571,129 research outputs found
Fixed energy universality for generalized Wigner matrices
We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the
spectrum for generalized symmetric and Hermitian Wigner matrices. Previous
results concerning the universality of random matrices either require an
averaging in the energy parameter or they hold only for Hermitian matrices if
the energy parameter is fixed. We develop a homogenization theory of the Dyson
Brownian motion and show that microscopic universality follows from mesoscopic
statistics
Entropy-energy inequalities for qudit states
We establish a procedure to find the extremal density matrices for any finite
Hamiltonian of a qudit system. These extremal density matrices provide an
approximate description of the energy spectra of the Hamiltonian. In the case
of restricting the extremal density matrices by pure states, we show that the
energy spectra of the Hamiltonian is recovered for and . We conjecture
that by means of this approach the energy spectra can be recovered for the
Hamiltonian of an arbitrary finite qudit system. For a given qudit system
Hamiltonian, we find new inequalities connecting the mean value of the
Hamiltonian and the entropy of an arbitrary state. We demonstrate that these
inequalities take place for both the considered extremal density matrices and
generic ones.Comment: 12 pages, 4 figures Accepted for publication in Journal of Physics A:
Mathematical and Theoretica
Bounds on quark mass matrices elements due to measured properties of the mixing matrix and present values of the quark masses
We obtain constraints on possible structures of mass matrices in the quark
sector by using as experimental restrictions the determined values of the quark
masses at the energy scale, the magnitudes of the quark mixing matrix
elements , , , and , and the
Jarlskog invariant . Different cases of specific mass matrices are
examined in detail. The quality of the fits for the Fritzsch and Stech type
mass matrices is about the same with and
, respectively. The fit for a simple
generalization (one extra parameter) of the Fritzsch type matrices, in the
physical basis, is much better with . For
comparison we also include the results using the quark masses at the 2 GeV
energy scale. The fits obtained at this energy scale are similar to that at
energy scale, implying that our results are unaffected by the evolution
of the quark masses from 2 to 91 GeV.Comment: Evolution effects include
Extracting the resonance parameters from experimental data on scattering of charged particles
A new parametrization of the multi-channel S-matrix is used to fit scattering
data and then to locate the resonances as its poles. The S-matrix is written in
terms of the corresponding "in" and "out" Jost matrices which are expanded in
the Taylor series of the collision energy E around an appropriately chosen
energy E0. In order to do this, the Jost matrices are written in a
semi-analytic form where all the factors (involving the channel momenta and
Sommerfeld parameters) responsible for their "bad behaviour" (i.e. responsible
for the multi-valuedness of the Jost matrices and for branching of the Riemann
surface of the energy) are given explicitly. The remaining unknown factors in
the Jost matrices are analytic and single-valued functions of the variable E
and are defined on a simple energy plane. The expansion is done for these
analytic functions and the expansion coefficients are used as the fitting
parameters. The method is tested on a two-channel model, using a set of
artificially generated data points with typical error bars and a typical random
noise in the positions of the points.Comment: 15 pages, 7 figures, 2 table
Exact S-Matrix for 2D String Theory
We formulate simple graphical rules which allow explicit calculation of
nonperturbative -matrices. This allows us to investigate the
constraint of nonperturbative unitarity, which indeed rules out some theories.
Nevertheless, we show that there is an infinite parameter family of
nonperturbatively unitary -matrices. We investigate the dependence of
the -matrix on one of these nonperturbative parameters. In particular, we
study the analytic structure, background dependence, and high-energy behavior
of some nonperturbative -matrices. The scattering amplitudes display
interesting resonant behavior both at high energies and in the complex energy
plane.Comment: 42p
Infrared alignment of SUSY flavor structures
The various experimental bounds on flavor-changing interactions severely
restrict the low-energy flavor structures of soft supersymmetry breaking
parameters. In this work, we show that with a particular assumption of Yukawa
couplings, the fermion mass and sfermion soft mass matrices are simultaneously
diagonalized by common mixing matrices and we then obtain an alignment solution
for the flavor problems. The required condition is generated by renormalization
group evolutions and achieved at low-energy scale independently of high-energy
structures of couplings. In this case, the diagonal entries of the soft scalar
mass matrices are determined by gaugino and Higgs soft masses. We also discuss
possible realizations of this scenario and the characteristic sparticle
spectrum in the models.Comment: 18 pages, 1 figur
Properties of contact matrices induced by pairwise interactions in proteins
The total conformational energy is assumed to consist of pairwise interaction
energies between atoms or residues, each of which is expressed as a product of
a conformation-dependent function (an element of a contact matrix, C-matrix)
and a sequence-dependent energy parameter (an element of a contact energy
matrix, E-matrix). Such pairwise interactions in proteins force native
C-matrices to be in a relationship as if the interactions are a Go-like
potential [N. Go, Annu. Rev. Biophys. Bioeng. 12. 183 (1983)] for the native
C-matrix, because the lowest bound of the total energy function is equal to the
total energy of the native conformation interacting in a Go-like pairwise
potential. This relationship between C- and E-matrices corresponds to (a) a
parallel relationship between the eigenvectors of the C- and E-matrices and a
linear relationship between their eigenvalues, and (b) a parallel relationship
between a contact number vector and the principal eigenvectors of the C- and
E-matrices; the E-matrix is expanded in a series of eigenspaces with an
additional constant term, which corresponds to a threshold of contact energy
that approximately separates native contacts from non-native ones. These
relationships are confirmed in 182 representatives from each family of the SCOP
database by examining inner products between the principal eigenvector of the
C-matrix, that of the E-matrix evaluated with a statistical contact potential,
and a contact number vector. In addition, the spectral representation of C- and
E-matrices reveals that pairwise residue-residue interactions, which depends
only on the types of interacting amino acids but not on other residues in a
protein, are insufficient and other interactions including residue
connectivities and steric hindrance are needed to make native structures the
unique lowest energy conformations.Comment: Errata in DOI:10.1103/PhysRevE.77.051910 has been corrected in the
present versio
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