251 research outputs found
Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics
We study self-adjoint operators defined by factorizing second order
differential operators in first order ones. We discuss examples where such
factorizations introduce singular interactions into simple quantum mechanical
models like the harmonic oscillator or the free particle on the circle. The
generalization of these examples to the many-body case yields quantum models of
distinguishable and interacting particles in one dimensions which can be solved
explicitly and by simple means. Our considerations lead us to a simple method
to construct exactly solvable quantum many-body systems of Calogero-Sutherland
type.Comment: 17 pages, LaTe
Critical sound attenuation in a diluted Ising system
The field-theoretic description of dynamical critical effects of the
influence of disorder on acoustic anomalies near the temperature of the
second-order phase transition is considered for three-dimensional Ising-like
systems. Calculations of the sound attenuation in pure and dilute Ising-like
systems near the critical point are presented. The dynamical scaling function
for the critical attenuation coefficient is calculated. The influence of
quenched disorder on the asymptotic behaviour of the critical ultrasonic
anomalies is discussed.Comment: 12 RevTeX pages, 4 figure
Lower order terms in Szego type limit theorems on Zoll manifolds
This is a detailed version of the paper math.FA/0212273. The main motivation
for this work was to find an explicit formula for a "Szego-regularized"
determinant of a zeroth order pseudodifferential operator (PsDO) on a Zoll
manifold. The idea of the Szego-regularization was suggested by V. Guillemin
and K. Okikiolu. They have computed the second term in a Szego type expansion
on a Zoll manifold of an arbitrary dimension. In the present work we compute
the third asymptotic term in any dimension. In the case of dimension 2, our
formula gives the above mentioned expression for the Szego-redularized
determinant of a zeroth order PsDO. The proof uses a new combinatorial
identity, which generalizes a formula due to G.A.Hunt and F.J.Dyson. This
identity is related to the distribution of the maximum of a random walk with
i.i.d. steps on the real line. The proof of this combinatorial identity
together with historical remarks and a discussion of probabilistic and
algebraic connections has been published separately.Comment: 39 pages, full version, submitte
Lieb-Thirring inequalities for geometrically induced bound states
We prove new inequalities of the Lieb-Thirring type on the eigenvalues of
Schr\"odinger operators in wave guides with local perturbations. The estimates
are optimal in the weak-coupling case. To illustrate their applications, we
consider, in particular, a straight strip and a straight circular tube with
either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page
Complex zeros of real ergodic eigenfunctions
We determine the limit distribution (as ) of complex
zeros for holomorphic continuations \phi_{\lambda}^{\C} to Grauert tubes of
real eigenfunctions of the Laplacian on a real analytic compact Riemannian
manifold with ergodic geodesic flow. If is an
ergodic sequence of eigenfunctions, we prove the weak limit formula
\frac{1}{\lambda_j} [Z_{\phi_{j_k}^{\C}}] \to \frac{i}{\pi} \bar{\partial}
{\partial} |\xi|_g, where [Z_{\phi_{j_k}^{\C}}] is the current of
integration over the complex zeros and where is with respect
to the adapted complex structure of Lempert-Sz\"oke and Guillemin-Stenzel.Comment: Added some examples and references. Also added a new Corollary, and
corrected some typo
Experimental study of direct photon emission in K- --> pi- pi0 gamma decay using ISTRA+ detector
The branching ratio in the charged-pion kinetic energy region of 55 to 90 MeV
for the direct photon emission in the K- --> pi- pi0 gamma decay has been
measured using in-flight decays detected with the ISTRA+ setup operating in the
25 GeV/c negative secondary beam of the U-70 PS. The value
Br(DE)=[0.37+-0.39(stat)+-0.10(syst)]*10^(-5) obtained from the analysis of 930
completely reconstructed events is consistent with the average value of two
stopped-kaon experiments, but it differs by 2.5 standard deviations from the
average value of three in-flight-kaon experiments. The result is also compared
with recent theoretical predictions.Comment: 13 pages, 8 figure
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