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arXiv:cond-mat/0310304 · Few-Body Systems

Condensates and Correlated Boson Systems

O. S�rensen, D. V. Fedorov, A. S. Jensen

Published May 1, 2004• 0 citations
arXivHTMLPDF
DOI
10.1007/s00601-004-0040-8

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Magnon condensation, which emerges in pumped bosonic systems at room temperature, continues to garner great interest for its long-lived coherence. While traditionally formulated in terms of Bose-Einstein condensation, which typically occurs at ultralow temperatures, it could potentially also be explained by Fröhlich condensation, a hypothesis of Bose-Einstein-like condensation in living systems at ambient temperatures. This prompts general questions relating to fundamental differences between coherence phenomena in open and isolated quantum systems. To that end, we introduce a simple model of bosonic condensation in an open quantum system (OQS) formulation, wherein bosons dissipatively interact with an oscillator (phonon) bath. Our derived equations of motion for expected boson occupations turn out to be similar in form to the rate equations governing Fröhlich condensation. Provided that specific system parameters result in correlations that amplify or diminish the condensation effects, we thereby posit that our treatment offers a better description of high-temperature condensation compared to traditional formulations obtained using equilibrium thermodynamics. By comparing our OQS derivation with the original uncorrelated and previous semiclassical rate equations, we furthermore highlight how both classical anticorrelations and quantum correlations alter the bosonic occupation distribution.
We review the properties of chaoticity and coherence in Bose-Einstein condensation and correlations, for a dense boson system in its mean-field represented approximately by a harmonic oscillator potential. The order parameter and the nature of the phase transition from the chaotic to the condensate states are studied for different fixed numbers of bosons. The two-particle correlation function in momentum space is calculated to investigate how the Bose-Einstein correlation depends on the degree of condensation and other momentum variables. We generalize the Bose-Einstein correlation analysis to three-particle correlations to show its dependence on the degree of condensation.
A theory of inhomogeneous boson systems is developed which takes into account both the single-particle condensate and pair correlations. A set of three coupled nonlinear integrodifferential equations is derived for the condensate wavefunction and the two Bogoliubov quasiparticle wavefunctions. Half-integral h/m circulation can exist only when the single-particle condensate is completely depleted. General considerations of off-diagonal long-range order and circulation quantization also lead to this conclusion.