365 research outputs found
Total Widths And Slopes From Complex Regge Trajectories
Maximally complex Regge trajectories are introduced for which both Re
and Im grow as ( small and
positive). Our expression reduces to the standard real linear form as the
imaginary part (proportional to ) goes to zero. A scaling formula for
the total widths emerges: constant for large M, in very
good agreement with data for mesons and baryons. The unitarity corrections also
enhance the space-like slopes from their time-like values, thereby resolving an
old problem with the trajectory in charge exchange. Finally, the
unitarily enhanced intercept, , \nolinebreak is in
good accord with the Donnachie-Landshoff total cross section analysis.Comment: 9 pages, 3 Figure
Entanglement and nonclassicality for multi-mode radiation field states
Nonclassicality in the sense of quantum optics is a prerequisite for
entanglement in multi-mode radiation states. In this work we bring out the
possibilities of passing from the former to the latter, via action of
classicality preserving systems like beamsplitters, in a transparent manner.
For single mode states, a complete description of nonclassicality is available
via the classical theory of moments, as a set of necessary and sufficient
conditions on the photon number distribution. We show that when the mode is
coupled to an ancilla in any coherent state, and the system is then acted upon
by a beamsplitter, these conditions turn exactly into signatures of NPT
entanglement of the output state. Since the classical moment problem does not
generalize to two or more modes, we turn in these cases to other familiar
sufficient but not necessary conditions for nonclassicality, namely the Mandel
parameter criterion and its extensions. We generalize the Mandel matrix from
one-mode states to the two-mode situation, leading to a natural classification
of states with varying levels of nonclassicality. For two--mode states we
present a single test that can, if successful, simultaneously show
nonclassicality as well as NPT entanglement. We also develop a test for NPT
entanglement after beamsplitter action on a nonclassical state, tracing
carefully the way in which it goes beyond the Mandel nonclassicality test. The
result of three--mode beamsplitter action after coupling to an ancilla in the
ground state is treated in the same spirit. The concept of genuine tripartite
entanglement, and scalar measures of nonclassicality at the Mandel level for
two-mode systems, are discussed. Numerous examples illustrating all these
concepts are presented.Comment: Latex, 46 page
Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz
We apply the maximum entropy principle to construct the natural invariant
density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel
function reconstruction technique that is based on the solution of Hausdorff
moment problem via maximizing Shannon entropy, we estimate the invariant
density and the Lyapunov exponent of nonlinear maps in one-dimension from a
knowledge of finite number of moments. The accuracy and the stability of the
algorithm are illustrated by comparing our results to a number of nonlinear
maps for which the exact analytical results are available. Furthermore, we also
consider a very complex example for which no exact analytical result for
invariant density is available. A comparison of our results to those available
in the literature is also discussed.Comment: 16 pages including 6 figure
Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory
The method of the quantum probability theory only requires simple structural
data of graph and allows us to avoid a heavy combinational argument often
necessary to obtain full description of spectrum of the adjacency matrix. In
the present paper, by using the idea of calculation of the probability
amplitudes for continuous-time quantum walk in terms of the quantum probability
theory, we investigate quantum central limit theorem for continuous-time
quantum walks on odd graphs.Comment: 19 page, 1 figure
Function reconstruction as a classical moment problem: A maximum entropy approach
We present a systematic study of the reconstruction of a non-negative
function via maximum entropy approach utilizing the information contained in a
finite number of moments of the function. For testing the efficacy of the
approach, we reconstruct a set of functions using an iterative entropy
optimization scheme, and study the convergence profile as the number of moments
is increased. We consider a wide variety of functions that include a
distribution with a sharp discontinuity, a rapidly oscillatory function, a
distribution with singularities, and finally a distribution with several spikes
and fine structure. The last example is important in the context of the
determination of the natural density of the logistic map. The convergence of
the method is studied by comparing the moments of the approximated functions
with the exact ones. Furthermore, by varying the number of moments and
iterations, we examine to what extent the features of the functions, such as
the divergence behavior at singular points within the interval, is reproduced.
