240 research outputs found
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_
Markovian kinetic equation approach to electron transport through quantum dot coupled to superconducting leads
We present a derivation of Markovian master equation for the out of
equilibrium quantum dot connected to two superconducting reservoirs, which are
described by the Bogoliubov-de Gennes Hamiltonians and have the chemical
potentials, the temperatures, and the complex order parameters as the relevant
quantities. We consider a specific example in which the quantum dot is
represented by the Anderson impurity model and study the transport properties,
proximity effect and Andreev bound states in equilibrium and far from
equilibrium setups.Comment: 10 pages, 6 figure
Statistical Properties of Strain and Rotation Tensors in Geodetic Network
This article deals with the characteristics of deformation of a body or a figure represented by discrete points of geodetic network. In each point of geodetic network kinematic quantities are considered normal strain, shear strain, and rotation. They are computed from strain and rotation tensors represented by displacement gradient matrix on the basis of known point displacement vector. Deformation analysis requires the appropriate treatment of kinematic quantities. Thus statistical properties of each quantity in a single point of geodetic network have to be known. Empirical results have shown that statistical properties are strongly related to the orientation in single point and local geometry of the geodetic network. Based on the known probability distribution of kinematic quantities the confidence areas for each quantity in a certain point can be defined. Based on this we can carry out appropriate statistical testing and decide whether the deformation of network in each point is statistically significant or not. On the other hand, we are able to ascertain the quality of the geometry of the geodetic network. The known characteristics of the probability distributions of two strain parameters and rotation in each point can serve as useful tools in the procedures of optimizing the geometry of the geodetic networks
Is efficiency of classical simulations of quantum dynamics related to integrability?
Efficiency of time-evolution of quantum observables, and thermal states of
quenched hamiltonians, is studied using time-dependent density matrix
renormalization group method in a family of generic quantum spin chains which
undergo a transition from integrable to non-integrable - quantum chaotic case
as control parameters are varied. Quantum states (observables) are represented
in terms of matrix-product-operators with rank D_\epsilon(t), such that
evolution of a long chain is accurate within fidelity error \epsilon up to time
t. We find that rank generally increases exponentially, D_\epsilon(t) \propto
\exp(const t), unless the system is integrable in which case we find polynomial
increase.Comment: 4 pages; v2. added paragraph discussing pure state
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
Detecting entanglement of random states with an entanglement witness
The entanglement content of high-dimensional random pure states is almost
maximal, nevertheless, we show that, due to the complexity of such states, the
detection of their entanglement using witness operators is rather difficult. We
discuss the case of unknown random states, and the case of known random states
for which we can optimize the entanglement witness. Moreover, we show that
coarse graining, modeled by considering mixtures of m random states instead of
pure ones, leads to a decay in the entanglement detection probability
exponential with m. Our results also allow to explain the emergence of
classicality in coarse grained quantum chaotic dynamics.Comment: 14 pages, 4 figures; minor typos correcte
Loschmidt echoes in two-body random matrix ensembles
Fidelity decay is studied for quantum many-body systems with a dominant
independent particle Hamiltonian resulting e.g. from a mean field theory with a
weak two-body interaction. The diagonal terms of the interaction are included
in the unperturbed Hamiltonian, while the off-diagonal terms constitute the
perturbation that distorts the echo. We give the linear response solution for
this problem in a random matrix framework. While the ensemble average shows no
surprising behavior, we find that the typical ensemble member as represented by
the median displays a very slow fidelity decay known as ``freeze''. Numerical
calculations confirm this result and show, that the ground state even on
average displays the freeze. This may contribute to explanation of the
``unreasonable'' success of mean field theories.Comment: 9 pages, 5 figures (6 eps files), RevTex; v2: slight modifications
following referees' suggestion
Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit
Numerical evidence is given for non-ergodic (non-mixing) behavior, exhibiting
ideal transport, of a simple non-integrable many-body quantum system in the
thermodynamic limit, namely kicked model of spinless fermions on a ring.
However, for sufficiently large kick parameters and we recover quantum
ergodicity, and normal transport, which can be described by random matrix
theory.Comment: 4 pages in RevTex (6 figures in PostScript included
The triangle map: a model of quantum chaos
We study an area preserving parabolic map which emerges from the Poincar\' e
map of a billiard particle inside an elongated triangle. We provide numerical
evidence that the motion is ergodic and mixing. Moreover, when considered on
the cylinder, the motion appear to follow a gaussian diffusive process.Comment: 4 pages in RevTeX with 4 figures (in 6 eps-files
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