123 research outputs found
Quantum mechanics with a time-dependent random unitary Hamiltonian: A perturbative study of the nonlinear Keldysh sigma-model
We analyze the perturbative series of the Keldysh-type sigma-model proposed
recently for describing the quantum mechanics with time-dependent Hamiltonians
from the unitary Wigner-Dyson random-matrix ensemble. We observe that vertices
of orders higher than four cancel, which allows us to reduce the calculation of
the energy-diffusion constant to that in a special kind of the matrix \phi^4
model. We further verify that the perturbative four-loop correction to the
energy-diffusion constant in the high-velocity limit cancels, in agreement with
the conjecture of one of the authors.Comment: 27 pages, 15 figures; typos corrected, one reference adde
Dyson Pairs and Zero-Mass Black Holes
It has been argued by Dyson in the context of QED in flat spacetime that
perturbative expansions in powers of the electric charge e cannot be convergent
because if e is purely imaginary then the vacuum should be unstable to the
production of charged pairs. We investigate the spontaneous production of such
Dyson pairs in electrodynamics coupled to gravity. They are found to consist of
pairs of zero-rest mass black holes with regular horizons. The properties of
these zero rest mass black holes are discussed. We also consider ways in which
a dilaton may be included and the relevance of this to recent ideas in string
theory. We discuss accelerating solutions and find that, in certain
circumstances, the `no strut' condition may be satisfied giving a regular
solution describing a pair of zero rest mass black holes accelerating away from
one another. We also study wormhole and tachyonic solutions and how they affect
the stability of the vacuum.Comment: 41 pages LaTex, 5 figure
The Future Evolution of White Dwarf Stars Through Baryon Decay and Time Varying Gravitational Constant
Motivated by the possibility that the fundamental ``constants'' of nature
could vary with time, this paper considers the long term evolution of white
dwarf stars under the combined action of proton decay and variations in the
gravitational constant. White dwarfs are thus used as a theoretical laboratory
to study the effects of possible time variations, especially their implications
for the future history of the universe. More specifically, we consider the
gravitational constant to vary according to the parametric relation , where the time scale is the same order as
the proton lifetime. We then study the long term fate and evolution of white
dwarf stars. This treatment begins when proton decay dominates the stellar
luminosity, and ends when the star becomes optically thin to its internal
radiation.Comment: 12 pages, 10 figures, accepted to Astrophysics and Space Scienc
Survival of contact processes on the hierarchical group
We consider contact processes on the hierarchical group, where sites infect
other sites at a rate depending on their hierarchical distance, and sites
become healthy with a constant recovery rate. If the infection rates decay too
fast as a function of the hierarchical distance, then we show that the critical
recovery rate is zero. On the other hand, we derive sufficient conditions on
the speed of decay of the infection rates for the process to exhibit a
nontrivial phase transition between extinction and survival. For our sufficient
conditions, we use a coupling argument that compares contact processes on the
hierarchical group with freedom two with contact processes on a renormalized
lattice. An interesting novelty in this renormalization argument is the use of
a result due to Rogers and Pitman on Markov functionals.Comment: Minor changes compared to previous version. Final version. 30 pages.
1 figur
Bosonic Excitations in Random Media
We consider classical normal modes and non-interacting bosonic excitations in
disordered systems. We emphasise generic aspects of such problems and parallels
with disordered, non-interacting systems of fermions, and discuss in particular
the relevance for bosonic excitations of symmetry classes known in the
fermionic context. We also stress important differences between bosonic and
fermionic problems. One of these follows from the fact that ground state
stability of a system requires all bosonic excitation energy levels to be
positive, while stability in systems of non-interacting fermions is ensured by
the exclusion principle, whatever the single-particle energies. As a
consequence, simple models of uncorrelated disorder are less useful for bosonic
systems than for fermionic ones, and it is generally important to study the
excitation spectrum in conjunction with the problem of constructing a
disorder-dependent ground state: we show how a mapping to an operator with
chiral symmetry provides a useful tool for doing this. A second difference
involves the distinction for bosonic systems between excitations which are
Goldstone modes and those which are not. In the case of Goldstone modes we
review established results illustrating the fact that disorder decouples from
excitations in the low frequency limit, above a critical dimension , which
in different circumstances takes the values and . For bosonic
excitations which are not Goldstone modes, we argue that an excitation density
varying with frequency as is a universal
feature in systems with ground states that depend on the disorder realisation.