The proximity of the reconstructed maximum entropy solution to the exact
solution is examined via Kullback-Leibler divergence and variation measures for
different number of moments.Comment: 20 pages, 17 figure
Generating Bounds for the Ground State Energy of the Infinite Quantum Lens Potential
Moment based methods have produced efficient multiscale quantization
algorithms for solving singular perturbation/strong coupling problems. One of
these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev.
Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converging
lower and upper bounds to a specific discrete state energy, once the signature
property of the associated wavefunction is known. This method is particularly
effective for multidimensional, bosonic ground state problems, since the
corresponding wavefunction must be of uniform signature, and can be taken to be
positive. Despite this, the vast majority of problems studied have been on
unbounded domains. The important problem of an electron in an infinite quantum
lens potential defines a challenging extension of EMM to systems defined on a
compact domain. We investigate this here, and introduce novel modifications to
the conventional EMM formalism that facilitate its adaptability to the required
boundary conditions.Comment: Submitted to J. Phys.
A Convergent Method for Calculating the Properties of Many Interacting Electrons
A method is presented for calculating binding energies and other properties
of extended interacting systems using the projected density of transitions
(PDoT) which is the probability distribution for transitions of different
energies induced by a given localized operator, the operator on which the
transitions are projected. It is shown that the transition contributing to the
PDoT at each energy is the one which disturbs the system least, and so, by
projecting on appropriate operators, the binding energies of equilibrium
electronic states and the energies of their elementary excitations can be
calculated. The PDoT may be expanded as a continued fraction by the recursion
method, and as in other cases the continued fraction converges exponentially
with the number of arithmetic operations, independent of the size of the
system, in contrast to other numerical methods for which the number of
operations increases with system size to maintain a given accuracy. These
properties are illustrated with a calculation of the binding energies and
zone-boundary spin- wave energies for an infinite spin-1/2 Heisenberg chain,
which is compared with analytic results for this system and extrapolations from
finite rings of spins.Comment: 30 pages, 4 figures, corrected pd
Vector Continued Fractions using a Generalised Inverse
A real vector space combined with an inverse for vectors is sufficient to
define a vector continued fraction whose parameters consist of vector shifts
and changes of scale. The choice of sign for different components of the vector
inverse permits construction of vector analogues of the Jacobi continued
fraction. These vector Jacobi fractions are related to vector and scalar-valued
polynomial functions of the vectors, which satisfy recurrence relations similar
to those of orthogonal polynomials. The vector Jacobi fraction has strong
convergence properties which are demonstrated analytically, and illustrated
numerically.Comment: Published form - minor change
Inverting the Sachs-Wolfe Formula: an Inverse Problem Arising in Early-Universe Cosmology
The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to
the temperature variations in the cosmic microwave background
radiation; can be observed in all directions around us. A standard
but idealised model of this effect leads to an infinite set of moment-like
equations: the integral of with respect to k ()
is equal to a given constant, , for . Here, P is the
power spectrum of the primordial density variations, is a spherical
Bessel function and y is a positive constant. It is shown how to solve these
equations exactly for ~. The same solution can be recovered, in
principle, if the first ~m equations are discarded. Comparisons with classical
moment problems (where is replaced by ) are made.Comment: In Press Inverse Problems 1999, 15 pages, 0 figures, Late
Two-band random matrices
Spectral correlations in unitary invariant, non-Gaussian ensembles of large
random matrices possessing an eigenvalue gap are studied within the framework
of the orthogonal polynomial technique. Both local and global characteristics
of spectra are directly reconstructed from the recurrence equation for
orthogonal polynomials associated with a given random matrix ensemble. It is
established that an eigenvalue gap does not affect the local eigenvalue
correlations which follow the universal sine and the universal multicritical
laws in the bulk and soft-edge scaling limits, respectively. By contrast,
global smoothed eigenvalue correlations do reflect the presence of a gap, and
are shown to satisfy a new universal law exhibiting a sharp dependence on the
odd/even dimension of random matrices whose spectra are bounded. In the case of
unbounded spectrum, the corresponding universal `density-density' correlator is
conjectured to be generic for chaotic systems with a forbidden gap and broken
time reversal symmetry.Comment: 12 pages (latex), references added, discussion enlarge
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