397 research outputs found
On the failure of subadditivity of the Wigner-Yanase entropy
It was recently shown by Hansen that the Wigner-Yanase entropy is, for
general states of quantum systems, not subadditive with respect to
decomposition into two subsystems, although this property is known to hold for
pure states. We investigate the question whether the weaker property of
subadditivity for pure states with respect to decomposition into more than two
subsystems holds. This property would have interesting applications in quantum
chemistry. We show, however, that it does not hold in general, and provide a
counterexample.Comment: LaTeX2e, 4 page
Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition
The distribution of energy level separations for lattices of sizes up to
282828 sites is numerically calculated for the Anderson model.
The results show one-parameter scaling. The size-independent universality of
the critical level spacing distribution allows to detect with high precision
the critical disorder . The scaling properties yield the critical
exponent, , and the disorder dependence of the correlation
length.Comment: 11 pages (RevTex), 3 figures included (tar-compressed and uuencoded
using UUFILES), to appear in Phys.Rev. B 51 (Rapid Commun.
Spectral Correlations from the Metal to the Mobility Edge
We have studied numerically the spectral correlations in a metallic phase and
at the metal-insulator transition. We have calculated directly the two-point
correlation function of the density of states . In the metallic phase,
it is well described by the Random Matrix Theory (RMT). For the first time, we
also find numerically the diffusive corrections for the number variance
predicted by Al'tshuler and Shklovski\u{\i}. At the
transition, at small energy scales, starts linearly, with a slope
larger than in a metal. At large separations , it is found to
decrease as a power law with and , in good agreement with recent microscopic
predictions. At the transition, we have also calculated the form factor , Fourier transform of . At large , the number variance
contains two terms \tilde{K}(0)t \to 0$.Comment: 7 RevTex-pages, 10 figures. Submitted to PR
Spin and Rotation in General Relativity
Rapporteur's Introduction to the GT8 session of the Ninth Marcel Grossmann
Meeting (Rome, 2000); to appear in the Proceedings.Comment: LaTeX file, no figures, 15 page
Infinite spin particles
We show that Wigner's infinite spin particle classically is described by a
reparametrization invariant higher order geometrical Lagrangian. The model
exhibit unconventional features like tachyonic behaviour and momenta
proportional to light-like accelerations. A simple higher order superversion
for half-odd integer particles is also derived. Interaction with external
vector fields and curved spacetimes are analyzed with negative results except
for (anti)de Sitter spacetimes. We quantize the free theories covariantly and
show that the resulting wave functions are fields containing arbitrary large
spins. Closely related infinite spin particle models are also analyzed.Comment: 43 pages, Late
Universal Cubic Eigenvalue Repulsion for Random Normal Matrices
Random matrix models consisting of normal matrices, defined by the sole
constraint , will be explored. It is shown that cubic
eigenvalue repulsion in the complex plane is universal with respect to the
probability distribution of matrices. The density of eigenvalues, all
correlation functions, and level spacing statistics are calculated. Normal
matrix models offer more probability distributions amenable to analytical
analysis than complex matrix models where only a model wth a Gaussian
distribution are solvable. The statistics of numerically generated eigenvalues
from gaussian distributed normal matrices are compared to the analytical
results obtained and agreement is seen.Comment: 15 pages, 2 eps figures. to appar in Physical Review
Quantum coherence in the presence of unobservable quantities
State representations summarize our knowledge about a system. When
unobservable quantities are introduced the state representation is typically no
longer unique. However, this non-uniqueness does not affect subsequent
inferences based on any observable data. We demonstrate that the inference-free
subspace may be extracted whenever the quantity's unobservability is guaranteed
by a global conservation law. This result can generalize even without such a
guarantee. In particular, we examine the coherent-state representation of a
laser where the absolute phase of the electromagnetic field is believed to be
unobservable. We show that experimental coherent states may be separated from
the inference-free subspaces induced by this unobservable phase. These physical
states may then be approximated by coherent states in a relative-phase Hilbert
space
Wigner Functions on a Lattice
The Wigner functions on the one dimensional lattice are studied. Contrary to
the previous claim in literature, Wigner functions exist on the lattice with
any number of sites, whether it is even or odd. There are infinitely many
solutions satisfying the conditions which reasonable Wigner functions should
respect. After presenting a heuristic method to obtain Wigner functions, we
give the general form of the solutions. Quantum mechanical expectation values
in terms of Wigner functions are also discussed.Comment: 11 pages, no figures, REVTE
On a pair of difference equations for the type orthogonal polynomials and related exactly-solvable quantum systems
We introduce a pair of novel difference equations, whose solutions are
expressed in terms of Racah or Wilson polynomials depending on the nature of
the finite-difference step. A number of special cases and limit relations are
also examined, which allow to introduce similar difference equations for the
orthogonal polynomials of the and types. It is shown that
the introduced equations allow to construct new models of exactly-solvable
quantum dynamical systems, such as spin chains with a nearest-neighbour
interaction and fermionic quantum oscillator models.Comment: 8 pages, to be published in Springer Proceedings in Mathematics &
Statistic
Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
Many natural and social systems develop complex networks, that are usually
modelled as random graphs. The eigenvalue spectrum of these graphs provides
information about their structural properties. While the semi-circle law is
known to describe the spectral density of uncorrelated random graphs, much less
is known about the eigenvalues of real-world graphs, describing such complex
systems as the Internet, metabolic pathways, networks of power stations,
scientific collaborations or movie actors, which are inherently correlated and
usually very sparse. An important limitation in addressing the spectra of these
systems is that the numerical determination of the spectra for systems with
more than a few thousand nodes is prohibitively time and memory consuming.
Making use of recent advances in algorithms for spectral characterization, here
we develop new methods to determine the eigenvalues of networks comparable in
size to real systems, obtaining several surprising results on the spectra of
adjacency matrices corresponding to models of real-world graphs. We find that
when the number of links grows as the number of nodes, the spectral density of
uncorrelated random graphs does not converge to the semi-circle law.
Furthermore, the spectral densities of real-world graphs have specific features
depending on the details of the corresponding models. In particular, scale-free
graphs develop a triangle-like spectral density with a power law tail, while
small-world graphs have a complex spectral density function consisting of
several sharp peaks. These and further results indicate that the spectra of
correlated graphs represent a practical tool for graph classification and can
provide useful insight into the relevant structural properties of real
networks.Comment: 14 pages, 9 figures (corrected typos, added references) accepted for
Phys. Rev.
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