581 research outputs found
Multiple addition theorem for discrete and continuous nonlinear problems
The addition relation for the Riemann theta functions and for its limits,
which lead to the appearance of exponential functions in soliton type equations
is discussed. The presented form of addition property resolves itself to the
factorization of N-tuple product of the shifted functions and it seems to be
useful for analysis of soliton type continuous and discrete processes in the
N+1 space-time. A close relation with the natural generalization of bi- and
tri-linear operators into multiple linear operators concludes the paper.Comment: 9 page
A Rapid Dynamical Monte Carlo Algorithm for Glassy Systems
In this paper we present a dynamical Monte Carlo algorithm which is
applicable to systems satisfying a clustering condition: during the dynamical
evolution the system is mostly trapped in deep local minima (as happens in
glasses, pinning problems etc.). We compare the algorithm to the usual Monte
Carlo algorithm, using as an example the Bernasconi model. In this model, a
straightforward implementation of the algorithm gives an improvement of several
orders of magnitude in computational speed with respect to a recent, already
very efficient, implementation of the algorithm of Bortz, Kalos and Lebowitz.Comment: RevTex 7 pages + 4 figures (uuencoded) appended; LPS preprin
Network synchronization: Optimal and Pessimal Scale-Free Topologies
By employing a recently introduced optimization algorithm we explicitely
design optimally synchronizable (unweighted) networks for any given scale-free
degree distribution. We explore how the optimization process affects
degree-degree correlations and observe a generic tendency towards
disassortativity. Still, we show that there is not a one-to-one correspondence
between synchronizability and disassortativity. On the other hand, we study the
nature of optimally un-synchronizable networks, that is, networks whose
topology minimizes the range of stability of the synchronous state. The
resulting ``pessimal networks'' turn out to have a highly assortative
string-like structure. We also derive a rigorous lower bound for the Laplacian
eigenvalue ratio controlling synchronizability, which helps understanding the
impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex
Networks 2007
Tests of Basic Quantum Mechanics in Oscillation Experiments
According to standard quantum theory, the time evolution operator of a
quantum system is independent of the state of the system. One can, however,
consider systems in which this is not the case: the evolution operator may
depend on the density operator itself. The presence of such modifications of
quantum theory can be tested in long baseline oscillation experiments.Comment: 8 pages, LaTeX; no macros neede
A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate Event Horizon related to an Extreme Reissner-Nordstr\"om Black Hole
Thermal Wightman functions of a massless scalar field are studied within the
framework of a ``near horizon'' static background model of an extremal R-N
black hole. This model is built up by using global Carter-like coordinates over
an infinite set of Bertotti-Robinson submanifolds glued together. The
analytical extendibility beyond the horizon is imposed as constraints on
(thermal) Wightman's functions defined on a Bertotti-Robinson sub manifold. It
turns out that only the Bertotti-Robinson vacuum state, i.e. , satisfies
the above requirement. Furthermore the extension of this state onto the whole
manifold is proved to coincide exactly with the vacuum state in the global
Carter-like coordinates. Hence a theorem similar to Bisognano-Wichmann theorem
for the Minkowski space-time in terms of Wightman functions holds with
vanishing ``Unruh-Rindler temperature''. Furtermore, the Carter-like vacuum
restricted to a Bertotti-Robinson region, resulting a pure state there, has
vanishing entropy despite of the presence of event horizons. Some comments on
the real extreme R-N black hole are given
Casimir effect due to a single boundary as a manifestation of the Weyl problem
The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases
the divergences can be eliminated by methods such as zeta-function
regularization or through physical arguments (ultraviolet transparency of the
boundary would provide a cutoff). Using the example of a massless scalar field
theory with a single Dirichlet boundary we explore the relationship between
such approaches, with the goal of better understanding the origin of the
divergences. We are guided by the insight due to Dowker and Kennedy (1978) and
Deutsch and Candelas (1979), that the divergences represent measurable effects
that can be interpreted with the aid of the theory of the asymptotic
distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases
the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having
geometrical origin, and an "intrinsic" term that is independent of the cutoff.
The Weyl terms make a measurable contribution to the physical situation even
when regularization methods succeed in isolating the intrinsic part.
Regularization methods fail when the Weyl terms and intrinsic parts of the
Casimir effect cannot be clearly separated. Specifically, we demonstrate that
the Casimir self-energy of a smooth boundary in two dimensions is a sum of two
Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a
geometrical term that is independent of cutoff, and a non-geometrical intrinsic
term. As by-products we resolve the puzzle of the divergent Casimir force on a
ring and correct the sign of the coefficient of linear tension of the Dirichlet
line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references
added, version to be published in J. Phys.
