35 research outputs found
Quantum quench dynamics of the Luttinger model
The dynamics of the Luttinger model after a quantum quench is studied. We
compute in detail one and two-point correlation functions for two types of
quenches: from a non-interacting to an interacting Luttinger model and
vice-versa. In the former case, the non-interacting Fermi gas features in the
momentum distribution and other correlation functions are destroyed as time
evolves. In the infinite-time limit, equal-time correlations are power-laws but
the critical exponents are found to differ from their equilibrium values. In
all cases, we find that these correlations are well described by a generalized
Gibbs ensemble [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)], which
assigns a momentum dependent temperature to each eigenmode.Comment: 16 pages, 3 figure
Quantum quench dynamics of the sine-Gordon model in some solvable limits
With regard to the thermalization problem in isolated quantum systems, we investigate the dynamics following a quantum quench of the sineGordon model (sGM) in the Luther-Emery and the semiclassical limits. We consider the quench from the gapped to the gapless phase, as well as the reverse one. By obtaining analytic expressions for the one- and two-point correlation functions of the order parameter operator at zero-temperature, the manifestations of integrability in the absence of thermalization in the sGM are studied. It is shown that correlations in the long-time regime after the quench are well described by a generalized Gibbs ensemble. We also consider the case where the system is initially in contact with a reservoir at finite temperature. The possible relevance of our results to current and future experiments with ultracold atomic systems is also considered.Instituto de Física La Plat
Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasi-periodic optical lattices
We compute the absorption spectrum of strongly repulsive one-dimensional
bosons in a disordered or quasi-periodic optical lattice. At commensurate
filling, the particle-hole resonances of the Mott insulator are broadened as
the disorder strength is increased. In the non-commensurate case, mapping the
problem to the Anderson model allows us to study the Bose-glass phase.
Surprisingly we find that a perturbative treatment in both cases, weak and
strong disorder, gives a good description at all frequencies. In particular we
find that the infrared absorption rate in the thermodynamic limit is quadratic
in frequency. This result is unexpected, since for other quantities like the
conductivity in one dimensional systems, perturbation theory is only applicable
at high frequencies. We discuss applications to recent experiments on optical
lattice systems, and in particular the effect of the harmonic trap.Comment: 11 pages, 8 figure
Quantum quench dynamics of the sine-Gordon model in some solvable limits
With regard to the thermalization problem in isolated quantum systems, we investigate the dynamics following a quantum quench of the sineGordon model (sGM) in the Luther-Emery and the semiclassical limits. We consider the quench from the gapped to the gapless phase, as well as the reverse one. By obtaining analytic expressions for the one- and two-point correlation functions of the order parameter operator at zero-temperature, the manifestations of integrability in the absence of thermalization in the sGM are studied. It is shown that correlations in the long-time regime after the quench are well described by a generalized Gibbs ensemble. We also consider the case where the system is initially in contact with a reservoir at finite temperature. The possible relevance of our results to current and future experiments with ultracold atomic systems is also considered.Instituto de Física La Plat
Thermalization in systems with bipartite eigenmode entanglement
It is analytically shown that the asymptotic correlations following a quantum quench in exactly solvable models can sometimes look essentially thermal provided the initial coupling between the system eigenmodes induces a large gap. We study this phenomenon using simple models, which also illustrate the relationship between the entanglement spectrum of the initial state and the generalized Gibbs ensemble describing the long-time correlations after the quench. We also show that the effective temperature characterizing the correlations is not related to the energy fluctuations after the quench, and therefore does not have thermodynamic meaning. The latter observation implies a breakdown of the fluctuation-dissipation theorem.Instituto de Física La Plat
Quantum quench dynamics of the sine-Gordon model in some solvable limits
In connection with the the thermalization problem in isolated quantum
systems, we investigate the dynamics following a quantum quench of the
sine-Gordon model in the Luther-Emery and the semiclassical limits. We consider
the quench from the gapped to the gapless phase as well as reversed one. By
obtaining analytic expressions for the one and two-point correlation functions
of the order parameter operator at zero-temperature, the manifestations of
integrability in the absence of thermalization in the sine-Gordon model are
studied. It is thus shown that correlations in the long time regime after the
quench are well described by a generalized Gibbs ensemble. We also consider the
case where the system is initially in contact with a reservoir at finite
temperature. The possible relevance of our results to current and future
experiments with ultracold atomic systems is also critically considered.Comment: 21 pages, no figures. To appear in New J. Phys
Thermalization in systems with bipartite eigenmode entanglement
It is analytically shown that the asymptotic correlations following a quantum quench in exactly solvable models can sometimes look essentially thermal provided the initial coupling between the system eigenmodes induces a large gap. We study this phenomenon using simple models, which also illustrate the relationship between the entanglement spectrum of the initial state and the generalized Gibbs ensemble describing the long-time correlations after the quench. We also show that the effective temperature characterizing the correlations is not related to the energy fluctuations after the quench, and therefore does not have thermodynamic meaning. The latter observation implies a breakdown of the fluctuation-dissipation theorem.Instituto de Física La Plat
Quantum quench and prethermalization dynamics in a two-dimensional fermi gas with long-range interactions
We study the effect of suddenly turning on a long-range interaction in a spinless Fermi gas in two dimensions. The short- to intermediate-time dynamics is described using the method of bosonization of the Fermi surface. The space-time dependence of the nonequilibrium fermion density matrix as well as the evolution after the quench of the discontinuity at the Fermi momentum of the momentum distribution are computed. We find that the asymptotic state predicted by bosonization is consistent with the existence of a prethermalization plateau, which is also predicted by a perturbative approach in terms of the fermionic degrees of freedom. The bosonized representation, however, explicitly allows for the construction of the generalized Gibbs ensemble describing the prethermalized state.Instituto de Física La Plat