1,374 research outputs found
On the comparison of volumes of quantum states
This paper aims to study the \a-volume of \cK, an arbitrary subset of the
set of density matrices. The \a-volume is a generalization of the
Hilbert-Schmidt volume and the volume induced by partial trace. We obtain
two-side estimates for the \a-volume of \cK in terms of its Hilbert-Schmidt
volume. The analogous estimates between the Bures volume and the \a-volume
are also established. We employ our results to obtain bounds for the
\a-volume of the sets of separable quantum states and of states with positive
partial transpose (PPT). Hence, our asymptotic results provide answers for
questions listed on page 9 in \cite{K. Zyczkowski1998} for large in the
sense of \a-volume.
\vskip 3mm PACS numbers: 02.40.Ft, 03.65.Db, 03.65.Ud, 03.67.M
Volatilization, Plant Uptake And Mineralization Of Nitrogen In Soils Treated With Sewage Sludge
Role of electron-electron and electron-phonon interaction effect in the optical conductivity of VO2
We have investigated the charge dynamics of VO2 by optical reflectivity
measurements. Optical conductivity clearly shows a metal-insulator transition.
In the metallic phase, a broad Drude-like structure is observed. On the other
hand, in the insulating phase, a broad peak structure around 1.3 eV is
observed. It is found that this broad structure observed in the insulating
phase shows a temperature dependence. We attribute this to the electron-phonon
interaction as in the photoemission spectra.Comment: 6 pages, 8 figures, accepted for publication in Phys. Rev.
Distributions of Conductance and Shot Noise and Associated Phase Transitions
For a chaotic cavity with two indentical leads each supporting N channels, we
compute analytically, for large N, the full distribution of the conductance and
the shot noise power and show that in both cases there is a central Gaussian
region flanked on both sides by non-Gaussian tails. The distribution is weakly
singular at the junction of Gaussian and non-Gaussian regimes, a direct
consequence of two phase transitions in an associated Coulomb gas problem.Comment: 5 pages, 3 figures include
Distribution of G-concurrence of random pure states
Average entanglement of random pure states of an N x N composite system is
analyzed. We compute the average value of the determinant D of the reduced
state, which forms an entanglement monotone. Calculating higher moments of the
determinant we characterize the probability distribution P(D). Similar results
are obtained for the rescaled N-th root of the determinant, called
G-concurrence. We show that in the limit this quantity becomes
concentrated at a single point G=1/e. The position of the concentration point
changes if one consider an arbitrary N x K bipartite system, in the joint limit
, K/N fixed.Comment: RevTeX4, 11 pages, 4 Encapsuled PostScript figures - Introduced new
results, Section II and V have been significantly improved - To appear on PR
Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence
The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional
and 15-dimensional in nature, respectively. The total volumes of the spaces
they occupy with respect to the Hilbert-Schmidt and Bures metrics are
obtainable as special cases of formulas of Zyczkowski and Sommers. We claim
that if one could determine certain metric-independent 3-dimensional
"eigenvalue-parameterized separability functions" (EPSFs), then these formulas
could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes
occupied by only the separable two-qubit states (and hence associated
separability probabilities). Motivated by analogous earlier analyses of
"diagonal-entry-parameterized separability functions", we further explore the
possibility that such 3-dimensional EPSFs might, in turn, be expressible as
univariate functions of some special relevant variable--which we hypothesize to
be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical
results we obtain are rather closely supportive of this hypothesis. Both the
real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude
roughly 50% at C=1/2, as well as a number of additional matching
discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.
Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
By using the method of orthogonal polynomials we analyze the statistical
properties of complex eigenvalues of random matrices describing a crossover
from Hermitian matrices characterized by the Wigner- Dyson statistics of real
eigenvalues to strongly non-Hermitian ones whose complex eigenvalues were
studied by Ginibre.
Two-point statistical measures (as e.g. spectral form factor, number variance
and small distance behavior of the nearest neighbor distance distribution
) are studied in more detail. In particular, we found that the latter
function may exhibit unusual behavior for some parameter
values.Comment: 4 pages, RevTE
Probability distributions of Linear Statistics in Chaotic Cavities and associated phase transitions
We establish large deviation formulas for linear statistics on the
transmission eigenvalues of a chaotic cavity, in the framework of
Random Matrix Theory. Given any linear statistics of interest , the probability distribution of generically
satisfies the large deviation formula
, where
is a rate function that we compute explicitly in many cases
(conductance, shot noise, moments) and corresponds to different
symmetry classes. Using these large deviation expressions, it is possible to
recover easily known results and to produce new formulas, such as a closed form
expression for (where
) for arbitrary integer . The universal limit
is also computed exactly. The
distributions display a central Gaussian region flanked on both sides by
non-Gaussian tails. At the junction of the two regimes, weakly non-analytical
points appear, a direct consequence of phase transitions in an associated
Coulomb gas problem. Numerical checks are also provided, which are in full
agreement with our asymptotic results in both real and Laplace space even for
moderately small . Part of the results have been announced in [P. Vivo, S.N.
Majumdar and O. Bohigas, {\it Phys. Rev. Lett.} {\bf 101}, 216809 (2008)].Comment: 31 pages, 16 figures. To appear in Phys. Rev. B. Added section IVD
about comparison with other theories and numerical simulation
Random graph states, maximal flow and Fuss-Catalan distributions
For any graph consisting of vertices and edges we construct an
ensemble of random pure quantum states which describe a system composed of
subsystems. Each edge of the graph represents a bi-partite, maximally entangled
state. Each vertex represents a random unitary matrix generated according to
the Haar measure, which describes the coupling between subsystems. Dividing all
subsystems into two parts, one may study entanglement with respect to this
partition. A general technique to derive an expression for the average
entanglement entropy of random pure states associated to a given graph is
presented. Our technique relies on Weingarten calculus and flow problems. We
analyze statistical properties of spectra of such random density matrices and
show for which cases they are described by the free Poissonian
(Marchenko-Pastur) distribution. We derive a discrete family of generalized,
Fuss-Catalan distributions and explicitly construct graphs which lead to
ensembles of random states characterized by these novel distributions of
eigenvalues.Comment: 37 pages, 24 figure
The origin of ultra high energy cosmic rays
We briefly discuss some open problems and recent developments in the
investigation of the origin and propagation of ultra high energy cosmic rays
(UHECRs).Comment: Invited Review Talk at TAUP 2005 (Zaragoza - September 10-14, 2005).
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