共查询到20条相似文献,搜索用时 531 毫秒
1.
W. H. Steeb A. J. van Tonder C. M. Villet S. J. M. Brits 《Foundations of Physics Letters》1988,1(2):147-162
From the eigenvalue equationH
\
n
() =E
n
()\
n
() withH
H
0 +V one can derive an autonomous system of first order differential equations for the eigenvaluesE
n
() and the matrix elementsV
mn
() where is the independent variable. To solve the dynamical system we need the initial valuesE
n
( = 0) and \
n
( = 0). Thus one finds the motion of the energy levelsE
n
(). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities on is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH
=H
0 +V
1 +
2
V
2 and give an application to a supersymmetric Hamiltonian. 相似文献
2.
W. -H. Steeb S. J. M. Brits N. Euler 《International Journal of Theoretical Physics》1990,29(6):637-642
From the eigenvalue H|n()=En() |n(), where HH0+V, one can derive an autonomous system of first-order differential equations for the eigenvaluesE
n() and the matrix elements Vmn(), where is the independent variable. We perform a Painlevé test for this system and discuss the connection with integrability. It turns out that the equations of motion do not pass the Painlevé test, but a weaker form. The first integrals are polynomials and can be related to the Kowalewski exponents. 相似文献
3.
Rinaldo Schinazi 《Journal of statistical physics》1994,74(5-6):1005-1016
The contact process onZ has one phase transition; let
c
be the critical value at which the transition occurs. Let
N
be the extinction time of the contact process on {0,...,N}. Durrett and Liu (1988), Durrett and Schonmann (1988), and Durrett, Schonmann, and Tanaka (1989) have respectively proved that the subcritical, supercritical, and critical phases can be characterized using a large finite system (instead ofZ) in the following way. There are constants 1() and 2() such that if <
c
, lim
N
N
/logN = 1/1(); if >
c
, lim
N
log
N
/N = 2(); if =
c
, lim
N
N
/N= and lim
N
N
/N
4=0 in probability. In this paper we consider the asymmetric contact process onZ when it has two distinct critical values
c1<
c2. The arguments of Durrett and Liu and of Durrett and Schonmann hold for <
c1 and >
c2. We show that for [
c1<
c2), lim
N
N
/N=-1/, (where
i
is an edge speed) and for =
c2, lim
N
log
N
/logN=2 in probability. 相似文献
4.
We studye()=inf spec(-+V) and examine whene()<0 for all 0. We prove thatc
2e()–d
2 for suitableV and all small ||.Research partially funded under NSF grant number DMS-9101716. 相似文献
5.
Walter Wyss 《Foundations of Physics Letters》1991,4(3):235-246
Fractional noiseN(t),t 0, is a stochastic process for every , and is defined as the fractional derivative or fractional integral of white noise. For = 1 we recover Brownian motion and for = 1/2 we findf
–1-noise. For 1/2 1, a superposition of fractional noise is related to the fractional diffusion equation. 相似文献
6.
Emil Straube 《Communications in Mathematical Physics》1981,81(1):27-30
Let (, , ) be a measure space with normalized measure,f: a nonsingular transformation. We prove: there exists anf-invariant normalized measure which is absolutely continuous with respect to if and only if there exist >0, and , 0<<1, such that (E)< implies (f
–k(E))< for allk0. 相似文献
7.
For real a correspondence is made between the Julia setB
forz(z–)2, in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB
is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325. 相似文献
8.
Barnsley M. F. Geronimo J. S. Harrington A. N. 《Communications in Mathematical Physics》1983,88(4):479-501
The Julia setB
for the mappingz (z–)2 is considered, where is a complex parameter. For 2 a new upper bound for the Hausdorff dimension is given, and the monic polynomials orthogonal with respect to the equilibrium measure onB
are introduced. A method for calculating all of the polynomials is provided, and certain identities which obtain among coefficients of the three-term recurrence relations are given. A unifying theme is the relationship betweenB
and -chains ± (± (± ...), which is explored for –1/42 and for with ||1/4, with the aid of the Böttcher equation. ThenB
is shown to be a Hölder continuous curve for ||<1/4.Supported by NSF Grant MCS-8104862Supported by NSF Grant MCS-8002731 相似文献
9.
A. D. W. B. Crumey 《Communications in Mathematical Physics》1987,111(2):167-179
The classical non-linear Schrödinger equation associated with a symmetric Lie algebra =km is known to possess a class of conserved quantities which from a realization of the algebrak []. The construction is now extended to provide a realization of the Kac-Moody algebrak[, –1] (with central extension). One can then define auxiliary quantities to obtain the full algebra [, –1]. This leads to the formal linearization of the system. 相似文献
10.
Akira Sakai 《Journal of statistical physics》2001,104(1-2):111-143
The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:()–
c as
c and ()(
c–)–1 as
c, where () and () are the spread probability and the susceptibility of the infection respectively, and
c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4. 相似文献
11.
Let S() be the S-matrix at energy for an abstract scattering system. We derive a bound, in terms of the interaction, on integrals of the form h () S()-
HS
2
d, where denotes the Hilbert-Schmidt norm.Supported by the Swiss National Science Foundation. 相似文献
12.
The uniform nearest particle system (UNPS) is studied, which is a continuoustime Markov process with state space
. The rigorous upper bound
(mf)
= ( – 1)/ for the order parameter
2, is given by the correlation identity and the FKG inequality. Then an improvement of this bound
(mf)
is shown in a similar fashion;
C( – 1)/|log( – 1) for >1. Recently, Mountford proved that the critical value c=1. Combining his result and our improved bound implies that if the critical exponent exists, it is strictly greater than the mean-field value 1 in the weak sense. 相似文献
13.
