Thermalization of Isolated Bose‐Einstein Condensates by Dynamical Heat Bath Generation

Abstract

If and how an isolated quantum system thermalizes despite its unitary time evolution is a long-standing, open problem of many-body physics. The eigenstate thermalization hypothesis (ETH) postulates that thermalization happens at the level of individual eigenstates of a system's Hamiltonian. However, the ETH requires stringent conditions to be validated, and it does not address how the thermal state is reached dynamically from an initial non-equilibrium state. We consider a Bose-Einstein condensate (BEC) trapped in a double-well potential with an initial population imbalance. We find that the system thermalizes although the initial conditions violate the ETH requirements. We identify three dynamical regimes. After an initial regime of undamped Josephson oscillations, the subsystem of incoherent excitations or quasiparticles (QP) becomes strongly coupled to the BEC subsystem by means of a dynamically generated, parametric resonance. When the energy stored in the QP system reaches its maximum, the number of QPs becomes effectively constant, and the system enters a quasi-hydrodynamic regime where the two subsystems are weakly coupled. In this final regime the BEC acts as a grand-canonical heat reservoir for the QP system (and vice versa), resulting in thermalization. We term this mechanism dynamical bath generation (DBG).

Theory of thermalization in an isolated Bose-Einstein condensate

“…In other words, during the process of thermalization, condensed and thermal particles act as mutual heat bath and help each other achieve equilibrium. The mechanism is similar to the one proposed in a many-body theory of Posazhennikova et al [10,11] who considered quantum tunneling of a binary system with a central barrier.…”

“…The thermalization time t th ≃ 40 and 200 in case (a) and (b), respectively. The black dotted lines correspond to the microcanonical S M given in (10). To see the effect of LHY quantum correction, in Fig.…”

Expansion dynamics in two-dimensional Bose-Hubbard lattices: Bose-Einstein condensate and thermal cloud

“…However, previous studies of the quench dynamics of Bose-Josephson junctions (BJJ) [10][11][12][13][14] showed that incoherent fluctuations become inevitably excitated after the quench even in gapped systems, due to the finite spectral distribution involved in the temporal evolution. The coupling of the BEC to these incoherent excitations plays an important role in the relaxation and thermalization dynamics [12][13][14].…”

“…However, previous studies of the quench dynamics of Bose-Josephson junctions (BJJ) [10][11][12][13][14] showed that incoherent fluctuations become inevitably excitated after the quench even in gapped systems, due to the finite spectral distribution involved in the temporal evolution. The coupling of the BEC to these incoherent excitations plays an important role in the relaxation and thermalization dynamics [12][13][14]. Exact numerical calculations of the expansion dynamics are possible only in one dimension [4,15], where true Bose-Einstein condensation does not occur and, hence, a distinction between BEC and incoherent excitations is not possible in the time-dependent situation.…”

“…To tackle the problem of the expansion of the coupled system of BEC and incoherent fluctuations we, therefore, adopt the semianalytical formalism developed earlier and applied for studies of nonequilibrium BJJs [10,12,13]. Our approach goes beyond mean-field approximations and systematically takes into account incoherent excitations.…”