Phase-space localization at the lowest Landau level
arXiv:2407.07675 · doi:10.1103/PhysRevA.110.063325
Abstract
We consider bosons with weak contact interactions in a harmonic trap and focus on states at the lowest Landau level. Motivated by the known nontrivial phase-space topography of the energy functional of the corresponding Gross-Pitaevskii equation, we explore Husimi distributions of quantum energy eigenstates in the classical phase space of the Schroedinger field. With interactions turned off, the energy levels are highly degenerate and the Husimi distributions do not manifest any particular localization properties. With interactions turned on, the degeneracy is lifted, and a selection of energy levels emerges whose Husimi distributions are localized around low-dimensional surfaces in the phase space.
v2: published version; MATLAB codes available at https://doi.org/10.5281/zenodo.12704876
References in corpus (26)
- Many-Body Physics with Ultracold Gases
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Exact Excited States of Non-Integrable Models
- Bose-Einstein Condensates with Large Number of Vortices
- The unitary gas in an isotropic harmonic trap: symmetry properties and applications
- Unified structure for exact towers of scar states in the AKLT and other models
- Vortex patterns in a fast rotating Bose-Einstein condensate
- Distinguishability, degeneracy and correlations in three harmonically trapped bosons in one-dimension
- Symmetries of Three Harmonically-Trapped Particles in One Dimension
- Ubiquitous quantum scarring does not prevent ergodicity
- Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates
- Genuine many-body quantum scars along unstable modes in Bose-Hubbard systems
- Quantum localization of chaotic eigenstates and the level spacing distribution
- On the Cubic Lowest Landau Level Equation
- Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap
- Dynamical quantum ergodicity from energy level statistics
- The two-body problem of ultra-cold atoms in a harmonic trap
- Exactly solvable model of two trapped quantum particles interacting via finite-range soft-core interactions
- Statistics of phase space localization measures and quantum chaos in the kicked top model
- Quantum resonant systems, integrable and chaotic
- Time-periodic quantum states of weakly interacting bosons in a harmonic trap
- Energy level splitting for weakly interacting bosons in a harmonic trap
- Harmonically Trapped Four-Boson System
- Identification of quantum scars via phase-space localization measures
- Breathing modes, quartic nonlinearities and effective resonant systems
- Time-periodicities in holographic CFTs