271 research outputs found
Dyson's Brownian Motion and Universal Dynamics of Quantum Systems
We establish a correspondence between the evolution of the distribution of
eigenvalues of a matrix subject to a random Gaussian perturbing
matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we
prove the equivalence conjectured by Altshuler et al between the space-time
correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit
and a set of two-variable correlations for disordered quantum systems
calculated by them. Multiple variable correlation functions are, however, shown
to be inequivalent for the two cases.Comment: 10 pages, revte
Universal Level dynamics of Complex Systems
. We study the evolution of the distribution of eigenvalues of a
matrix subject to a random perturbation drawn from (i) a generalized Gaussian
ensemble (ii) a non-Gaussian ensemble with a measure variable under the change
of basis. It turns out that, in the case (i), a redefinition of the parameter
governing the evolution leads to a Fokker-Planck equation similar to the one
obtained when the perturbation is taken from a standard Gaussian ensemble (with
invariant measure). This equivalence can therefore help us to obtain the
correlations for various physically-significant cases modeled by generalized
Gaussian ensembles by using the already known correlations for standard
Gaussian ensembles.
For large -values, our results for both cases (i) and (ii) are similar to
those obtained for Wigner-Dyson gas as well as for the perturbation taken from
a standard Gaussian ensemble. This seems to suggest the independence of
evolution, in thermodynamic limit, from the nature of perturbation involved as
well as the initial conditions and therefore universality of dynamics of the
eigenvalues of complex systems.Comment: 11 Pages, Latex Fil
Density of states for almost diagonal random matrices
We study the density of states (DOS) for disordered systems whose spectral
statistics can be described by a Gaussian ensemble of almost diagonal Hermitian
random matrices. The matrices have independent random entries with small off-diagonal elements: . Using the recently suggested method of a {\it virial expansion in
the number of interacting energy levels} (Journ.Phys.A {\bf 36}, 8265), we
calculate the leading correction to the Poissonian DOS in the cases of the
Gaussian Orthogonal and Unitary Ensembles. We apply the general formula to the
critical power-law banded random matrices and the unitary
Moshe-Neuberger-Shapiro model and compare DOS of these models.Comment: submitted to Phys. Rev.
Alternative Technique for "Complex" Spectra Analysis
. The choice of a suitable random matrix model of a complex system is very
sensitive to the nature of its complexity. The statistical spectral analysis of
various complex systems requires, therefore, a thorough probing of a wide range
of random matrix ensembles which is not an easy task. It is highly desirable,
if possible, to identify a common mathematcal structure among all the ensembles
and analyze it to gain information about the ensemble- properties. Our
successful search in this direction leads to Calogero Hamiltonian, a
one-dimensional quantum hamiltonian with inverse-square interaction, as the
common base. This is because both, the eigenvalues of the ensembles, and, a
general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary
initial conditions. The varying nature of the complexity is reflected in the
different form of the evolution parameter in each case. A complete
investigation of Calogero Hamiltonian can then help us in the spectral analysis
of complex systems.Comment: 20 pages, No figures, Revised Version (Minor Changes
A generalized plasma and interpolation between classical random matrix ensembles
The eigenvalue probability density functions of the classical random matrix
ensembles have a well known analogy with the one component log-gas at the
special couplings \beta = 1,2 and 4. It has been known for some time that there
is an exactly solvable two-component log-potential plasma which interpolates
between the \beta =1 and 4 circular ensemble, and an exactly solvable
two-component generalized plasma which interpolates between \beta = 2 and 4
circular ensemble. We extend known exact results relating to the latter --- for
the free energy and one and two-point correlations --- by giving the general
(k_1+k_2)-point correlation function in a Pfaffian form. Crucial to our working
is an identity which expresses the Vandermonde determinant in terms of a
Pfaffian. The exact evaluation of the general correlation is used to exhibit a
perfect screening sum rule.Comment: 21 page
Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states
Photonic analogues of the relativistic Kronig-Penney model and of
relativistic surface Tamm states are proposed for light propagation in fibre
Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in
the FBG realizes the relativistic Kronig-Penney model, the band structure of
which being mapped into the spectral response of the FBG. For the semi-infinite
FBG Tamm surface states can appear and can be visualized as narrow resonance
peaks in the transmission spectrum of the grating
Can forest management based on natural disturbances maintain ecological resilience?
Given the increasingly global stresses on forests, many ecologists argue that managers must maintain ecological resilience: the capacity of ecosystems to absorb disturbances without undergoing fundamental change. In this review we ask: Can the emerging paradigm of natural-disturbance-based management (NDBM) maintain ecological resilience in managed forests? Applying resilience theory requires careful articulation of the ecosystem state under consideration, the disturbances and stresses that affect the persistence of possible alternative states, and the spatial and temporal scales of management relevance. Implementing NDBM while maintaining resilience means recognizing that (i) biodiversity is important for long-term ecosystem persistence, (ii) natural disturbances play a critical role as a generator of structural and compositional heterogeneity at multiple scales, and (iii) traditional management tends to produce forests more homogeneous than those disturbed naturally and increases the likelihood of unexpected catastrophic change by constraining variation of key environmental processes. NDBM may maintain resilience if silvicultural strategies retain the structures and processes that perpetuate desired states while reducing those that enhance resilience of undesirable states. Such strategies require an understanding of harvesting impacts on slow ecosystem processes, such as seed-bank or nutrient dynamics, which in the long term can lead to ecological surprises by altering the forest's capacity to reorganize after disturbance
Recombinant MVA-prime elicits neutralizing antibody responses by inducing antigen-specific B cells in the germinal center.
The RV144 HIV-1 vaccine trial has been the only clinical trial to date that has shown any degree of efficacy and associated with the presence of vaccine-elicited HIV-1 envelope-specific binding antibody and CD4+ T-cell responses. This trial also showed that a vector-prime protein boost combined vaccine strategy was better than when used alone. Here we have studied three different priming vectors-plasmid DNA, recombinant MVA, and recombinant VSV, all encoding clade C transmitted/founder Env 1086 C gp140, for priming three groups of six non-human primates each, followed by a protein boost with adjuvanted 1086 C gp120 protein. Our data showed that MVA-priming favors the development of higher antibody binding titers and neutralizing activity compared with other vectors. Analyses of the draining lymph nodes revealed that MVA-prime induced increased germinal center reactivity characterized by higher frequencies of germinal center (PNA <sup>hi</sup> ) B cells, higher frequencies of antigen-specific B-cell responses as well as an increased frequency of the highly differentiated (ICOS <sup>hi</sup> CD150 <sup>lo</sup> ) Tfh-cell subset
Novel metallic states at low temperatures
We present an overview of unconventional metallic states arising close to magnetic quantum critical points with a focus on d-electron systems. The applicability and potential breakdowns of traditional self-consistent field theories of such materials are discussed as well as related phenomena in other systems
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