共查询到20条相似文献,搜索用时 15 毫秒
1.
David Ruelle 《Communications in Mathematical Physics》1996,175(1):63-88
A Milnor-Thurston type dynamical zeta function
L
(Z) is associated with a family of maps of the interval (–1, 1). Changing the direction of time produces a new zeta function
L
(Z). These zeta functions satisfy a functional equation
L
(Z)
L
(Z)=
0(Z) (where amounts to sign changes and, generically,01). The functional equation has non-trivial implications for the analytic properties of
L
(Z). 相似文献
2.
David Ruelle 《Communications in Mathematical Physics》1989,125(2):239-262
Letf:XX be an expanding map of a compact space (small distances are increased by a factor >1). A generating function(z) is defined which countsf-periodic points with a weight. One can express in terms of nonstandard Fredholm determinants of certain transfer operators, which can be studied by methods borrowed from statistical mechanics. In this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of(z). Gibbs distributions and applications to Julia sets are also discussed. Some new results are proved, and some natural conjectures are proposed.This is an expanded version of the Bowen lectures given by the author at U.C. Berkeley in November 1988 相似文献
3.
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
4.
Z. Haba 《Letters in Mathematical Physics》1996,37(2):223-231
Let
t
be an analytic solution of the Schrödinger equation with the initial condition . Let
t
be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then
t
(x)
t
(x)1 (
t
(x)), where
t
(x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations. 相似文献
5.
Quantum shot noise consists of individual pulses which contribute time-dependent (operator) potentials toward a total potentialV(t). The averaged quantity T exp
t0
t
dtV(t) in general can no longer be calculated explicitly, in contrast to the classical case, and expansions are of interest. Noncommutative cumulant expansions are not directly applicable if the correlation functions ofV(t) have singularities, as happens in applications. It is shown here that these expansions, when applied to quantum shot noise, can be partially summed to give expansions in powers of the pulse density. Three types of such expansions are established explicitly, and for two of them the derivation is direct. For one of them the first-order approximation is closely connected to the so-called unified theory of spectral-line broadening. 相似文献
6.
We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) L
, is found to be =1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts 0.8. Our value for differs from earlier measurements of this quantity by other methods yielding =1.17±0.05 and 1.22±0.08 by Havlin et al.On leave from the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China. 相似文献
7.
We consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacity in an applied electric fieldE with Dirichlet boundary conditions. The system has a phase transition from a low-coupling phase with equally spaced particles to a high-coupling phase with particles clustered into dipolar pairs. An exact expression for the partition function is developed. In zero applied field the zeros in the plane occupy the imaginary axis from –i to –ic and ic to i for some c. They also occupy the diamond shape of four straight lines from ±ic to c and from ±ic to –c. The fugacity acts like a temperature or coupling variable. The symmetry-breaking field is the applied electric fieldE. A finite-size scaling representation for the partition in scaled coupling and scaled electric field is developed. It has standard mean field form. When the scaled coupling is real, the zeros in the scaled field lie on the imaginary axis and pinch the real scaled field axis as the scaled coupling increases. The scaled partition function considered as a function of two complex variables, scaled coupling and scaled field, has zeros on a two-dimensional surface in a domain of four real variables. A numerical discussion of some of the properties of this surface is presented. 相似文献
8.
Let H be a semibounded perturbation of the Laplacian H
0 in L
2(
d
). For an admissible function sufficient conditions are given for the completeness of the scattering system (H), (H
0). If is the exponential function and if e– H
is an integral operator we denote the kernel of the difference D
= e– H
– e– H
0 by D
(x, y), > 0. The singularly continuous spectrum of H is empty ifd dx
d dy |D(x,y)| (1 + |y|2)< for some > 1. This result is applied to potential perturbations and to perturbations by imposing Dirichlet boundary conditions. 相似文献
9.
