExpand
Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences
Starting from a generic generally covariant quantum theory, we introduce a logarithmic correction to the quantum wave equation. We demonstrate the emergence of evolution time from the group ofExpand
Theory of Bose-Einstein condensation in trapped gases
The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of theExpand
Nonlinear Ginzburg-Landau-type approach to quantum dissipation.
  • J. López
  • Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
We formally derive two nonlinear Ginzburg-Landau type models starting from the Wigner-Fokker-Planck system, which rules the evolution of a quantum electron gas interacting with a heat bath inExpand
Application of the nonlinear Schrödinger equation with a logarithmic inhomogeneous term to nuclear physics.
  • Hefter
  • Physics, Medicine
  • Physical review. A, General physics
  • 1985
TLDR
It is pointed out that the different length scales a associated with atomic and nuclear physics, for example, lead to different typical energies b for these systems, which necessitates the interpretation of the respective NLSE as an equation for extended objects as well as the prediction 130< or =K < or =250 MeV. Expand
Effective wave equations for the dynamics of cigar-shaped and disk-shaped Bose condensates
Starting from the three-dimensional (3D) Gross-Pitaevskii equation and using a variational approach, we derive an effective 1D wave equation that describes the axial dynamics of a Bose condensateExpand
Dilute quantum droplets.
  • A. Bulgac
  • Physics, Medicine
  • Physical review letters
  • 2002
TLDR
Under these conditions both Bose-Einstein and Fermi-Dirac systems could become self-bound and either boson droplets or fermion "designer nuclei" of various sizes and densities could be manufactured. Expand
Vacuum Cherenkov effect in logarithmic nonlinear quantum theory
Abstract We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics – cone angle, flash duration,Expand
...
1
2
3
4
5
...