Neutrino masses in the Lepton Number Violating MSSM
We consider the most general supersymmetric model with minimal particle
content and an additional discrete Z_3 symmetry (instead of R-parity), which
allows lepton number violating terms and results in non-zero Majorana neutrino
masses. We investigate whether the currently measured values for lepton masses
and mixing can be reproduced. We set up a framework in which Lagrangian
parameters can be initialised without recourse to assumptions concerning
trilinear or bilinear superpotential terms, CP-conservation or
intergenerational mixing and analyse in detail the one loop corrections to the
neutrino masses. We present scenarios in which the experimental data are
reproduced and show the effect varying lepton number violating couplings has on
the predicted atmospheric and solar mass^2 differences. We find that with
bilinear lepton number violating couplings in the superpotential of the order 1
MeV the atmospheric mass scale can be reproduced. Certain trilinear
superpotential couplings, usually, of the order of the electron Yukawa coupling
can give rise to either atmospheric or solar mass scales and bilinear
supersymmetry breaking terms of the order 0.1 GeV^2 can set the solar mass
scale. Further details of our calculation, Lagrangian, Feynman rules and
relevant generic loop diagrams, are presented in three Appendices.Comment: 48 pages, 7 figures, v2 references added, typos corrected, published
versio
On the Thermodynamics of Simple Non-Isentropic Perfect Fluids in General Relativity
We examine the consistency of the thermodynamics of irrotational and
non-isentropic perfect fluids complying with matter conservation by looking at
the integrability conditions of the Gibbs-Duhem relation. We show that the
latter is always integrable for fluids of the following types: (a) static, (b)
isentropic (admits a barotropic equation of state), (c) the source of a
spacetime for which , where is the dimension of the orbit of the
isometry group. This consistency scheme is tested also in two large classes of
known exact solutions for which , in general: perfect fluid Szekeres
solutions (classes I and II). In none of these cases, the Gibbs-Duhem relation
is integrable, in general, though specific particular cases of Szekeres class
II (all complying with ) are identified for which the integrability of
this relation can be achieved. We show that Szekeres class I solutions satisfy
the integrability conditions only in two trivial cases, namely the spherically
symmetric limiting case and the Friedman-Roberson-Walker (FRW) cosmology.
Explicit forms of the state variables and equations of state linking them are
given explicitly and discussed in relation to the FRW limits of the solutions.
We show that fixing free parameters in these solutions by a formal
identification with FRW parameters leads, in all cases examined, to unphysical
temperature evolution laws, quite unrelated to those of their FRW limiting
cosmologies.Comment: 29 pages, Plain.Te
Anderson localization on the Cayley tree : multifractal statistics of the transmission at criticality and off criticality
In contrast to finite dimensions where disordered systems display
multifractal statistics only at criticality, the tree geometry induces
multifractal statistics for disordered systems also off criticality. For the
Anderson tight-binding localization model defined on a tree of branching ratio
K=2 with generations, we consider the Miller-Derrida scattering geometry
[J. Stat. Phys. 75, 357 (1994)], where an incoming wire is attached to the root
of the tree, and where outcoming wires are attached to the leaves of
the tree. In terms of the transmission amplitudes , the total
Landauer transmission is , so that each channel
is characterized by the weight . We numerically measure the
typical multifractal singularity spectrum of these weights as a
function of the disorder strength and we obtain the following conclusions
for its left-termination point . In the delocalized phase ,
is strictly positive and is associated with a
moment index . At criticality, it vanishes and is
associated with the moment index . In the localized phase ,
is associated with some moment index . We discuss the
similarities with the exact results concerning the multifractal properties of
the Directed Polymer on the Cayley tree.Comment: v2=final version (16 pages
The quantum state vector in phase space and Gabor's windowed Fourier transform
Representations of quantum state vectors by complex phase space amplitudes,
complementing the description of the density operator by the Wigner function,
have been defined by applying the Weyl-Wigner transform to dyadic operators,
linear in the state vector and anti-linear in a fixed `window state vector'.
Here aspects of this construction are explored, with emphasis on the connection
with Gabor's `windowed Fourier transform'. The amplitudes that arise for simple
quantum states from various choices of window are presented as illustrations.
Generalized Bargmann representations of the state vector appear as special
cases, associated with Gaussian windows. For every choice of window, amplitudes
lie in a corresponding linear subspace of square-integrable functions on phase
space. A generalized Born interpretation of amplitudes is described, with both
the Wigner function and a generalized Husimi function appearing as quantities
linear in an amplitude and anti-linear in its complex conjugate.
Schr\"odinger's time-dependent and time-independent equations are represented
on phase space amplitudes, and their solutions described in simple cases.Comment: 36 pages, 6 figures. Revised in light of referees' comments, and
further references adde
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