370 research outputs found
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
Complexity and non-separability of classical Liouvillian dynamics
We propose a simple complexity indicator of classical Liouvillian dynamics,
namely the separability entropy, which determines the logarithm of an effective
number of terms in a Schmidt decomposition of phase space density with respect
to an arbitrary fixed product basis. We show that linear growth of separability
entropy provides stricter criterion of complexity than Kolmogorov-Sinai
entropy, namely it requires that dynamics is exponentially unstable, non-linear
and non-markovian.Comment: Revised version, 5 pages (RevTeX), with 6 pdf-figure
Fidelity and Purity Decay in Weakly Coupled Composite Systems
We study the stability of unitary quantum dynamics of composite systems (for
example: central system + environment) with respect to weak interaction between
the two parts. Unified theoretical formalism is applied to study different
physical situations: (i) coherence of a forward evolution as measured by purity
of the reduced density matrix, (ii) stability of time evolution with respect to
small coupling between subsystems, and (iii) Loschmidt echo measuring dynamical
irreversibility. Stability has been measured either by fidelity of pure states
of a composite system, or by the so-called reduced fidelity of reduced density
matrices within a subsystem. Rigorous inequality among fidelity,
reduced-fidelity and purity is proved and a linear response theory is developed
expressing these three quantities in terms of time correlation functions of the
generator of interaction. The qualitatively different cases of regular
(integrable) or mixing (chaotic in the classical limit) dynamics in each of the
subsystems are discussed in detail. Theoretical results are demonstrated and
confirmed in a numerical example of two coupled kicked tops.Comment: 21 pages, 12 eps figure
A map from 1d Quantum Field Theory to Quantum Chaos on a 2d Torus
Dynamics of a class of quantum field models on 1d lattice in Heisenberg
picture is mapped into a class of `quantum chaotic' one-body systems on
configurational 2d torus (or 2d lattice) in Schr\" odinger picture. Continuum
field limit of the former corresponds to quasi-classical limit of the latter.Comment: 4 pages in REVTeX, 1 eps-figure include
Engineering fidelity echoes in Bose-Hubbard Hamiltonians
We analyze the fidelity decay for a system of interacting bosons described by
a Bose-Hubbard Hamiltonian. We find echoes associated with "non-universal"
structures that dominate the energy landscape of the perturbation operator.
Despite their classical origin, these echoes persist deep into the quantum
(perturbative) regime and can be described by an improved random matrix
modeling. In the opposite limit of strong perturbations (and high enough
energies), classical considerations reveal the importance of self-trapping
phenomena in the echo efficiency.Comment: 6 pages, use epl2.cls class, 5 figures Cross reference with nlin,
quant-phy
Estimating purity in terms of correlation functions
We prove a rigorous inequality estimating the purity of a reduced density
matrix of a composite quantum system in terms of cross-correlation of the same
state and an arbitrary product state. Various immediate applications of our
result are proposed, in particular concerning Gaussian wave-packet propagation
under classically regular dynamics.Comment: 3 page
Dynamical properties of a particle in a wave packet: scaling invariance and boundary crisis
Some dynamical properties present in a problem concerning the acceleration of
particles in a wave packet are studied. The dynamics of the model is described
in terms of a two-dimensional area preserving map. We show that the phase space
is mixed in the sense that there are regular and chaotic regions coexisting. We
use a connection with the standard map in order to find the position of the
first invariant spanning curve which borders the chaotic sea. We find that the
position of the first invariant spanning curve increases as a power of the
control parameter with the exponent 2/3. The standard deviation of the kinetic
energy of an ensemble of initial conditions obeys a power law as a function of
time, and saturates after some crossover. Scaling formalism is used in order to
characterize the chaotic region close to the transition from integrability to
nonintegrability and a relationship between the power law exponents is derived.
The formalism can be applied in many different systems with mixed phase space.
Then, dissipation is introduced into the model and therefore the property of
area preservation is broken, and consequently attractors are observed. We show
that after a small change of the dissipation, the chaotic attractor as well as
its basin of attraction are destroyed, thus leading the system to experience a
boundary crisis. The transient after the crisis follows a power law with
exponent -2.Comment: Chaos, Solitons & Fractals, 201
Uni-directional transport properties of a serpent billiard
We present a dynamical analysis of a classical billiard chain -- a channel
with parallel semi-circular walls, which can serve as a model for a bended
optical fiber. An interesting feature of this model is the fact that the phase
space separates into two disjoint invariant components corresponding to the
left and right uni-directional motions. Dynamics is decomposed into the jump
map -- a Poincare map between the two ends of a basic cell, and the time
function -- traveling time across a basic cell of a point on a surface of
section. The jump map has a mixed phase space where the relative sizes of the
regular and chaotic components depend on the width of the channel. For a
suitable value of this parameter we can have almost fully chaotic phase space.
We have studied numerically the Lyapunov exponents, time auto-correlation
functions and diffusion of particles along the chain. As a result of a
singularity of the time function we obtain marginally-normal diffusion after we
subtract the average drift. The last result is also supported by some
analytical arguments.Comment: 15 pages, 9 figure (19 .(e)ps files
Echoes in classical dynamical systems
Echoes arise when external manipulations to a system induce a reversal of its
time evolution that leads to a more or less perfect recovery of the initial
state. We discuss the accuracy with which a cloud of trajectories returns to
the initial state in classical dynamical systems that are exposed to additive
noise and small differences in the equations of motion for forward and backward
evolution. The cases of integrable and chaotic motion and small or large noise
are studied in some detail and many different dynamical laws are identified.
Experimental tests in 2-d flows that show chaotic advection are proposed.Comment: to be published in J. Phys.
Dephasing-induced diffusive transport in anisotropic Heisenberg model
We study transport properties of anisotropic Heisenberg model in a disordered
magnetic field experiencing dephasing due to external degrees of freedom. In
the absence of dephasing the model can display, depending on parameter values,
the whole range of possible transport regimes: ideal ballistic conduction,
diffusive, or ideal insulating behavior. We show that the presence of dephasing
induces normal diffusive transport in a wide range of parameters. We also
analyze the dependence of spin conductivity on the dephasing strength. In
addition, by analyzing the decay of spin-spin correlation function we discover
a presence of long-range order for finite chain sizes. All our results for a
one-dimensional spin chain at infinite temperature can be equivalently
rephrased for strongly-interacting disordered spinless fermions.Comment: 15 pages, 9 PS figure
- …