Logarithmic Schr{ö}dinger equation with quadratic potential
arXiv:2106.02367 · doi:10.1088/1361-6544/ac3144
Abstract
We analyze dynamical properties of the logarithmic Schr{ö}dinger equation under a quadratic potential. The sign of the nonlinearity is such that it is known that in the absence of external potential, every solution is dispersive, with a universal asymptotic profile. The introduction of a harmonic potential generates solitary waves, corresponding to generalized Gaussons. We prove that they are orbitally stable, using an inequality related to relative entropy, which may be thought of as dual to the classical logarithmic Sobolev inequality. In the case of a partial confinement, we show a universal dispersive behavior for suitable marginals. For repulsive harmonic potentials, the dispersive rate is dictated by the potential, and no universal behavior must be expected.
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References in corpus (12)
- Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences
- Existence and Stability of standing waves for supercritical NLS with a Partial Confinement
- Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent
- Universal dynamics for the defocusing logarithmic Schrodinger equation
- Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory
- Error estimates of a regularized finite difference method for the logarithmic Schrödinger equation
- Scattering for nonlinear Schrodinger equation under partial harmonic confinement
- Orbital stability of Gausson solutions to logarithmic Schrödinger equations
- Stability of Logarithmic Bose-Einstein Condensate in Harmonic Trap
- A note on the nonlinear Schrödinger equation in a general domain
- The focusing logarithmic Schrödinger equation: analysis of breathers and nonlinear superposition
- Convergence rate in Wasserstein distance and semiclassical limit for the defocusing logarithmic Schr{ö}dinger equation
Cited by in corpus (4)
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- Logarithmic Gross-Pitaevskii equation
- Logarithmic Schrödinger Equations in Infinite Dimensions