Feynman cycles in the Bose gas

Abstract

We study the lengths of the cycles formed by trajectories in the Feynman-Kac representation of the Bose gas. We discuss the occurrence of infinite cycles and their relation to Bose-Einstein condensation.

17 pages

References in corpus (5)

• Percolation transition in the Bose gas II
• Large deviations for ideal quantum systems
• The Canonical Perfect Bose Gas in Casimir Boxes
• Long Cycles in a Perturbed Mean Field Model of a Boson Gas
• The relation between Feynman cycles and off-diagonal long-range order

Cited by in corpus (13)

• Many-Body Physics with Ultracold Gases
• Spatial random permutations and infinite cycles
• Rigorous Upper Bound on the Critical Temperature of Dilute Bose Gases
• Critical Temperature of Dilute Bose Gases
• A path-integral analysis of interacting Bose gases and loop gases
• Macroscopic loops in the Bose gas, Spin O(N) and related models
• Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas
• Scaling approach to existence of long cycles in Casimir boxes
• Formation of infinite loops for an interacting bosonic loop soup
• Emergence of interlacements from the finite volume Bose soup
• Long Cycles in the Infinite-Range-Hopping Bose-Hubbard Model with Hard Cores
• Off-diagonal long-range order for the free Bose gas via the Feynman--Kac formula
• Infinite cycles of interacting bosons