A dynamical theory of thermalization in composite quantum systems

Osamu Fukushima

Nicole Yunger Halpern, Philippe Faist, Jonathan Oppenheim +1 more

The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented by operators that fail to commute. Whether such a system thermalizes and what form the thermal state has are questions about truly quantum thermodynamics. Here we investigate this thermal state from three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system-and-bath composite, tracing out the bath yields the system's thermal state. This state is expected to be the equilibrium point, we argue, of typical dynamics. Finally, we define a resource-theory model for thermodynamic exchanges of noncommuting observables. Complete passivity-the inability to extract work from equilibrium states-implies the thermal state's form, too. Our work opens new avenues into equilibrium in the presence of quantum noncommutation.

Marcos Rigol, Vanja Dunjko, Maxim Olshanii

Marzuq Yussif Etsie Adam Adam

We present a perturbative derivation of the generalized Langevin equation starting from a relativistic quantum field theory at finite temperature. Considering a complex scalar field coupled to a thermal mediator, we use a collective field formulation (Hubbard-Stratonovich transformation) to decouple the non-linear density constraint associated with a localized composite degree of freedom. By performing a saddle-point expansion and explicitly integrating out the collective fluctuations, we obtain the dynamic response kernel for the macroscopic center-of-mass coordinate. We show that localizing the density spontaneously breaks translational invariance, naturally generating a harmonic restoring force that results in an Ornstein-Uhlenbeck process. Furthermore, we resolve the vanishing friction paradox of the free-field limit by employing a resummed Dyson-Schwinger approach. We explicitly demonstrate that the thermal width of the dressed propagator generates finite Ohmic dissipation via Landau damping of the Källén-Lehmann spectral functions. This work provides a transparent, effective field theory bridge between microscopic thermal quantum fields and macroscopic open quantum systems.

Sheng-Wen Li, Da Xu, Xulin Liu +1 more

We study the thermalization of a composite quantum system consisting of several subsystems, where only a small one of the subsystem contacts with a heat bath in equilibrium, while the rest of the composite system is contact free. We show that the whole composite system still can be thermalized after a relaxation time long enough, if the energy level structure of the composite system is connected, which means any two energy levels of the composite system can be connected by direct or indirect quantum transitions. With an example where an multi-level system interacts with a set of harmonic oscillators via non-demolition coupling, we find that the speed of relaxation to the global thermal state is suppressed by the multi-Franck-Condon factor due to the displacements of the Fock states when the degrees of freedom is large.

HyungWon Kim, Mari Carmen Bañuls, David A. Huse +1 more