共查询到20条相似文献,搜索用时 35 毫秒
1.
K. Ravishankar 《Journal of statistical physics》1989,54(1-2):531-537
A sequence of i.i.d. matrix-valued random variables
with probabilityp and
with probability 1–p is considered. Leta() = a
0
+ O(), c() = c
0
+ O() lim
0
b() = Oa
0,c
0, >0, andb()>0 for all >0. It is shown show that the top Lyapunov exponent of the matrix productX
n
X
n-1...X
1, = limn (1/n) n X
n
X
n-1...X
1 satisfies a power law with an exponent 1/2. That is, lim 0(ln /ln ) = 1/2. 相似文献
2.
T. V. Dudnikova A. I. Komech N. E. Ratanov Y. M. Suhov 《Journal of statistical physics》2002,108(5-6):1219-1253
The paper considers the wave equation, with constant or variable coefficients in
n
, with odd n3. We study the asymptotics of the distribution
t
of the random solution at time t as t . It is assumed that the initial measure
0 has zero mean, translation-invariant covariance matrices, and finite expected energy density. We also assume that
0 satisfies a Rosenblatt- or Ibragimov–Linnik-type space mixing condition. The main result is the convergence of
t
to a Gaussian measure
as t , which gives a Central Limit Theorem (CLT) for the wave equation. The proof for the case of constant coefficients is based on an analysis of long-time asymptotics of the solution in the Fourier representation and Bernstein's room-corridor argument. The case of variable coefficients is treated by using a version of the scattering theory for infinite energy solutions, based on Vainberg's results on local energy decay. 相似文献
3.
The exact analytic result is obtained for the Fourier transform of the generating functionF(R,s)=
n=0
s
n
P(R,n), whereP(R,n) is the probability density for the end-to-end distanceR inn steps of a random walk with persistence. The moments R
2(n), R
4(n), and R
6(n) are calculated and approximate results forP(R,n) and R
–1(n) are given. 相似文献
4.
L. Castell 《Communications in Mathematical Physics》1970,17(2):127-132
The explicit form of the conformal-invariant phase shift analysis in thes-channel for a scattering process involving two incoming and two outgoing particles is derived for the two-dimensional world model. The high energy behaviour of the scattering amplitudes is determined completely (up to a constant factor) by the requirement of conformal invariance. It is not possible to obtain this high energy limit by neglecting the masses right from the beginning. The main mathematical problem is the determination of the Clebsch-Gordan coefficients forSU
0(1, 1) in the momentum basis. 相似文献
5.
Krystyna Bugajska 《International Journal of Theoretical Physics》1987,26(7):623-636
We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g
0). We use relations between different Lorentzian structures unequivalent tog
0 and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog
0 by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e. 相似文献
6.
We prove the almost sure existence of a pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding densityg has support equal to
, and satisfies
, for some > 0. This includes the case of Gaussian distributions. We show that the almost sure spectrum is
, provided the magnetic field B0. We prove that for each positive integer n, there exists a field strength B
n
, such that for all B>B
n
, the almost sure spectrum is pure point at all energies
except in intervals of width
about each lower Landau level
, for m < n. We also prove that for any B0, the integrated density of states is Lipschitz continuous away from the Landau energiesE
n
(B). This follows from a new Wegner estimate for the finite-area magnetic Hamiltonians with random potentials. 相似文献
7.
We present a regular class of exact black hole solutions of the Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner–Nordström one. The class is endowed with four parameters, which can be thought of as the mass m, charge q, and a sort of dipole and quadrupole moments and , respectively. For 3, 4, and |q|2s
c
m the corresponding solutions are regular charged black holes. For = 3, they also satisfy the weak energy condition. For = = 0 we recover the Reissner–Nordström singular solution and for = 3, = 4 the family includes a previous regular black hole reported by the authors. 相似文献
8.
Let {X
t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew
–1(X
t), where {w(x):xd} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function
F(q,t)=E
0
(qd) is completely monotonic int (E
0 denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor
S(q, w)=2
0
cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|2, whereD is the diffusion constant. 相似文献
9.