The self-avoiding walk in a quenched random environment is studied using real-space and field-theoretic renormalization and Flory arguments. These methods indicate that the system is described, ford
c
=4, and, for large disorder ford>d
c
, by a strong disorder fixed point corresponding to a glass state in which the polymer is confined to the lowest energy path. This fixed point is characterized by scaling laws for the size of the walk,LN
p withN the number of steps, and the fluctuations in the free energy,fL
p. The bound 1/-d/2 is obtained. Exact results on hierarchical lattices yield>
pure and suggests that this inequality holds ford=2 and 3, although=
pure cannot be excluded, particularly ford=2. Ford>d
c
there is a transition between strong and weak disorder phases at which=
pure. The strong-disorder fixed point for SAWs on percolation clusters is discussed. The analogy with directed walks is emphasized. 相似文献
10.
The -function of a one-dimensional classical hard-rod system with exponential pair interaction is defined as the generating function for the partition function of the system with periodic boundary conditions. It is shown, here, that the -function for this system is simply related to the traces of the restrictions of the Ruelle's transfer matrix, and related operators to a suitable function space. This -function does not, in general, extend to a meromorphic function. 相似文献
11.
Andreas Knauf 《Journal of statistical physics》1993,73(1-2):423-431
We present numerical and analytical evidence for a first-order phase transition of the ferromagnetic spin chain with partition functionZ()=(–1)/() at the inverse temperature cr=2. 相似文献
12.
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
13.
Let
l
be the critical exponent associated with the probability thatl independentN-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions 2=0.6240±0.0005±0.0011 and 3=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions 2=5/8 and 3=35/24. 相似文献
14.
The relation between the aperiodic solution of the Lorenz model and that of a stochastic anharmonic oscillator is explored. The stochastic oscillator is constructed by replacing (t) in the Lorenz model by a stochastic variable(t) of specified statistics. The resulting system is of course not isomorphic to the Lorenz model, but does share with it a number of statistical properties. Thus, within the confines of these measures the two systems are physically very similar. 相似文献
15.
The zeta function continuation method is applied to compute the Casimir energy on spheresS
N. Both odd and even dimensional spheres are studied. For the appropriate conformally modified Laplacian the Casimir energy is shown to be finite for all dimensions even though, generically, it should diverge in odd dimensions due to the presence of a pole in the associated zeta function (s). The residue of this pole is computed and shown to vanish in our case. An explicit analytic continuation of (s) is constructed for all values ofN. This enables us to calculate exactly and we find that the Casimir energy vanishes in all even dimensions. For odd dimensions is never zero but alternates in sign asN increases through odd values. Some results are also derived for the Casimir energy of other operators of Laplacian type. 相似文献
16.
We present exact explicit expressions for the row spin-spin correlation functions
00
n0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for
00
n0. 相似文献
17.
Alan D. Sokal 《Journal of statistical physics》1981,25(1):25-50
A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1
, 1,d 1 + 1/ (for d),dv, 3 + (for d), 4 , and 2m 2m+2 (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952. 相似文献
18.
A. Flammang 《Zeitschrift für Physik B Condensed Matter》1977,28(1):47-50
From exact perimeter polynomials of Sykes et al ind=3 dimensions we determine the average perimeter s
n
of clusters, the width of the distribution about the average value, and the numberc
n
of clusters containingn occupied sites each. The exponent, defined through log (c
n
) —n
for largen, is found to be consistent with the predictions (p < p
c
) = 1 and (p>p
c
)=(d—1)/d. 相似文献
19.
We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self-diffusion coefficientD
N() in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set ofN neighboring sites. We obtain positive upper and lower bounds onF
N()=N{(1–)–[DN()/DN(0)]}/[(1–)]x for [0, 1]. Computer simulations for the square, triangular, and one-dimensional lattices suggest thatF
N becomes effectively independent ofN forN20. 相似文献
20.
Given a piecewise monotone transformationT of the interval and a piecewise continuous complex weight functiong of bounded variation, we prove that the Ruelle zeta function (z) of (T, g) extends meromorphically to {z<-1} (where =lim g°Tn-1...g°Tg
1/n
) and thatz is a pole of if and only ifz
–1 is an eigenvalue of the corresponding transfer operator L. We do not assume that L leaves a reference measure invariant.Research partially supported by the Fonds National Suisse 相似文献