32 research outputs found
Quantum dynamical phase transition in a system with many-body interactions
We introduce a microscopic Hamiltonian model of a two level system with
many-body interactions with an environment whose excitation dynamics is fully
solved within the Keldysh formalism. If a particle starts in one of the states
of the isolated system, the return probability oscillates with the Rabi
frequency . For weak interactions with the environment
we find a slower oscillation whose
amplitude decays with a decoherence rate . However, beyond a finite critical interaction with the environment,
, the decoherence rate becomes
. The oscillation
period diverges showing a \emph{quantum dynamical phase transition}to a Quantum
Zeno phase.Comment: 5 pages, 3 figures, minor changes, fig.2 modified, added reference
Dynamical Origin of Decoherence in Clasically Chaotic Systems
The decay of the overlap between a wave packet evolved with a Hamiltonian H
and the same state evolved with H}+ serves as a measure of the
decoherence time . Recent experimental and analytical evidence on
classically chaotic systems suggest that, under certain conditions,
depends on H but not on . By solving numerically a
Hamiltonian model we find evidence of that property provided that the system
shows a Wigner-Dyson spectrum (which defines quantum chaos) and the
perturbation exceeds a crytical value defined by the parametric correlations of
the spectra.Comment: Typos corrected, published versio
Non-Markovian decay beyond the Fermi Golden Rule: Survival Collapse of the polarization in spin chains
The decay of a local spin excitation in an inhomogeneous spin chain is
evaluated exactly: I) It starts quadratically up to a spreading time t_{S}. II)
It follows an exponential behavior governed by a self-consistent Fermi Golden
Rule. III) At longer times, the exponential is overrun by an inverse power law
describing return processes governed by quantum diffusion. At this last
transition time t_{R} a survival collapse becomes possible, bringing the
polarization down by several orders of magnitude. We identify this strongly
destructive interference as an antiresonance in the time domain. These general
phenomena are suitable for observation through an NMR experiment.Comment: corrected versio
Survival Probability of a Local Excitation in a Non-Markovian Environment: Survival Collapse, Zeno and Anti-Zeno effects
The decay dynamics of a local excitation interacting with a non-Markovian
environment, modeled by a semi-infinite tight-binding chain, is exactly
evaluated. We identify distinctive regimes for the dynamics. Sequentially: (i)
early quadratic decay of the initial-state survival probability, up to a
spreading time , (ii) exponential decay described by a self-consistent
Fermi Golden Rule, and (iii) asymptotic behavior governed by quantum diffusion
through the return processes and leading to an inverse power law decay. At this
last cross-over time a survival collapse becomes possible. This could
reduce the survival probability by several orders of magnitude. The cross-overs
times and allow to assess the range of applicability of the
Fermi Golden Rule and give the conditions for the observation of the Zeno and
Anti-Zeno effect
Decoherence as Decay of the Loschmidt Echo in a Lorentz Gas
Classical chaotic dynamics is characterized by the exponential sensitivity to
initial conditions. Quantum mechanics, however, does not show this feature. We
consider instead the sensitivity of quantum evolution to perturbations in the
Hamiltonian. This is observed as an atenuation of the Loschmidt Echo, ,
i.e. the amount of the original state (wave packet of width ) which is
recovered after a time reversed evolution, in presence of a classically weak
perturbation. By considering a Lorentz gas of size , which for large is
a model for an {\it unbounded} classically chaotic system, we find numerical
evidence that, if the perturbation is within a certain range, decays
exponentially with a rate determined by the Lyapunov exponent
of the corresponding classical dynamics. This exponential decay
extends much beyond the Eherenfest time and saturates at a time
, where is the effective dimensionality of the Hilbert space. Since quantifies the increasing uncontrollability of the quantum phase
(decoherence) its characterization and control has fundamental interest.Comment: 3 ps figures, uses Revtex and epsfig. Major revision to the text, now
including discussion and references on averaging and Ehrenfest time. Figures
2 and 3 content and order change
Resonances in Fock Space: Optimization of a SASER device
We model the Fock space for the electronic resonant tunneling through a
double barrier including the coherent effects of the electron-phonon
interaction. The geometry is optimized to achieve the maximal optical phonon
emission required by a SASER (ultrasound emitter) device.Comment: 4 pages, 3 figures, to be published in Proceedings of the VI Latin
American Workshop on Nonlinear Phenomena, special issue of Physica
Sensitivity to perturbations in a quantum chaotic billiard
The Loschmidt echo (LE) measures the ability of a system to return to the
initial state after a forward quantum evolution followed by a backward
perturbed one. It has been conjectured that the echo of a classically chaotic
system decays exponentially, with a decay rate given by the minimum between the
width of the local density of states and the Lyapunov exponent. As the
perturbation strength is increased one obtains a cross-over between both
regimes. These predictions are based on situations where the Fermi Golden Rule
(FGR) is valid. By considering a paradigmatic fully chaotic system, the
Bunimovich stadium billiard, with a perturbation in a regime for which the FGR
manifestly does not work, we find a cross over from to Lyapunov decay.
We find that, challenging the analytic interpretation, these conjetures are
valid even beyond the expected range.Comment: Significantly revised version. To appear in Physical Review E Rapid
Communication
On general relation between quantum ergodicity and fidelity of quantum dynamics
General relation is derived which expresses the fidelity of quantum dynamics,
measuring the stability of time evolution to small static variation in the
hamiltonian, in terms of ergodicity of an observable generating the
perturbation as defined by its time correlation function. Fidelity for ergodic
dynamics is predicted to decay exponentially on time-scale proportional to
delta^(-2) where delta is the strength of perturbation, whereas faster,
typically gaussian decay on shorter time scale proportional to delta^(-1) is
predicted for integrable, or generally non-ergodic dynamics. This surprising
result is demonstrated in quantum Ising spin-1/2 chain periodically kicked with
a tilted magnetic field where we find finite parameter-space regions of
non-ergodic and non-integrable motion in thermodynamic limit.Comment: Slightly revised version, 4.5 RevTeX pages, 2 figure
Universality of the Lyapunov regime for the Loschmidt echo
The Loschmidt echo (LE) is a magnitude that measures the sensitivity of
quantum dynamics to perturbations in the Hamiltonian. For a certain regime of
the parameters, the LE decays exponentially with a rate given by the Lyapunov
exponent of the underlying classically chaotic system. We develop a
semiclassical theory, supported by numerical results in a Lorentz gas model,
which allows us to establish and characterize the universality of this Lyapunov
regime. In particular, the universality is evidenced by the semiclassical limit
of the Fermi wavelength going to zero, the behavior for times longer than
Ehrenfest time, the insensitivity with respect to the form of the perturbation
and the behavior of individual (non-averaged) initial conditions. Finally, by
elaborating a semiclassical approximation to the Wigner function, we are able
to distinguish between classical and quantum origin for the different terms of
the LE. This approach renders an understanding for the persistence of the
Lyapunov regime after the Ehrenfest time, as well as a reinterpretation of our
results in terms of the quantum--classical transition.Comment: 33 pages, 17 figures, uses Revtex