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This study analyzes quantum depletion in Bose-Einstein condensates at zero temperature. Researchers derived a formula for the generating function of quantum depletion and an upper bound for its tails.

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Area of Science:

  • Quantum physics
  • Condensed matter physics

Background:

  • Bose gases exhibit Bose-Einstein condensation at zero temperature.
  • The Gross-Pitaevskii regime describes weakly interacting Bose gases.
  • Quantum depletion refers to bosons outside the condensate.

Purpose of the Study:

  • To investigate quantum depletion in Bose-Einstein condensates.
  • To derive an asymptotic formula for the generating function of quantum depletion.
  • To establish an upper bound for the tails of quantum depletion.

Main Methods:

  • Analysis of a Bose gas on a unit torus at zero temperature.
  • Application of the Gross-Pitaevskii regime.
  • Derivation of asymptotic formulas.
  • Proof of upper bounds for probability distributions.

Main Results:

  • An explicit asymptotic formula for the generating function of quantum depletion was derived.
  • An upper bound for the tails of quantum depletion was proven.
  • The study provides quantitative insights into the non-condensate fraction.

Conclusions:

  • The derived formula and bound offer a deeper understanding of quantum depletion.
  • This research contributes to the theoretical framework of Bose-Einstein condensates.
  • The findings are relevant for systems exhibiting Bose-Einstein condensation.