522 research outputs found
Explicit solution of the Lindblad equation for nearly isotropic boundary driven XY spin 1/2 chain
Explicit solution for the 2-point correlation function in a non-equilibrium
steady state of a nearly isotropic boundary-driven open XY spin 1/2 chain in
the Lindblad formulation is provided. A non-equilibrium quantum phase
transition from exponentially decaying correlations to long-range order is
discussed analytically. In the regime of long-range order a new phenomenon of
correlation resonances is reported, where the correlation response of the
system is unusually high for certain discrete values of the external bulk
parameter, e.g. the magnetic field.Comment: 20 Pages, 5 figure
Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
We calculate a nonequilibrium steady state of a quantum XX chain in the
presence of dephasing and driving due to baths at chain ends. The obtained
state is exact in the limit of weak driving while the expressions for one- and
two-point correlations are exact for an arbitrary driving strength. In the
steady state the magnetization profile and the spin current display diffusive
behavior. Spin-spin correlation function on the other hand has long-range
correlations which though decay to zero in either the thermodynamical limit or
for equilibrium driving. At zero dephasing a nonequilibrium phase transition
occurs from a ballistic transport having short-range correlations to a
diffusive transport with long-range correlations.Comment: 5 page
Berry-Robnik level statistics in a smooth billiard system
Berry-Robnik level spacing distribution is demonstrated clearly in a generic
quantized plane billiard for the first time. However, this ultimate
semi-classical distribution is found to be valid only for extremely small
semi-classical parameter (effective Planck's constant) where the assumption of
statistical independence of regular and irregular levels is achieved. For
sufficiently larger semiclassical parameter we find (fractional power-law)
level repulsion with phenomenological Brody distribution providing an adequate
global fit.Comment: 10 pages in LaTeX with 4 eps figures include
Regular and Irregular States in Generic Systems
In this work we present the results of a numerical and semiclassical analysis
of high lying states in a Hamiltonian system, whose classical mechanics is of a
generic, mixed type, where the energy surface is split into regions of regular
and chaotic motion. As predicted by the principle of uniform semiclassical
condensation (PUSC), when the effective tends to 0, each state can be
classified as regular or irregular. We were able to semiclassically reproduce
individual regular states by the EBK torus quantization, for which we devise a
new approach, while for the irregular ones we found the semiclassical
prediction of their autocorrelation function, in a good agreement with
numerics. We also looked at the low lying states to better understand the onset
of semiclassical behaviour.Comment: 25 pages, 14 figures (as .GIF files), high quality figures available
upon reques
Stability of quantum motion and correlation decay
We derive a simple and general relation between the fidelity of quantum
motion, characterizing the stability of quantum dynamics with respect to
arbitrary static perturbation of the unitary evolution propagator, and the
integrated time auto-correlation function of the generator of perturbation.
Surprisingly, this relation predicts the slower decay of fidelity the faster
decay of correlations is. In particular, for non-ergodic and non-mixing
dynamics, where asymptotic decay of correlations is absent, a qualitatively
different and faster decay of fidelity is predicted on a time scale 1/delta as
opposed to mixing dynamics where the fidelity is found to decay exponentially
on a time-scale 1/delta^2, where delta is a strength of perturbation. A
detailed discussion of a semi-classical regime of small effective values of
Planck constant is given where classical correlation functions can be used to
predict quantum fidelity decay. Note that the correct and intuitively expected
classical stability behavior is recovered in the classical limit hbar->0, as
the two limits delta->0 and hbar->0 do not commute. In addition we also discuss
non-trivial dependence on the number of degrees of freedom. All the theoretical
results are clearly demonstrated numerically on a celebrated example of a
quantized kicked top.Comment: 32 pages, 10 EPS figures and 2 color PS figures. Higher resolution
color figures can be obtained from authors; minor changes, to appear in
J.Phys.A (March 2002
Quantum freeze of fidelity decay for chaotic dynamics
We show that the mechanism of quantum freeze of fidelity decay for
perturbations with zero time-average, recently discovered for a specific case
of integrable dynamics [New J. Phys. 5 (2003) 109], can be generalized to
arbitrary quantum dynamics. We work out explicitly the case of chaotic
classical counterpart, for which we find semi-classical expressions for the
value and the range of the plateau of fidelity. After the plateau ends, we find
explicit expressions for the asymptotic decay, which can be exponential or
Gaussian depending on the ratio of the Heisenberg time to the decay time.
Arbitrary initial states can be considered, e.g. we discuss coherent states and
random states.Comment: 4 pages, 3 ps figures ; v2 corrected mistake in formula for t_
Separating the regular and irregular energy levels and their statistics in Hamiltonian system with mixed classical dynamics
We look at the high-lying eigenstates (from the 10,001st to the 13,000th) in
the Robnik billiard (defined as a quadratic conformal map of the unit disk)
with the shape parameter . All the 3,000 eigenstates have been
numerically calculated and examined in the configuration space and in the phase
space which - in comparison with the classical phase space - enabled a clear
cut classification of energy levels into regular and irregular. This is the
first successful separation of energy levels based on purely dynamical rather
than special geometrical symmetry properties. We calculate the fractional
measure of regular levels as which is in remarkable
agreement with the classical estimate . This finding
confirms the Percival's (1973) classification scheme, the assumption in
Berry-Robnik (1984) theory and the rigorous result by Lazutkin (1981,1991). The
regular levels obey the Poissonian statistics quite well whereas the irregular
sequence exhibits the fractional power law level repulsion and globally
Brody-like statistics with . This is due to the strong
localization of irregular eigenstates in the classically chaotic regions.
Therefore in the entire spectrum we see that the Berry-Robnik regime is not yet
fully established so that the level spacing distribution is correctly captured
by the Berry-Robnik-Brody distribution (Prosen and Robnik 1994).Comment: 20 pages, file in plain LaTeX, 7 figures upon request submitted to J.
Phys. A. Math. Gen. in December 199
High order non-unitary split-step decomposition of unitary operators
We propose a high order numerical decomposition of exponentials of hermitean
operators in terms of a product of exponentials of simple terms, following an
idea which has been pioneered by M. Suzuki, however implementing it for complex
coefficients. We outline a convenient fourth order formula which can be written
compactly for arbitrary number of noncommuting terms in the Hamiltonian and
which is superiour to the optimal formula with real coefficients, both in
complexity and accuracy. We show asymptotic stability of our method for
sufficiently small time step and demonstrate its efficiency and accuracy in
different numerical models.Comment: 10 pages, 4 figures (5 eps files) Submitted to J. of Phys. A: Math.
Ge
Anomalous slow fidelity decay for symmetry breaking perturbations
Symmetries as well as other special conditions can cause anomalous slowing
down of fidelity decay. These situations will be characterized, and a family of
random matrix models to emulate them generically presented. An analytic
solution based on exponentiated linear response will be given. For one
representative case the exact solution is obtained from a supersymmetric
calculation. The results agree well with dynamical calculations for a kicked
top.Comment: 4 pages, 2 figure
Anomalous power law of quantum reversibility for classically regular dynamics
The Loschmidt Echo M(t) (defined as the squared overlap of wave packets
evolving with two slightly different Hamiltonians) is a measure of quantum
reversibility. We investigate its behavior for classically quasi-integrable
systems. A dominant regime emerges where M(t) ~ t^{-alpha} with alpha=3d/2
depending solely on the dimension d of the system. This power law decay is
faster than the result ~ t^{-d} for the decay of classical phase space
densities
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