574 research outputs found
Bounds for mixing time of quantum walks on finite graphs
Several inequalities are proved for the mixing time of discrete-time quantum
walks on finite graphs. The mixing time is defined differently than in
Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for
particular examples of walks on a cycle, a hypercube and a complete graph,
quantum walks provide no speed-up in mixing over the classical counterparts. In
addition, non-unitary quantum walks (i.e., walks with decoherence) are
considered and a criterion for their convergence to the unique stationary
distribution is derived.Comment: This is the journal version (except formatting); it is a significant
revision of the previous version, in particular, it contains a new result
about the convergence of quantum walks with decoherence; 16 page
Quark interchange effects in the KN interaction
We study the short range repulsion in the KN system due to quark-gluon exchange. Phase shifts for spin-spin, color Coloumb and spin-orbit interactions are presented
Multipeakons and a theorem of Stieltjes
A closed form of the multi-peakon solutions of the Camassa-Holm equation is
found using a theorem of Stieltjes on continued fractions. An explicit formula
is obtained for the scattering shifts.Comment: 6 page
Flavor SU(4) breaking between effective couplings
Using a framework in which all elements are constrained by Dyson-Schwinger
equation studies in QCD, and therefore incorporates a consistent, direct and
simultaneous description of light- and heavy-quarks and the states they
constitute, we analyze the accuracy of SU(4)-flavor symmetry relations between
{\pi}{\rho}{\pi}, K{\rho}K and D{\rho}D couplings. Such relations are widely
used in phenomenological analyses of the interactions between matter and
charmed mesons. We find that whilst SU(3)-flavor symmetry is accurate to 20%,
SU(4) relations underestimate the D{\rho}D coupling by a factor of five.Comment: 5 pages, two figure
Mapping of composite hadrons into elementary hadrons and effective hadronic Hamiltonians
A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces and shares similarities with the quasiparticle method of Weinberg. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, hermitian Hamiltonians with a clear physical interpretation are obtained. Applications and comparisons with other composite-particle formalisms of the recent literature are made using the nonrelativistic quark model
Charge Symmetry Breaking in 500 MeV Nucleon-Trinucleon Scattering
Elastic nucleon scattering from the 3He and 3H mirror nuclei is examined as a
test of charge symmetry violation. The differential cross-sections are
calculated at 500 MeV using a microsopic, momentum-space optical potential
including the full coupling of two spin 1/2 particles and an exact treatment of
the Coulomb force. The charge-symmetry-breaking effects investigated arise from
a violation within the nuclear structure, from the p-nucleus Coulomb force, and
from the mass-differences of the charge symmetric states. Measurements likely
to reveal reliable information are noted.Comment: 5 page
About the ergodic regime in the analogical Hopfield neural networks. Moments of the partition function
In this paper we introduce and exploit the real replica approach for a
minimal generalization of the Hopfield model, by assuming the learned patterns
to be distributed accordingly to a standard unit Gaussian. We consider the high
storage case, when the number of patterns is linearly diverging with the number
of neurons. We study the infinite volume behavior of the normalized momenta of
the partition function. We find a region in the parameter space where the free
energy density in the infinite volume limit is self-averaging around its
annealed approximation, as well as the entropy and the internal energy density.
Moreover, we evaluate the corrections to their extensive counterparts with
respect to their annealed expressions. The fluctuations of properly introduced
overlaps, which act as order parameters, are also discussed.Comment: 15 page
A variational approach to strongly damped wave equations
We discuss a Hilbert space method that allows to prove analytical
well-posedness of a class of linear strongly damped wave equations. The main
technical tool is a perturbation lemma for sesquilinear forms, which seems to
be new. In most common linear cases we can furthermore apply a recent result
due to Crouzeix--Haase, thus extending several known results and obtaining
optimal analyticity angle.Comment: This is an extended version of an article appeared in
\emph{Functional Analysis and Evolution Equations -- The G\"unter Lumer
Volume}, edited by H. Amann et al., Birkh\"auser, Basel, 2008. In the latest
submission to arXiv only some typos have been fixe
Spectral properties of a short-range impurity in a quantum dot
The spectral properties of the quantum mechanical system consisting of a
quantum dot with a short-range attractive impurity inside the dot are
investigated in the zero-range limit. The Green function of the system is
obtained in an explicit form. In the case of a spherically symmetric quantum
dot, the dependence of the spectrum on the impurity position and the strength
of the impurity potential is analyzed in detail. It is proven that the
confinement potential of the dot can be recovered from the spectroscopy data.
The consequences of the hidden symmetry breaking by the impurity are
considered. The effect of the positional disorder is studied.Comment: 30 pages, 6 figures, Late
The inverse spectral problem for the discrete cubic string
Given a measure on the real line or a finite interval, the "cubic string"
is the third order ODE where is a spectral parameter. If
equipped with Dirichlet-like boundary conditions this is a nonselfadjoint
boundary value problem which has recently been shown to have a connection to
the Degasperis-Procesi nonlinear water wave equation. In this paper we study
the spectral and inverse spectral problem for the case of Neumann-like boundary
conditions which appear in a high-frequency limit of the Degasperis--Procesi
equation. We solve the spectral and inverse spectral problem for the case of
being a finite positive discrete measure. In particular, explicit
determinantal formulas for the measure are given. These formulas generalize
Stieltjes' formulas used by Krein in his study of the corresponding second
order ODE .Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse
Problems (http://www.iop.org/EJ/journal/IP
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