2,221 research outputs found
Fluctuations and Ergodicity of the Form Factor of Quantum Propagators and Random Unitary Matrices
We consider the spectral form factor of random unitary matrices as well as of
Floquet matrices of kicked tops. For a typical matrix the time dependence of
the form factor looks erratic; only after a local time average over a suitably
large time window does a systematic time dependence become manifest. For
matrices drawn from the circular unitary ensemble we prove ergodicity: In the
limits of large matrix dimension and large time window the local time average
has vanishingly small ensemble fluctuations and may be identified with the
ensemble average. By numerically diagonalizing Floquet matrices of kicked tops
with a globally chaotic classical limit we find the same ergodicity. As a
byproduct we find that the traces of random matrices from the circular
ensembles behave very much like independent Gaussian random numbers. Again,
Floquet matrices of chaotic tops share that universal behavior. It becomes
clear that the form factor of chaotic dynamical systems can be fully faithful
to random-matrix theory, not only in its locally time-averaged systematic time
dependence but also in its fluctuations.Comment: 12 pages, RevTEX, 4 figures in eps forma
How often is a random quantum state k-entangled?
The set of trace preserving, positive maps acting on density matrices of size
d forms a convex body. We investigate its nested subsets consisting of
k-positive maps, where k=2,...,d. Working with the measure induced by the
Hilbert-Schmidt distance we derive asymptotically tight bounds for the volumes
of these sets. Our results strongly suggest that the inner set of
(k+1)-positive maps forms a small fraction of the outer set of k-positive maps.
These results are related to analogous bounds for the relative volume of the
sets of k-entangled states describing a bipartite d X d system.Comment: 19 pages in latex, 1 figure include
Trace distance from the viewpoint of quantum operation techniques
In the present paper, the trace distance is exposed within the quantum
operations formalism. The definition of the trace distance in terms of a
maximum over all quantum operations is given. It is shown that for any pair of
different states, there are an uncountably infinite number of maximizing
quantum operations. Conversely, for any operation of the described type, there
are an uncountably infinite number of those pairs of states that the maximum is
reached by the operation. A behavior of the trace distance under considered
operations is studied. Relations and distinctions between the trace distance
and the sine distance are discussed.Comment: 26 pages, no figures. The bibliography is extended, explanatory
improvement
Real-Time Reconfigurable Adaptive Speech Recognition Command and Control Apparatus and Method
An adaptive speech recognition and control system and method for controlling various mechanisms and systems in response to spoken instructions and in which spoken commands are effective to direct the system into appropriate memory nodes, and to respective appropriate memory templates corresponding to the voiced command is discussed. Spoken commands from any of a group of operators for which the system is trained may be identified, and voice templates are updated as required in response to changes in pronunciation and voice characteristics over time of any of the operators for which the system is trained. Provisions are made for both near-real-time retraining of the system with respect to individual terms which are determined not be positively identified, and for an overall system training and updating process in which recognition of each command and vocabulary term is checked, and in which the memory templates are retrained if necessary for respective commands or vocabulary terms with respect to an operator currently using the system. In one embodiment, the system includes input circuitry connected to a microphone and including signal processing and control sections for sensing the level of vocabulary recognition over a given period and, if recognition performance falls below a given level, processing audio-derived signals for enhancing recognition performance of the system
Statistical properties of random density matrices
Statistical properties of ensembles of random density matrices are
investigated. We compute traces and von Neumann entropies averaged over
ensembles of random density matrices distributed according to the Bures
measure. The eigenvalues of the random density matrices are analyzed: we derive
the eigenvalue distribution for the Bures ensemble which is shown to be broader
then the quarter--circle distribution characteristic of the Hilbert--Schmidt
ensemble. For measures induced by partial tracing over the environment we
compute exactly the two-point eigenvalue correlation function.Comment: 8 revtex pages with one eps file included, ver. 2 - minor misprints
correcte
Thermodynamic Properties and Phase Transitions in a Mean-Field Ising Spin Glass on Lattice Gas: the Random Blume-Emery-Griffiths-Capel Model
The study of the mean-field static solution of the Random
Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched
random magnetic interaction, is performed. The model exhibits a paramagnetic
phase, described by a stable Replica Symmetric solution. When the temperature
is decreased or the density increases, the system undergoes a phase transition
to a Full Replica Symmetry Breaking spin-glass phase. The nature of the
transition can be either of the second order (like in the
Sherrington-Kirkpatrick model) or, at temperature below a given critical value,
of the first order in the Ehrenfest sense, with a discontinuous jump of the
order parameter and accompanied by a latent heat. In this last case coexistence
of phases takes place. The thermodynamics is worked out in the Full Replica
Symmetry Breaking scheme, and the relative Parisi equations are solved using a
pseudo-spectral method down to zero temperature.Comment: 24 pages, 12 figure
Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
Assuming the validity of random matrices for describing the statistics of a
closed chaotic quantum system, we study analytically some statistical
properties of the S-matrix characterizing scattering in its open counterpart.
In the first part of the paper we attempt to expose systematically ideas
underlying the so-called stochastic (Heidelberg) approach to chaotic quantum
scattering. Then we concentrate on systems with broken time-reversal invariance
coupled to continua via M open channels. By using the supersymmetry method we
derive:
(i) an explicit expression for the density of S-matrix poles (resonances) in
the complex energy plane
(ii) an explicit expression for the parametric correlation function of
densities of eigenphases of the S-matrix.
We use it to find the distribution of derivatives of these eigenphases with
respect to the energy ("partial delay times" ) as well as with respect to an
arbitrary external parameter.Comment: 51 pages, RevTEX , three figures are available on request. To be
published in the special issue of the Journal of Mathematical Physic
Calculation of the unitary part of the Bures measure for N-level quantum systems
We use the canonical coset parameterization and provide a formula with the
unitary part of the Bures measure for non-degenerate systems in terms of the
product of even Euclidean balls. This formula is shown to be consistent with
the sampling of random states through the generation of random unitary
matrices
The 3-SAT problem with large number of clauses in -replica symmetry breaking scheme
In this paper we analyze the structure of the UNSAT-phase of the
overconstrained 3-SAT model by studying the low temperature phase of the
associated disordered spin model. We derive the Replica Symmetry
Broken equations for a general class of disordered spin models which includes
the Sherrington - Kirkpatrick model, the Ising -spin model as well as the
overconstrained 3-SAT model as particular cases. We have numerically solved the
Replica Symmetry Broken equations using a pseudo-spectral code down to
and including zero temperature. We find that the UNSAT-phase of the
overconstrained 3-SAT model is of the -RSB kind: in order to get a
stable solution the replica symmetry has to be broken in a continuous way,
similarly to the SK model in external magnetic field.Comment: 19 pages, 7 figures; some section improved; iopart styl
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