共查询到20条相似文献,搜索用时 703 毫秒
1.
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
2.
Michael Aizenman 《Communications in Mathematical Physics》1980,73(1):83-94
It is shown that any Gibbs state of the two dimensional ferromagnetic Ising system is of the form ++(1–)–, with some [0, 1]. This excludes the possibility of a locally stable phase coexistence and of translation symmetry breaking, which are known to occur in higher dimensions. Use is made in the proof of the stochastic aspects of the geometry of the interface lines.Supported in part by the U.S. National Science Foundation under the grant PHY — 7825390 相似文献
3.
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
4.
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
5.
The spectrum of the mass operator on the soliton sectors of the anisotropic (|ø|4)2—and the (ø4)2—quantum field models in the two phase region is analyzed. It is proven that, for small enough >0, the mass gapm
s() on the soliton sector is positive, andm
s()=0(–1). This involves estimatingm
s() from below by a quantity () analogous to the surface tension in the statistical mechanics of two dimensional, classical spin systems and then estimating () by methods of Euclidean field theory. In principle, our methods apply to any two dimensional quantum field model with a spontaneously broken, internal symmetry group.A Sloan Foundation Fellow; Research supported in part by the U.S. National Science Foundation under Grant No. MPS 75-11864.Supported in part by the National Science Foundation under Grant No. PHY 76-17191 相似文献
6.
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
7.
S. N. Mensov 《Radiophysics and Quantum Electronics》1979,22(4):309-315
Conclusions For holography using a convergent subject beam arrangement, the effect associated with increased extrafocal information density is most pronounced when the parameter 2ac/F is small. This relationship between the object parameters (a and c) and the characteristics of the holographic system (, F) is encountered most frequently in problems of microfilming (ac) and radar imaging (ac,a
2/F is small). It is only in the case 2acF99 with an accuracy of not worse than 1%, that we can assert that the sizes of the minimal Fourier holograms will coincide.Gorkii State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 22, No. 4, pp. 449–457, April, 1979. 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.
E. Leutheusser 《Zeitschrift für Physik B Condensed Matter》1984,55(3):235-240
A nonlinear equation of motion of an overdamped oscillator exhibiting a glass-like transition at a critical coupling constant
c
is presented and solved exactly. Below
c
, in the fluid phase, the oscillator coordinatex(t) decays to zero, while above
c
, in the amorphous phase, it decays to a nonzero infinite time limit. Near
c
the motion is slowed down by a nonlinear feedback mechanism andx(t) decays exponentially to its long time limit with a relaxation time diverging as (1 – /
c
)–3/2 and (/
c
–1)–1 for <
c
and >
c
respectively. At
c
x(t) exhibits a power law decay proportional tot
– with exponent -1/2. 相似文献
10.
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
11.
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
12.
M. V. Jakobson 《Communications in Mathematical Physics》1981,81(1):39-88
Given a one-parameter familyf
(x) of maps of the interval [0, 1], we consider the set of parameter values for whichf
has an invariant measure absolutely continuous with respect to Lebesgue measure. We show that this set has positive measure, for two classes of maps: i)f
(x)=f(x) where 0<4 andf(x) is a functionC
3-near the quadratic mapx(1–x), and ii)f
(x)=f(x) (mod 1) wheref isC
3,f(0)=f(1)=0 andf has a unique nondegenerate critical point in [0, 1]. 相似文献
13.
We study spectral properties of the discrete Laplacian H on the half space Z+
d+1 = Zd× Z+ with a boundary condition (n,-1) = tan( ... n + )(n,0), where [0,1]d. We denote by H0 the Dirichlet Laplacian on Z+
d+1. Whenever is independent over rationals (H) = R. Khoruzenko and Pastur have shown for a set of 's of Lebesgue measure 1, the spectrum of H on R\ (H0) is pure point and that corresponding eigenfunctions decay exponentially. In this Letter we show that if is independent over rationals, then the spectrum of H on the set (H0) is purely absolutely continuous. 相似文献
14.
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
15.
H. Zolądek 《Journal of statistical physics》1987,47(3-4):543-550
A standard random walk on a one-dimensional integer lattice is considered where the probability ofk self-intersections of a path =(0, (1),..., (n) is proportional toe
–k
. It is proven that for <0,n
–1/3(n) converges to a certain continuous random variable. For >0 the formulas are given for the asymptotic Westerwater velocity of a generic path and for the variance of the fluctuations about the asymptotic motion. 相似文献
16.
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
17.
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
18.
Errico Presutti Mario Pulvirenti Brunello Tirozzi 《Communications in Mathematical Physics》1976,47(1):81-95
Existence of dynamics for infinitely many hard-spheres inv dimensions is proven in a set of full equilibrium measure.Singular unbounded perturbations are considered with pair potentials diverging as (x – a)–, >2 anda is the hard-core diameter. Long range forces are allowed with potentials decreasing at infinity asx
, <v. The result corrects and generalizes a proof given in a previous paper by the same authors.Research partially supported by a CNR fellowship Posit. 204530.Research partially supported by a CNR fellowship. 相似文献
19.
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
20.
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