Relaxation dynamics of an exactly solvable electron-phonon model
arXiv:1006.0927 · doi:10.1103/PhysRevB.82.085109
Abstract
We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a stationary density matrix. Two initial nonequilibrium situations are considered. A sudden quench of the electron-phonon coupling, starting from the noninteracting canonical equilibrium at temperature T in the electron as well as in the phonon subsystems, leads to a rather simple dynamics. A richer time evolution emerges if the initial state is taken as the product of the phonon vacuum and the filled Fermi sea supplemented by a highly excited additional electron. Our model has a natural set of constants of motion, with as many elements as degrees of freedom. In accordance with earlier studies of such type of models we find that expectation values which become stationary can be described by the density matrix of a generalized Gibbs ensemble which differs from that of a canonical ensemble. For the model at hand it appears to be evident that the eigenmode occupancy operators should be used in the construction of the stationary density matrix.
15 pages, 11 figures, published version
References in corpus (16)
- Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
- Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
- Breakdown of thermalization in finite one-dimensional systems
- The Luttinger model following a sudden interaction switch-on
- Interaction Quench in the Hubbard model
- Exact relaxation in a class of non-equilibrium quantum lattice systems
- Dephasing and the steady state in quantum many-particle systems
- Strongly correlated fermions after a quantum quench
- Quantum quench dynamics of the Luttinger model
- Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
- Nonthermal steady states after an interaction quench in the Falicov-Kimball model
- Relaxation of a one-dimensional Mott insulator after an interaction quench
- Exploring local quantum many-body relaxation by atoms in optical superlattices
- Correlations in an expanding gas of hard-core bosons
- Unitary perturbation theory approach to real-time evolution problems
- Time-dependent evolution of two coupled Luttinger liquids