We study a certain family of Schrödinger operators whose eigenfunctions (, ) satisfy a differential equation in the spectral parameter of the formB(,
)=(x). We show that the flows of a hierarchy of master symmetries for KdV are tangent to the manifolds that compose the strata of this class ofbispectral potentials. This extends and complements a result of Duistermaat and Grünbaum concerning a similar property for the Adler and Moser potentials and the flows of the KdV hierarchy. 相似文献
14.
In this paper, we study the spectrum of the Dirichlet Laplacian in a bounded (or, more generally, of finite volume) open set R
n
(n1) with fractal boundary of interior Minkowski dimension (n–1,n]. By means of the technique of tessellation of domains, we give the exact second term of the asymptotic expansion of the counting functionN() (i.e. the number of positive eigenvalues less than ) as +, which is of the form /2 times a negative, bounded and left-continuous function of . This explains the reason why the modified Weyl-Berry conjecture does not hold generally forn2. In addition, we also obtain explicit upper and lower bounds on the second term ofN(). 相似文献
15.
A. M. Prokhorov G. P. Shipulo A. A. Spikhalsky V. A. Sychugov A. A. Zlenko 《Optical and Quantum Electronics》1979,11(1):11-22
A simple method is suggested for calculation of reflection, radiation and transmission coefficients for the distributed feedback structure in the second diffraction order. The method is based on a slight difference between coefficients of reflectionR and radiationI of the surface wave for = (where is the light wavelength corresponding to a precise resonance for the grating length I) and those for =l (where l is the light wavelength corresponding to the resonance for the finite grating length). The simplicity of the method makes it possible to use it for optimization of the distributed feedback structure by a number of parameters. The technique can be used in the case of thin-film and diffused waveguides for both TE and TM modes. 相似文献
16.
We present a modified London model suggested by Brandt [1–3] which introduces a finite vortex core size appropriate for isotropic superconductors in which the average internal field is less than approximately (1/4)H
c2. TheSR lineshape resulting from this model possesses a distinctive shape due to the magnetic penetration depth and the vortex core diameter (approximately equal to twice the coherence length ). However, for a given lineshape, there is a large range of values of and which produce nearly the same lineshape. Lineshape smearing caused by disorder in the vortex lattice increases uncertainty in values for and . If well-determined values of either (T) or (T) are not available from another technique, both of them can be determined bySR measurements alone if runs in more than one applied field at the same temperature are fit with and as shared parameters. We also present our method of estimating the degree of disorder in the vortex lattice. 相似文献
17.
The charge fluctuations in classical Coulomb systems 总被引:1,自引:0,他引:1
We study the asymptotic behavior of the charge fluctuations (Q
– (Q
)2 in infinite classical systems of charged particles, and show, under certain clustering assumptions, that if the charge fluctuations are not extensive, then they are necessarily of the order of the surface ¦¦. Moreover, when the canonical sum rules that are typical for equilibrium states of particles interacting with long-range forces hold true, we prove a central limit theorem for the normalized charge variable ¦¦–1/2((Q
– (Q
)) in two and three dimensions. In one dimension, the probability distribution of the charge itself converges. The latter case is illustrated by the example of the one-dimensional Coulomb gas. 相似文献
18.
We consider the limit-periodic Jacobi matrices associated with the real Julia sets of f
(z)=z
2– for which [2, ) can be seen as the strength of the limit-periodic coefficients. The typical local spectral exponent of their spectral measures is shown to be a harmonic function in decreasing logarithmically from 1 to 0. 相似文献
19.
F. Gesztesy D. Gurarie H. Holden M. Klaus L. Sadun B. Simon P. Vogl 《Communications in Mathematical Physics》1988,118(4):597-634
We consider eigenvaluesE
of the HamiltonianH
=–+V+W,W compactly supported, in the limit. ForW0 we find monotonic convergence ofE
to the eigenvalues of a limiting operatorH
(associated with an exterior Dirichlet problem), and we estimate the rate of convergence for 1-dimensional systems. In 1-dimensional systems withW0, or withW changing sign, we do not find convergence. Instead, we find a cascade phenomenon, in which, as , each eigenvalueE
stays near a Dirichlet eigenvalue for a long interval (of lengthO(
)) of the scaling range, quickly drops to the next lower Dirichlet eigenvalue, stays there for a long interval, drops again, and so on. As a result, for most large values of the discrete spectrum ofH
is close to that ofE
, but when reaches a transition region, the entire spectrum quickly shifts down by one. We also explore the behavior of several explicit models, as .Max Kade Foundation FellowPartially supported by USNSF under Grant DMS-8416049On leave of absence from Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106, USA. Partially supported by USNSF under Grant DMS-8620231 and the Case Institute of Technology, RIG 相似文献
20.
Akitaka Kishimoto 《Letters in Mathematical Physics》1979,3(3):193-196
If the energy spectrum of an extremal invariant state is not the whole real line, it is shown that is either pure or uniquely decomposed into mutually disjoint pure states in the way that =-1
F
0
t
dt where is a pure state satisfying = with >0. Next we give a slightly generalized version of Borchers' theorem [1] on the innerness of some automorphism group of a von Neumann algebra with a spectrum condition. 相似文献