Fr\"ohlich Condensation of Bosons: Graph texture of curl flux network for nonequilibrium properties

Feihong Liu; Chase Slowey; Xuanhua Wang; Dangyuan Lei; Jeremie Torres; Zhiyue Lu; Zhedong Zhang

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arXiv · 2506.00792

Fr\"ohlich Condensation of Bosons: Graph texture of curl flux network for nonequilibrium properties

Feihong Liu·Chase Slowey·Xuanhua Wang·Dangyuan Lei·Jeremie Torres·Zhiyue Lu·Zhedong Zhang

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Abstract

Nonequilibrium condensates of bosons subject to energy pump and dissipation are investigated, manifesting the Fr\"ohlich coherence proposed in 1968. A quantum theory is developed to capture such a nonequilibrium nature, yielding a certain graphic structure arising from the detailed-balance breaking. The results show a network of probability curl fluxes that reveals a graph topology. The winding number associated with the flux network is thus identified as a new order parameter for the phase transition towards the Fr\"ohlich condensation (FC), not attainable by the symmetry breaking. Our work demonstrates a global property of the FCs, in significant conjunction with the coherence of cavity polaritons that may exhibit robust cooperative phases driven far from equilibrium.

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Feihong Liu, Chase Slowey, Xuanhua Wang, Dangyuan Lei, Jeremie Torres, Zhiyue Lu, Zhedong Zhang. 2025-06-01. Fr\"ohlich Condensation of Bosons: Graph texture of curl flux network for nonequilibrium properties. https://arxiv.org/abs/2506.00792

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