The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime
Cristina Caraci, Serena Cenatiempo, Benjamin Schlein
Abstract
Abstract We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in N (Gross–Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit $$N \rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>→</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> .
Topics & Concepts
BosonTorusPhysicsExcitationBose gasSpectrum (functional analysis)Gross–Pitaevskii equationGround stateOperator (biology)Quantum mechanicsLimit (mathematics)Scattering lengthUnit (ring theory)ScatteringQuantum electrodynamicsBose–Einstein condensateMathematicsMathematical analysisGeometryChemistryMathematics educationRepressorBiochemistryTranscription factorGeneCold Atom Physics and Bose-Einstein CondensatesPhysics of Superconductivity and MagnetismQuantum, superfluid, helium dynamics