296 research outputs found
Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics
We re-examine the problem of the "Loschmidt echo", which measures the
sensitivity to perturbation of quantum chaotic dynamics. The overlap squared
of two wave packets evolving under slightly different Hamiltonians is
shown to have the double-exponential initial decay in the main part of phase space. The
coefficient is the self-averaging Lyapunov exponent. The average
decay is single exponential with a different
coefficient . The volume of phase space that contributes to
vanishes in the classical limit for times less than the
Ehrenfest time . It is only after
the Ehrenfest time that the average decay is representative for a typical
initial condition.Comment: 4 pages, 4 figures, [2017: fixed broken postscript figures
Chaos for Liouville probability densities
Using the method of symbolic dynamics, we show that a large class of
classical chaotic maps exhibit exponential hypersensitivity to perturbation,
i.e., a rapid increase with time of the information needed to describe the
perturbed time evolution of the Liouville density, the information attaining
values that are exponentially larger than the entropy increase that results
from averaging over the perturbation. The exponential rate of growth of the
ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the
map. These findings generalize and extend results obtained for the baker's map
[R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.
Semiclassical properties and chaos degree for the quantum baker's map
We study the chaotic behaviour and the quantum-classical correspondence for
the baker's map. Correspondence between quantum and classical expectation
values is investigated and it is numerically shown that it is lost at the
logarithmic timescale. The quantum chaos degree is computed and it is
demonstrated that it describes the chaotic features of the model. The
correspondence between classical and quantum chaos degrees is considered.Comment: 30 pages, 4 figures, accepted for publication in J. Math. Phy
Classical limit in terms of symbolic dynamics for the quantum baker's map
We derive a simple closed form for the matrix elements of the quantum baker's
map that shows that the map is an approximate shift in a symbolic
representation based on discrete phase space. We use this result to give a
formal proof that the quantum baker's map approaches a classical Bernoulli
shift in the limit of a small effective Plank's constant.Comment: 12 pages, LaTex, typos correcte
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
On kinematics and dynamics of independent pion emission
Multiparticle boson states, proposed recently for 'independently' emitted
pions in heavy ion collisions, are reconsidered in standard second quantized
formalism and shown to emerge from a simplistic chaotic current dynamics.
Compact equations relate the density operator, the generating functional of
multiparticle counts, and the correlator of the external current to each other.
'Bose-Einstein-condensation' is related to the external pulse. A quantum master
equation is advocated for future Monte-Carlo simulations.Comment: 10 pages LaTeX, Sec.7 adde
Strategies for Real-Time Position Control of a Single Atom in Cavity QED
Recent realizations of single-atom trapping and tracking in cavity QED open
the door for feedback schemes which actively stabilize the motion of a single
atom in real time. We present feedback algorithms for cooling the radial
component of motion for a single atom trapped by strong coupling to
single-photon fields in an optical cavity. Performance of various algorithms is
studied through simulations of single-atom trajectories, with full dynamical
and measurement noise included. Closed loop feedback algorithms compare
favorably to open-loop "switching" analogs, demonstrating the importance of
applying actual position information in real time. The high optical information
rate in current experiments enables real-time tracking that approaches the
standard quantum limit for broadband position measurements, suggesting that
realistic active feedback schemes may reach a regime where measurement
backaction appreciably alters the motional dynamics.Comment: 12 pages, 10 figures, submitted to J. Opt. B Quant. Semiclass. Op
Qubit-Qutrit Separability-Probability Ratios
Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for
the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to
high numerical accuracy, the formulas of Sommers and Zyczkowski
(quant-ph/0304041) for the (N^2-1)-dimensional volume and (N^2-2)-dimensional
hyperarea of the (separable and nonseparable) N x N density matrices, based on
the Bures (minimal monotone) metric -- and also their analogous formulas
(quant-ph/0302197) for the (non-monotone) Hilbert-Schmidt metric. With the same
seven billion well-distributed (``low-discrepancy'') sample points, we estimate
the unknown volumes and hyperareas based on five additional (monotone) metrics
of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate
all of these seven volume and seven hyperarea (unknown) quantities when
restricted to the separable density matrices. The ratios of separable volumes
(hyperareas) to separable plus nonseparable volumes (hyperareas) yield
estimates of the separability probabilities of generically rank-six (rank-five)
density matrices. The (rank-six) separability probabilities obtained based on
the 35-dimensional volumes appear to be -- independently of the metric (each of
the seven inducing Haar measure) employed -- twice as large as those (rank-five
ones) based on the 34-dimensional hyperareas. Accepting such a relationship, we
fit exact formulas to the estimates of the Bures and Hilbert-Schmidt separable
volumes and hyperareas.(An additional estimate -- 33.9982 -- of the ratio of
the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite
clearly close to integral too.) The doubling relationship also appears to hold
for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit
exact formulas for the Hilbert-Schmidt separable volumes and hyperareas.Comment: 36 pages, 15 figures, 11 tables, final PRA version, new last
paragraph presenting qubit-qutrit probability ratios disaggregated by the two
distinct forms of partial transpositio
Entanglement purification of unknown quantum states
A concern has been expressed that ``the Jaynes principle can produce fake
entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 59}, 1799 (1999)]. In
this paper we discuss the general problem of distilling maximally entangled
states from copies of a bipartite quantum system about which only partial
information is known, for instance in the form of a given expectation value. We
point out that there is indeed a problem with applying the Jaynes principle of
maximum entropy to more than one copy of a system, but the nature of this
problem is classical and was discussed extensively by Jaynes. Under the
additional assumption that the state of the copies of the
quantum system is exchangeable, one can write down a simple general expression
for . We show how to modify two standard entanglement purification
protocols, one-way hashing and recurrence, so that they can be applied to
exchangeable states. We thus give an explicit algorithm for distilling
entanglement from an unknown or partially known quantum state.Comment: 20 pages RevTeX 3.0 + 1 figure (encapsulated Postscript) Submitted to
Physical Review
Continuous Quantum Measurement and the Emergence of Classical Chaos
We formulate the conditions under which the dynamics of a continuously
measured quantum system becomes indistinguishable from that of the
corresponding classical system. In particular, we demonstrate that even in a
classically chaotic system the quantum state vector conditioned by the
measurement remains localized and, under these conditions, follows a trajectory
characterized by the classical Lyapunov exponent.Comment: 5 pages, multicol revte
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