1,962 research outputs found
Nodal domains on quantum graphs
We consider the real eigenfunctions of the Schr\"odinger operator on graphs,
and count their nodal domains. The number of nodal domains fluctuates within an
interval whose size equals the number of bonds . For well connected graphs,
with incommensurate bond lengths, the distribution of the number of nodal
domains in the interval mentioned above approaches a Gaussian distribution in
the limit when the number of vertices is large. The approach to this limit is
not simple, and we discuss it in detail. At the same time we define a random
wave model for graphs, and compare the predictions of this model with analytic
and numerical computations.Comment: 19 pages, uses IOP journal style file
Symplectic tracking using point magnets and a reference orbit made of circular arcs and straight lines
Symplectic tracking of beam particles using point magnets is achieved using a
reference orbit made of circular arcs and straight lines that join smoothly
with each other. For this choice of the reference orbit, results are given for
the transfer functions, transfer matrices, and the transit times of the magnets
and drift spaces. These results provide a symplectic integrator, and allow the
linear orbit parameters to be computed by multiplying transfer matrices. It is
shown that this integrator is a second-order integrator, and that the transfer
functions can be derived from a hamiltonian.Comment: 16 pages, PDF fil
Nonlocal spectral properties of disordered alloys
A general method is proposed for calculating a fully k-dependent, continuous,
and causal spectral function A(k,E) within the recently introduced nonlocal
version of the coherent-potential approximation (NLCPA). The method involves
the combination of both periodic and anti-periodic solutions to the associated
cluster problem and also leads to correct bulk quantities for small cluster
sizes. We illustrate the method by investigating the Fermi surface of a
two-dimensional alloy. Dramatically, we find a smeared electronic topological
transition not predicted by the conventional CPA.Comment: 17 pages, 5 figures, Submitted to: J. Phys.: Condens. Matter
Editorial receipt 25 May 200
Proof that the Hydrogen-antihydrogen Molecule is Unstable
In the framework of nonrelativistic quantum mechanics we derive a necessary
condition for four Coulomb charges ,
where all masses are assumed finite, to form the stable system. The obtained
stability condition is physical and is expressed through the required minimal
ratio of Jacobi masses. In particular this provides the rigorous proof that the
hydrogen-antihydrogen molecule is unstable. This is the first result of this
sort for four particles.Comment: Submitted to Phys.Rev.Let
Effective capillary interaction of spherical particles at fluid interfaces
We present a detailed analysis of the effective force between two smooth
spherical colloids floating at a fluid interface due to deformations of the
interface. The results hold in general and are applicable independently of the
source of the deformation provided the capillary deformations are small so that
a superposition approximation for the deformations is valid. We conclude that
an effective long--ranged attraction is possible if the net force on the system
does not vanish. Otherwise, the interaction is short--ranged and cannot be
computed reliably based on the superposition approximation. As an application,
we consider the case of like--charged, smooth nanoparticles and
electrostatically induced capillary deformation. The resulting long--ranged
capillary attraction can be easily tuned by a relatively small external
electrostatic field, but it cannot explain recent experimental observations of
attraction if these experimental systems were indeed isolated.Comment: 23 page
Sub-leading contributions to the black hole entropy in the brick wall approach
[Abridged] We compute the canonical entropy of a quantum scalar field around
static and spherically symmetric black holes through the brick wall approach at
the higher orders (in fact, up to the sixth order in \hbar) in the WKB
approximation. We explicitly show that the brick wall model generally predicts
corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. In
four dimensions, we find that the corrections to the Bekenstein-Hawking entropy
are of the form (A^n \log A), while, in six dimensions, the corrections behave
as (A^m + A^n \log A), where A denotes the area of the black hole event
horizon, and (m, n) < 1. We compare our results with the corrections to the
Bekenstein-Hawking entropy that have been obtained through the other approaches
in the literature, and discuss the implications.Comment: 21 pages, Revtex 4; Final verson - 22 pages, References added,
Accepted in Phys. Rev.
Optimal Renormalization-Group Improvement of R(s) via the Method of Characteristics
We discuss the application of the method of characteristics to the
renormalization-group equation for the perturbative QCD series within the
electron-positron annihilation cross-section. We demonstrate how one such
renormalization-group improvement of this series is equivalent to a closed-form
summation of the first four towers of renormalization-group accessible
logarithms to all orders of perturbation theory
Exact Solutions of a Model for Granular Avalanches
We present exact solutions of the non-linear {\sc bcre} model for granular
avalanches without diffusion. We assume a generic sandpile profile consisting
of two regions of constant but different slope. Our solution is constructed in
terms of characteristic curves from which several novel predictions for
experiments on avalanches are deduced: Analytical results are given for the
shock condition, shock coordinates, universal quantities at the shock, slope
relaxation at large times, velocities of the active region and of the sandpile
profile.Comment: 7 pages, 2 figure
Gas-dynamic shock heating of post-flare loops due to retraction following localized, impulsive reconnection
We present a novel model in which shortening of a magnetic flux tube
following localized, three-dimensional reconnection generates strong
gas-dynamic shocks around its apex. The shortening releases magnetic energy by
progressing away from the reconnection site at the Alfven speed. This launches
inward flows along the field lines whose collision creates a pair of
gas-dynamic shocks. The shocks raise both the mass density and temperature
inside the newly shortened flux tube. Reconnecting field lines whose initial
directions differ by more that 100 degrees can produce a concentrated knot of
plasma hotter that 20 MK, consistent with observations. In spite of these high
temperatures, the shocks convert less than 10% of the liberated magnetic energy
into heat - the rest remains as kinetic energy of bulk motion. These
gas-dynamic shocks arise only when the reconnection is impulsive and localized
in all three dimensions; they are distinct from the slow magnetosonic shocks of
the Petschek steady-state reconnection model
Fredholm's Minors of Arbitrary Order: Their Representations as a Determinant of Resolvents and in Terms of Free Fermions and an Explicit Formula for Their Functional Derivative
We study the Fredholm minors associated with a Fredholm equation of the
second type. We present a couple of new linear recursion relations involving
the th and th minors, whose solution is a representation of the th
minor as an determinant of resolvents. The latter is given a simple
interpretation in terms of a path integral over non-interacting fermions. We
also provide an explicit formula for the functional derivative of a Fredholm
minor of order with respect to the kernel. Our formula is a linear
combination of the th and the th minors.Comment: 17 pages, Latex, no figures connection to supplementary compound
matrices mentioned, references added, typos correcte
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