313 research outputs found
Berry Phase of a Resonant State
We derive closed analytical expressions for the complex Berry phase of an
open quantum system in a state which is a superposition of resonant states and
evolves irreversibly due to the spontaneous decay of the metastable states. The
codimension of an accidental degeneracy of resonances and the geometry of the
energy hypersurfaces close to a crossing of resonances differ significantly
from those of bound states. We discuss some of the consequences of these
differences for the geometric phase factors, such as: Instead of a diabolical
point singularity there is a continuous closed line of singularities formally
equivalent to a continuous distribution of `magnetic' charge on a diabolical
circle; different classes of topologically inequivalent non-trivial closed
paths in parameter space, the topological invariant associated to the sum of
the geometric phases, dilations of the wave function due to the imaginary part
of the Berry phase and others.Comment: 28 pages Latex, three uuencoded postcript figure
Random Networks with given Rich-club Coefficient
In complex networks it is common to model a network or generate a surrogate
network based on the conservation of the network's degree distribution. We
provide an alternative network model based on the conservation of connection
density within a set of nodes. This density is measure by the rich-club
coefficient. We present a method to generate surrogates networks with a given
rich-club coefficient. We show that by choosing a suitable local linking term,
the generated random networks can reproduce the degree distribution and the
mixing pattern of real networks. The method is easy to implement and produces
good models of real networks.Comment: revised version, new figure
Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories
The most general action, quadratic in the B fields as well as in the
curvature F, having SO(3,1) or SO(4) as the internal gauge group for a
four-dimensional BF theory is presented and its symplectic geometry is
displayed. It is shown that the space of solutions to the equations of motion
for the BF theory can be endowed with symplectic structures alternative to the
usual one. The analysis also includes topological terms and cosmological
constant. The implications of this fact for gravity are briefly discussed.Comment: 13 pages, LaTeX file, no figure
S_3-flavour symmetry as realized in lepton flavour violating processes
A variety of lepton flavour violating effects related to the recent discovery
of neutrino oscillations and mixings is here systematically discussed in terms
of an S_3-flavour permutational symmetry. After a brief review of some relevant
results on lepton masses and mixings, that had been derived in the framework of
a Minimal S_3-Invariant Extension of the Standard Model, we derive explicit
analytical expressions for the matrices of the Yukawa couplings and compute the
branching ratios of some selected flavour changing neutral current (FCNC)
processes, as well as, the contribution of the exchange of neutral flavour
changing scalars to the anomaly of the muon's magnetic moment as functions of
the masses of the charged leptons and the neutral Higgs bosons. We find that
the S_3 x Z_2 flavour symmetry and the strong mass hierarchy of the charged
leptons strongly suppress the FCNC processes in the leptonic sector well below
the present experimental upper bounds by many orders of magnitude. The
contribution of FCNC to the anomaly of the muon's magnetic moment is small but
non-negligible.Comment: 23 pages, one figure. To appear in J. Phys A: Mathematical and
Theoretical (SPE QTS5
Analogs of the double-Reissner-Nordstrom solution in magnetostatics and dilaton gravity: mathematical description and some physical properties
In this paper we consider a magnetic analog of the double-Reissner-Nordstrom
solution and construct the corresponding magnetic potential A_\varphi in the
explicit form. The behavior of the resulting solution under the Harrison
transformation then naturally singles out the asymmetric black diholes -
configurations composed of two non-extreme black holes possessing unequal
masses, and charges equal in magnitude but opposite in sign - as its most
general subclass for which equilibrium of the black-hole constituents can be
achieved with the aid of the external magnetic (or electric) field. We also
generalize the double-Reissner-Nordstrom solution to the dilaton gravity with
arbitrary dilaton coupling, yielding as the result the 4-dimensional
double-Gibbons-Maeda spacetime. The study of some physical properties of the
solutions obtained leads, in particular, to very simple formulas for the areas
of the horizons and surface gravities.Comment: 18 pages, 1 figure; title changed, typos corrected; a considerably
extended version which includes the discussion of the magnetostatic case and
the explicit formula for the magnetic potentia
Rigged Hilbert Space Approach to the Schrodinger Equation
It is shown that the natural framework for the solutions of any Schrodinger
equation whose spectrum has a continuous part is the Rigged Hilbert Space
rather than just the Hilbert space. The difficulties of using only the Hilbert
space to handle unbounded Schrodinger Hamiltonians whose spectrum has a
continuous part are disclosed. Those difficulties are overcome by using an
appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an
eigenket to each energy in the spectrum of the Hamiltonian, regardless of
whether the energy belongs to the discrete or to the continuous part of the
spectrum. The collection of eigenkets corresponding to both discrete and
continuous spectra forms a basis system that can be used to expand any physical
wave function. Thus the RHS treats discrete energies (discrete spectrum) and
scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page
Temporally correlated zero-range process with open boundaries: Steady state and fluctuations
19 pages, 14 figures, v2: minor revisions, close to final published version at http://dx.doi.org/10.1103/PhysRevE.92.02213
Phase transitions in packet traffic on regular networks: a comparison of source types and topologies
Abstract We extend the packet traffic network models developed in recent years for rectangular grids to other regular networks, and to fragmented networks. The packet transfer mechanism is open-loop as before. The nodes of the network are either hosts or routers. Both can receive and transmit packets towards their destination; hosts can also create and receive packets. Long range dependent traffic with varying Hurst parameter is introduced at the host nodes of these networks, and comparative studies of the onset of congestion are carried out. Results show statistical robustness when the rectangular grid is adapted to form other regular networks. Qualitative behavior is the same, and simple mean field models accurately predict critical points as in the rectangular case. R/S-statistics show the presence of long range dependence even when sources are short range dependent. Results indicate that this long range dependence is closely linked to the queueing mechanism
Structural constraints in complex networks
We present a link rewiring mechanism to produce surrogates of a network where
both the degree distribution and the rich--club connectivity are preserved. We
consider three real networks, the AS--Internet, the protein interaction and the
scientific collaboration. We show that for a given degree distribution, the
rich--club connectivity is sensitive to the degree--degree correlation, and on
the other hand the degree--degree correlation is constrained by the rich--club
connectivity. In particular, in the case of the Internet, the assortative
coefficient is always negative and a minor change in its value can reverse the
network's rich--club structure completely; while fixing the degree distribution
and the rich--club connectivity restricts the assortative coefficient to such a
narrow range, that a reasonable model of the Internet can be produced by
considering mainly the degree distribution and the rich--club connectivity. We
also comment on the suitability of using the maximal random network as a null
model to assess the rich--club connectivity in real networks.Comment: To appear in New Journal of Physics (www.njp.org
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