Thermal Relaxation of a QED Cavity

Abstract

Abstract. We study repeated interactions of the quantized electromagnetic field in a cavity with single two-levels atoms. Using the Markovian nature of the resulting quantum evolution we study its large time asymptotics. We show that, whenever the atoms are distributed according to the canonical ensemble at temperature T > 0 and some generic non-degeneracy condition is satisfied, the cavity field relaxes towards some invariant state. Under some more stringent non-resonance condition, this invariant state is thermal equilibrium at some renormalized temperature T * . Our result is non-perturbative in the strength of the atom-field coupling. The relaxation process is slow (non-exponential) due to the presence of infinitely many metastable states of the cavity field.

Scattering induced current in a tight-binding band

“…Thermalization of the field through repeated interaction with two-level atoms was proven for the Jaynes-Cummings Hamiltonian in Ref. 6. The model treated here is very similar to the one studied in Ref.…”

Quantum repeated interactions and the chaos game

“…For all other w value, we propose the following strategy. Starting from equation (26), changing the variable x → 1 − x and using the Taylor expansion ln(1 − x) = − ∞ n=1 x n /n one can express S * as a sum over all moments x n (which recursively can be calculated exactly using (22)):…”

Discrete Approximation of the Free Fock Space

“…These results have found many interesting applications and developments in quantum statistical mechanics, for they furnished a way to obtain quantum Langevin equations describing the dissipation of open quantum systems as a continuous-time limit of basic Hamiltonian interactions of the system with the environment: repeated quantum interactions (cf [4,7,8] for example).…”

“…Brownian motion, Poisson processes, ...), one recovers well-known approximations of these processes by random walks. This means that these different probabilistic situations and approximations are all encoded by the approximation of the three basic quantum noises: creation, annihilation and second quantization operators.These results have found many interesting applications and developments in quantum statistical mechanics, for they furnished a way to obtain quantum Langevin equations describing the dissipation of open quantum systems as a continuous-time limit of basic Hamiltonian interactions of the system with the environment: repeated quantum interactions (cf [4,7,8] for example).When considering the fermionic Fock space, even if it has not been written anywhere, it is easy to show that a similar structure holds, after a Jordan-Wigner transform on the spin-chain.2000 Mathematics Subject Classification. Primary 46L54.…”