5,319 research outputs found
Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach
We determine the asymptotic level spacing distribution for the Laguerre
Ensemble in a single scaled interval, , containing no levels,
E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the
Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by
both Edelman and Forrester, while for , the leading terms of
, found by Tracy and Widom, are reproduced without the use of the
Bessel kernel and the associated Painlev\'e transcendent. In the same
approximation, the next leading term, due to a ``finite temperature''
perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe
Does Inflation Provide Natural Initial Conditions for the Universe?
If our universe underwent inflation, its entropy during the inflationary
phase was substantially lower than it is today. Because a low-entropy state is
less likely to be chosen randomly than a high-entropy one, inflation is
unlikely to arise through randomly-chosen initial conditions. To resolve this
puzzle, we examine the notion of a natural state for the universe, and argue
that it is a nearly-empty spacetime. If empty space has a small vacuum energy,
however, inflation can begin spontaneously in this background. This scenario
explains why a universe like ours is likely to have begun via a period of
inflation, and also provides an origin for the cosmological arrow of time.Comment: Submitted to Gravity Research Foundation Essay Competition; based on
hep-th/041027
Phonon emission and arrival times of electrons from a single-electron source
In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical-phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy
Anthropic tuning of the weak scale and of m_u/m_d in two-Higgs-doublet models
It is shown that in a model in which up-type and down-type fermions acquire
mass from different Higgs doublets, the anthropic tuning of the Higgs mass
parameters can explain the fact that the observed masses of the and
quarks are nearly the same with slightly heavier. If Yukawa couplings are
assumed not to "scan" (vary among domains), this would also help explain why
the t quark is much heavier than the b quark. It is also pointed out that the
existence of dark matter invalidates some earlier anthropic arguments against
the viability of domains where the Standard Model Higgs has positive ,
but makes other even stronger arguments possible.Comment: 31 pages, 7 figure
Relativistic Dyson Rings and Their Black Hole Limit
In this Letter we investigate uniformly rotating, homogeneous and
axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding
field equations are solved by means of a multi-domain spectral method, which
yields highly accurate numerical solutions. For a prescribed, sufficiently
large ratio of inner to outer coordinate radius, the toroids exhibit a
continuous transition to the extreme Kerr black hole. Otherwise, the most
relativistic configuration rotates at the mass-shedding limit. For a given
mass-density, there seems to be no bound to the gravitational mass as one
approaches the black-hole limit and a radius ratio of unity.Comment: 13 pages, 1 table, 5 figures, v2: some discussion and two references
added, accepted for publication in Astrophys. J. Let
Periodic orbit theory and spectral rigidity in pseudointegrable systems
We calculate numerically the periodic orbits of pseudointegrable systems of
low genus numbers that arise from rectangular systems with one or two
salient corners. From the periodic orbits, we calculate the spectral rigidity
using semiclassical quantum mechanics with reaching up to
quite large values. We find that the diagonal approximation is applicable when
averaging over a suitable energy interval. Comparing systems of various shapes
we find that our results agree well with calculated directly from
the eigenvalues by spectral statistics. Therefore, additional terms as e.g.
diffraction terms seem to be small in the case of the systems investigated in
this work. By reducing the size of the corners, the spectral statistics of our
pseudointegrable systems approaches the one of an integrable system, whereas
very large differences between integrable and pseudointegrable systems occur,
when the salient corners are large. Both types of behavior can be well
understood by the properties of the periodic orbits in the system
Quantum Heisenberg Chain with Long-Range Ferromagnetic Interactions at Low Temperature
A modified spin-wave theory is applied to the one-dimensional quantum
Heisenberg model with long-range ferromagnetic interactions. Low-temperature
properties of this model are investigated. The susceptibility and the specific
heat are calculated; the relation between their behaviors and strength of the
long-range interactions is obtained. This model includes both the
Haldane-Shastry model and the nearest-neighbor Heisenberg model; the
corresponding results in this paper are in agreement with the solutions of both
the models. It is shown that there exists an ordering transition in the region
where the model has longer-range interactions than the HS model. The critical
temperature is estimated.Comment: 17 pages(LaTeX REVTeX), 1 figure appended (PostScript), Technical
Report of ISSP A-274
Black Holes Surrounded by Uniformly Rotating Rings
Highly accurate numerical solutions to the problem of Black Holes surrounded
by uniformly rotating rings in axially symmetric, stationary spacetimes are
presented. The numerical methods developed to handle the problem are discussed
in some detail. Related Newtonian problems are described and numerical results
provided, which show that configurations can reach an inner mass-shedding limit
as the mass of the central object increases. Exemplary results for the full
relativistic problem for rings of constant density are given and the
deformation of the event horizon due to the presence of the ring is
demonstrated. Finally, we provide an example of a system for which the angular
momentum of the central Black Hole divided by the square of its mass exceeds
one.Comment: 12 pages, 14 figures, revtex, v4: minor changes, Eq. (17) corrected,
corresponds to version in PR
Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions
Quantum Heisenberg ferromagnets with long-range interactions decayin as
in one and two dimensions are investigated by means of the Green's
function method. It is shown that there exists a finite-temperature phase
transition in the region for the -dimensional case and that no
transitions at any finite temperature exist for ; the critical
temperature is also estimated. We study the magnetic properties of this model.
We calculate the critical exponents' dependence on ; these exponents also
satisfy a scaling relation. Some of the results were also found using the
modified spin-wave theory and are in remarkable agreement with each other.Comment: 13 pages(LaTeX REVTeX), 2 figures not included (postscript files
available on request), submitted to Phys.Rev.
Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization
Hamiltonian light-front field theory can be used to solve for hadron states
in QCD. To this end, a method has been developed for systematic renormalization
of Hamiltonian light-front field theories, with the hope of applying the method
to QCD. It assumed massless particles, so its immediate application to QCD is
limited to gluon states or states where quark masses can be neglected. This
paper builds on the previous work by including particle masses
non-perturbatively, which is necessary for a full treatment of QCD. We show
that several subtle new issues are encountered when including masses
non-perturbatively. The method with masses is algebraically and conceptually
more difficult; however, we focus on how the methods differ. We demonstrate the
method using massive phi^3 theory in 5+1 dimensions, which has important
similarities to QCD.Comment: 7 pages, 2 figures. Corrected error in Eq. (11), v3: Added extra
disclaimer after Eq. (2), and some clarification at end of Sec. 3.3. Final
published versio
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