70 research outputs found
Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate
We investigate the dynamics of a quantum oscillator, whose evolution is
monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double
well potential. It is demonstrated that the oscillator may experience various
degrees of decoherence depending on the variable being measured and the state
in which the BEC is prepared. These range from a `coherent' regime in which
only the variances of the oscillator position and momentum are affected by
measurement, to a slow (power law) or rapid (Gaussian) decoherence of the mean
values themselves.Comment: 4 pages, 3 figures, lette
Stochastic exclusion processes versus coherent transport
Stochastic exclusion processes play an integral role in the physics of
non-equilibrium statistical mechanics. These models are Markovian processes,
described by a classical master equation. In this paper a quantum mechanical
version of a stochastic hopping process in one dimension is formulated in terms
of a quantum master equation. This allows the investigation of coherent and
stochastic evolution in the same formal framework. The focus lies on the
non-equilibrium steady state. Two stochastic model systems are considered, the
totally asymmetric exclusion process and the fully symmetric exclusion process.
The steady state transport properties of these models is compared to the case
with additional coherent evolution, generated by the -Hamiltonian
Entanglement as a signature of quantum chaos
We explore the dynamics of entanglement in classically chaotic systems by
considering a multiqubit system that behaves collectively as a spin system
obeying the dynamics of the quantum kicked top. In the classical limit, the
kicked top exhibits both regular and chaotic dynamics depending on the strength
of the chaoticity parameter in the Hamiltonian. We show that the
entanglement of the multiqubit system, considered for both bipartite and
pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite
entanglement is enhanced in the chaotic region, pairwise entanglement is
suppressed. Furthermore, we define a time-averaged entangling power and show
that this entangling power changes markedly as moves the system from
being predominantly regular to being predominantly chaotic, thus sharply
identifying the edge of chaos. When this entangling power is averaged over
initial states, it yields a signature of global chaos. The qualitative behavior
of this global entangling power is similar to that of the classical Lyapunov
exponent.Comment: 8 pages, 8 figure
Many-body symbolic dynamics of a classical oscillator chain
We study a certain type of the celebrated Fermi-Pasta-Ulam particle chain,
namely the inverted FPU model, where the inter-particle potential has a form of
a quartic double well. Numerical evidence is given in support of a simple
symbolic description of dynamics (in the regime of sufficiently high potential
barrier between the wells) in terms of an (approximate) Markov process. The
corresponding transition matrix is formally identical to a ferromagnetic
Heisenberg quantum spin-1/2 chain with long range coupling, whose
diagonalization yields accurate estimates for a class of time correlation
functions of the model.Comment: 22 pages in LaTeX with 14 figures; submitted to Nonlinearity ;
corrected page offset proble
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
Slow dynamics in translation-invariant quantum lattice models
Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a method based on degenerate perturbation theory that reveals slow dynamical regimes and delocalization processes in general translation invariant models, along with accurate estimates of their delocalization time scales. Our results shed light on the fundamental questions of the robustness of quantum integrable systems and the possibility of many-body localization without disorder. As an example, we construct a large class of one-dimensional lattice models where, despite the absence of asymptotic localization, the transient dynamics is exceptionally slow, i.e., the dynamics is indistinguishable from that of many-body localized systems for the system sizes and time scales accessible in experiments and numerical simulations
Entangled random pure states with orthogonal symmetry: exact results
We compute analytically the density of Schmidt
eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure,
and the average R\'enyi entropy for reduced
density matrices of entangled random pure states with orthogonal symmetry
. The results are valid for arbitrary dimensions of the
corresponding Hilbert space partitions, and are in excellent agreement with
numerical simulations.Comment: 15 pages, 5 figure
Quantum state transfer in a XX chain with impurities
One spin excitation states are involved in the transmission of quantum states
and entanglement through a quantum spin chain, the localization properties of
these states are crucial to achieve the transfer of information from one
extreme of the chain to the other. We investigate the bipartite entanglement
and localization of the one excitation states in a quantum chain with one
impurity. The bipartite entanglement is obtained using the Concurrence and the
localization is analyzed using the inverse participation ratio. Changing the
strength of the exchange coupling of the impurity allows us to control the
number of localized or extended states. The analysis of the inverse
participation ratio allows us to identify scenarios where the transmission of
quantum states or entanglement can be achieved with a high degree of fidelity.
In particular we identify a regime where the transmission of quantum states
between the extremes of the chain is executed in a short transmission time
, where is the number of spins in the chain, and with a large
fidelity
Hypersensitivity and chaos signatures in the quantum baker's maps
Classical chaotic systems are distinguished by their sensitive dependence on
initial conditions. The absence of this property in quantum systems has lead to
a number of proposals for perturbation-based characterizations of quantum
chaos, including linear growth of entropy, exponential decay of fidelity, and
hypersensitivity to perturbation. All of these accurately predict chaos in the
classical limit, but it is not clear that they behave the same far from the
classical realm. We investigate the dynamics of a family of quantizations of
the baker's map, which range from a highly entangling unitary transformation to
an essentially trivial shift map. Linear entropy growth and fidelity decay are
exhibited by this entire family of maps, but hypersensitivity distinguishes
between the simple dynamics of the trivial shift map and the more complicated
dynamics of the other quantizations. This conclusion is supported by an
analytical argument for short times and numerical evidence at later times.Comment: 32 pages, 6 figure
Compact smallest eigenvalue expressions in Wishart-Laguerre ensembles with or without fixed-trace
The degree of entanglement of random pure states in bipartite quantum systems
can be estimated from the distribution of the extreme Schmidt eigenvalues. For
a bipartition of size M\geq N, these are distributed according to a
Wishart-Laguerre ensemble (WL) of random matrices of size N x M, with a
fixed-trace constraint. We first compute the distribution and moments of the
smallest eigenvalue in the fixed trace orthogonal WL ensemble for arbitrary
M\geq N. Our method is based on a Laplace inversion of the recursive results
for the corresponding orthogonal WL ensemble by Edelman. Explicit examples are
given for fixed N and M, generalizing and simplifying earlier results. In the
microscopic large-N limit with M-N fixed, the orthogonal and unitary WL
distributions exhibit universality after a suitable rescaling and are therefore
independent of the constraint. We prove that very recent results given in terms
of hypergeometric functions of matrix argument are equivalent to more explicit
expressions in terms of a Pfaffian or determinant of Bessel functions. While
the latter were mostly known from the random matrix literature on the QCD Dirac
operator spectrum, we also derive some new results in the orthogonal symmetry
class.Comment: 25 pag., 4 fig - minor changes, typos fixed. To appear in JSTA
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