We illustrate our conclusions with extensive analytical and some numerical
calculations for a variety of models in one dimension
Banking union in historical perspective: the initiative of the European Commission in the 1960s-1970s
This article shows that planning for the organization of EU banking regulation and supervision did not just appear on the agenda in recent years with discussions over the creation of the eurozone banking union. It unveils a hitherto neglected initiative of the European Commission in the 1960s and early 1970s. Drawing on extensive archival work, this article explains that this initiative, however, rested on a number of different assumptions, and emerged in a much different context. It first explains that the Commission's initial project was not crisis-driven; that it articulated the link between monetary integration and banking regulation; and finally that it did not set out to move the supervisory framework to the supranational level, unlike present-day developments
The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin
We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in
the absence of an external field. Spin wave theory suggests that in a suitable
temperature regime the system behaves effectively as a system of
non-interacting bosons (magnons). We prove this fact at the level of the
specific free energy: if and the inverse temperature in such a way that stays constant, we rigorously show that
the free energy per unit volume converges to the one suggested by spin wave
theory. The proof is based on the localization of the system in small boxes and
on upper and lower bounds on the local free energy, and it also provides
explicit error bounds on the remainder.Comment: 11 pages, pdfLate
Moments of vicious walkers and M\"obius graph expansions
A system of Brownian motions in one-dimension all started from the origin and
conditioned never to collide with each other in a given finite time-interval
is studied. The spatial distribution of such vicious walkers can be
described by using the repulsive eigenvalue-statistics of random Hermitian
matrices and it was shown that the present vicious walker model exhibits a
transition from the Gaussian unitary ensemble (GUE) statistics to the Gaussian
orthogonal ensemble (GOE) statistics as the time is going on from 0 to .
In the present paper, we characterize this GUE-to-GOE transition by presenting
the graphical expansion formula for the moments of positions of vicious
walkers. In the GUE limit , only the ribbon graphs contribute and the
problem is reduced to the classification of orientable surfaces by genus.
Following the time evolution of the vicious walkers, however, the graphs with
twisted ribbons, called M\"obius graphs, increase their contribution to our
expansion formula, and we have to deal with the topology of non-orientable
surfaces. Application of the recent exact result of dynamical correlation
functions yields closed expressions for the coefficients in the M\"obius
expansion using the Stirling numbers of the first kind.Comment: REVTeX4, 11 pages, 1 figure. v.2: calculations of the Green function
and references added. v.3: minor additions and corrections made for
publication in Phys.Rev.
Dynamic Evolution Model of Isothermal Voids and Shocks
We explore self-similar hydrodynamic evolution of central voids embedded in
an isothermal gas of spherical symmetry under the self-gravity. More
specifically, we study voids expanding at constant radial speeds in an
isothermal gas and construct all types of possible void solutions without or
with shocks in surrounding envelopes. We examine properties of void boundaries
and outer envelopes. Voids without shocks are all bounded by overdense shells
and either inflows or outflows in the outer envelope may occur. These
solutions, referred to as type void solutions, are further
divided into subtypes and
according to their characteristic behaviours across the sonic critical line
(SCL). Void solutions with shocks in envelopes are referred to as type
voids and can have both dense and quasi-smooth edges.
Asymptotically, outflows, breezes, inflows, accretions and static outer
envelopes may all surround such type voids. Both cases of
constant and varying temperatures across isothermal shock fronts are analyzed;
they are referred to as types and
void shock solutions. We apply the `phase net matching procedure' to construct
various self-similar void solutions. We also present analysis on void
generation mechanisms and describe several astrophysical applications. By
including self-gravity, gas pressure and shocks, our isothermal self-similar
void (ISSV) model is adaptable to various astrophysical systems such as
planetary nebulae, hot bubbles and superbubbles in the interstellar medium as
well as supernova remnants.Comment: 24 pages, 13 figuers, accepted by ApS
Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices
Spatially and temporally inhomogeneous evolution of one-dimensional vicious
walkers with wall restriction is studied. We show that its continuum version is
equivalent with a noncolliding system of stochastic processes called Brownian
meanders. Here the Brownian meander is a temporally inhomogeneous process
introduced by Yor as a transform of the Bessel process that is a motion of
radial coordinate of the three-dimensional Brownian motion represented in the
spherical coordinates. It is proved that the spatial distribution of vicious
walkers with a wall at the origin can be described by the eigenvalue-statistics
of Gaussian ensembles of Bogoliubov-deGennes Hamiltonians of the mean-field
theory of superconductivity, which have the particle-hole symmetry. We report
that the time evolution of the present stochastic process is fully
characterized by the change of symmetry classes from the type to the type
I in the nonstandard classes of random matrix theory of Altland and
Zirnbauer. The relation between the non-colliding systems of the generalized
meanders of Yor, which are associated with the even-dimensional Bessel
processes, and the chiral random matrix theory is also clarified.Comment: REVTeX4, 16 pages, 4 figures. v2: some additions and correction
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