1,489 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
On the Green-Functions of the classical offshell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg
In previous paper derivations of the Green function have been given for 5D
off-shell electrodynamics in the framework of the manifestly covariant
relativistic dynamics of Stueckelberg (with invariant evolution parameter
). In this paper, we reconcile these derivations resulting in different
explicit forms, and relate our results to the conventional fundamental
solutions of linear 5D wave equations published in the mathematical literature.
We give physical arguments for the choice of the Green function retarded in the
fifth variable .Comment: 16 pages, 1 figur
Locating Boosted Kerr and Schwarzschild Apparent Horizons
We describe a finite-difference method for locating apparent horizons and
illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our
model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to
this spacetime metric and then carry out a 3+1 decomposition. The result is a
slicing of Kerr/Schwarzschild in which the black hole is propagated and Lorentz
contracted. We show that our method can locate distorted apparent horizons
efficiently and accurately.Comment: Submitted to Physical Review D. 12 pages and 22 figure
Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints
The statistical mechanics of quantum-classical systems with holonomic
constraints is formulated rigorously by unifying the classical Dirac bracket
and the quantum-classical bracket in matrix form.
The resulting Dirac quantum-classical theory, which conserves the holonomic
constraints exactly, is then used to formulate time evolution and statistical
mechanics. The correct momentum-jump approximation for constrained system
arises naturally from this formalism. Finally, in analogy with what was found
in the classical case, it is shown that the rigorous linear response function
of constrained quantum-classical systems contains non-trivial additional terms
which are absent in the response of unconstrained systems.Comment: Submitted to Journal of Chemical Physic
Quantitative estimates of discrete harmonic measures
A theorem of Bourgain states that the harmonic measure for a domain in
is supported on a set of Hausdorff dimension strictly less than
\cite{Bourgain}. We apply Bourgain's method to the discrete case, i.e., to the
distribution of the first entrance point of a random walk into a subset of , . By refining the argument, we prove that for all \b>0 there
exists \rho (d,\b)N(d,\b), any , and any | \{y\in\Z^d\colon \nu_{A,x}(y)
\geq n^{-\b} \}| \leq n^{\rho(d,\b)}, where denotes the
probability that is the first entrance point of the simple random walk
starting at into . Furthermore, must converge to as \b \to
\infty.Comment: 16 pages, 2 figures. Part (B) of the theorem is ne
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
The Exotic Statistics of Leapfrogging Smoke Rings
The leapfrogging motion of smoke rings is a three dimensional version of the
motion that in two dimensions leads to exotic exchange statistics. The
statistical phase factor can be computed using the hydrodynamical Euler
equation, which is a universal law for describing the properties of a large
class of fluids. This suggests that three dimensional exotic exchange
statistics is a common property of closed vortex loops in a variety of quantum
liquids and gases, from helium superfluids to Bose-Einstein condensed alkali
gases, metallic hydrogen in its liquid phases and maybe even nuclear matter in
extreme conditions.Comment: 9 pages 1 figur
Upper and lower bounds on the mean square radius and criteria for occurrence of quantum halo states
In the context of non-relativistic quantum mechanics, we obtain several upper
and lower limits on the mean square radius applicable to systems composed by
two-body bound by a central potential. A lower limit on the mean square radius
is used to obtain a simple criteria for the occurrence of S-wave quantum halo
sates.Comment: 12 pages, 2 figure
Seven exercises planned to stimulate the flow of ideas in creative composition
Thesis (Ed.M.)--Boston Universit
Solving the brachistochrone and other variational problems with soap films
We show a method to solve the problem of the brachistochrone as well as other
variational problems with the help of the soap films that are formed between
two suitable surfaces. We also show the interesting connection between some
variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction,
has been submitted to the American Journal of Physic
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