300 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 Coulomb Luttinger model
We study the non-equilibrium dynamics of the Luttinger model after suddenly
turning on and off the bare Coulomb interaction between the fermions. We
analyze several correlation functions such as the one particle density matrix
and vertex correlations, its finite time dynamics and the stationary state
limit. Correlations exhibit a non-linear light cone effect: the spreading of
the initial signal accelerates as a consequence of the quantum nature of the
excitations, whose peculiar dispersion of plasmonic type in 1D gives rise to a
logarithmic divergence in the group velocity at . In addition we show that
both the static and dynamic stationary state correlations can be reproduced
with a simple generalised Gibbs ensemble despite the long-range character of
the interactions which precludes the application of the Lieb-Robinson bounds.
We propose a suitable experimental setup in which these effect can be observed
based on ultracold ions loaded on linear traps.Comment: 13 pages, 7 figure
Equations of Motion for the Out-of-Equilibrium Dynamics of Isolated Quantum Systems from the Projection Operator Technique
We present a rigorous framework to obtain evolution equations for the
momentum distribution and higher order correlation functions in weakly
interacting systems based on the Projection Operator Technique. These equations
can be numerically solved in an efficient way. We compare the solution of the
equations with known results for 1D models and find an excellent agreement.Comment: 6 pages, 1 figure, added brief discussion about the validity of the
approximation
Thermalization and Quantum Correlations in Exactly Solvable Models
The generalized Gibbs ensemble introduced for describing few body
correlations in exactly solvable systems following a quantum quench is related
to the nonergodic way in which operators sample, in the limit of infinite time
after the quench, the quantum correlations present in the initial state. The
nonergodicity of the correlations is thus shown \emph{analytically} to imply
the equivalence with the generalized Gibbs ensemble for quantum Ising and
XX spin chains as well as for the Luttinger model the thermodynamic limit,
and for a broad class of initial states and correlation functions of both local
and nonlocal operators.Comment: 12 pages, 4 figures. Expanded in response to Referee criticis
Fourier transform of the 2kF Luttinger liquid density correlation function with different spin and charge velocities
We obtain a closed-form analytical expression for the zero-temperature Fourier transform of the 2kF component of the density-density correlation function in a Luttinger liquid with different spin and charge velocities. For frequencies near the spin and charge singularities, approximate analytical forms are given and compared with the exact result. We find power-law-like singularities leading to either divergence or cusps, depending on the values of the Luttinger parameters, and compute the corresponding exponents. Exact integral expressions and numerical results are given for the finite-temperature case as well. We show, in particular, how the temperature rounds the singularities in the correlation function
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 FÃsica La Plat
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