Bose-Einstein condensation on hyperbolic spaces
arXiv:2202.01538 · doi:10.1063/5.0088383
Abstract
A well-known conjecture in mathematical physics asserts that the interacting Bose gas exhibits Bose-Einstein condensation (BEC) in the thermodynamic limit. We consider the Bose gas on certain hyperbolic spaces. In this setting, one obtains a short proof of BEC in the infinite-volume limit from the existence of a volume-independent spectral gap of the Laplacian.
arXiv comment27 pages, v1->v2: minor changes and added references
References in corpus (28)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Quantum Simulators: Architectures and Opportunities
- Proof of Bose-Einstein Condensation for Dilute Trapped Gases
- Hyperbolic Lattices in Circuit Quantum Electrodynamics
- Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases
- Ground State Energy of the Low Density Bose Gas
- Quantum Simulation of Coherent Hawking-Unruh Radiation
- The Second Order Upper Bound for the Ground Energy of a Bose Gas
- Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry
- Hyperbolic band theory
- Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics
- Bose-Einstein Quantum Phase Transition in an Optical Lattice Model
- Gross-Pitaevskii Theory of the Rotating Bose Gas
- Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime
- Ground states of large bosonic systems: The gross-pitaevskii limit revisited
- Universality of Hofstadter butterflies on hyperbolic lattices
- Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
- Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
- Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
- Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
- Quantum phase transitions of interacting bosons on hyperbolic lattices
- Random hyperbolic surfaces of large genus have first eigenvalues greater than
- Hyperbolic Bloch equations: atom-cluster kinetics of an interacting Bose gas
- Another proof of BEC in the GP-limit
- Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature
- The Second Order Correction to the Ground State Energy of the Dilute Bose Gas
- On Bose-Einstein condensates in the Thomas-Fermi regime
- Bose-Einstein condensation of scalar fields on hyperbolic manifolds