Consider the system of particles on
d
where particles are of two types—A andB—and execute simple random walks in continuous time. Particles do not interact with their own type, but when anA-particle meets aB-particle, both disappear, i.e., are annihilated. This system serves as a model for the chemical reactionA+B inert. We analyze the limiting behavior of the densities
A
(t) and
B
(t) when the initial state is given by homogeneous Poisson random fields. We prove that for equal initial densities
A
(0)=
B
(0) there is a change in behavior fromd4, where
A
(t)=
B
(t)C/t
d
/4, tod4, where
A
(t)=
B
(t)C/tast. For unequal initial densities
A
(0)<
B
(0),
A
(t)e
–cl ind=1,
A
(t)e
–Ct/logt
ind=2, and
A
(t)e
–Ct
ind3. The termC depends on the initial densities and changes withd. Techniques are from interacting particle systems. The behavior for this two-particle annihilation process has similarities to those for coalescing random walks (A+AA) and annihilating random walks (A+Ainert). The analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system. 相似文献
10.
Remco van der Hofstad Achim Klenke Wolfgang König 《Journal of statistical physics》2002,106(3-4):477-520
A polymer chain with attractive and repulsive forces between the building blocks is modeled by attaching a weight e
–
for every self-intersection and e
/(2d) for every self-contact to the probability of an n-step simple random walk on
d
, where , >0 are parameters. It is known that for d=1 and > the chain collapses down to finitely many sites, while for d=1 and < it spreads out ballistically. Here we study for d=1 the critical case = corresponding to the collapse transition and show that the end-to-end distance runs on the scale
n
=
(log n)–1/4. We describe the asymptotic shape of the accordingly scaled local times in terms of an explicit variational formula and prove that the scaled polymer chain occupies a region of size
n
times a constant. Moreover, we derive the asymptotics of the partition function. 相似文献
11.
Two random aggregation models are used in demonstrating the properties of the random displacementsr
i
of the center of mass of aggregating particles. It is found that r
i
is a randomly decreasing sequence that scales with the cluster size (steps)s and
i
=1/s
r
i
s
1/D
, whereD is the fractal dimension. The center-of-mass random walk is a consistent representation of the dynamics of aggregation. 相似文献
12.
M. P. Korkina 《Russian Physics Journal》1978,21(12):1586-1590
Metrics induced by a conformally invariant scalar field in both the absence and presence of electric charge are obtained and investigated. It is shown that the structure of the considered space-time is significantly different in three cases: 1)qa2+
G2/3g
2
/4; 2)q2+G2/3=r
g
2
/4 and 3)q2+G2/3>r
g
2
/4. In the first case the space has a throat; in the second case there is a black hole, and in the third the space — time has the properties of the Reissner — Nordström space forq2>r
g
2
/4.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 80–85, December, 1978. 相似文献
13.
Possible generalization of Boltzmann-Gibbs statistics 总被引:31,自引:0,他引:31
Constantino Tsallis 《Journal of statistical physics》1988,52(1-2):479-487
With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS
q
k [1 –
i=1
W
p
i
q
]/(q-1), whereq characterizes the generalization andp
i are the probabilities associated withW (microscopic) configurations (W). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq1 limit. 相似文献
14.
In paper [1] Fang derived an expression for the complex conductivity of plasma assuming that the distribution function of the electrons is Maxwellian and the collision frequency is directly proportional to their velocity. Since the assumptions are approximately satisfied in the positive column of a d-c glow discharge in Ne, the applicability of Fang's relation is investigated for this case.
[1] , . , .相似文献
15.
We present a dynamical approach to the study of the singularity of infinitely convolved Bernoulli measuresv
, for the golden section. We introducev
as the transverse measure of the maximum entropy measure on the repelling set invariant for contracting maps of the square, the fat baker's transformation. Our approach strongly relies on the Markov structure of the underlying dynamical system. Indeed, if =golden mean, the fat baker's transformation has a very simple Markov coding. The ambiguity (of order two) of this coding, which appears when projecting on the line, due to passages for the central, overlapping zone, can be expressed by means of products of matrices (of order two). This product has a Markov distribution inherited by the Markov structure of the map. The dimension of the projected measure is therefore associated to the growth of this product; our dimension formula appears in a natural way as a version of the Furstenberg-Guivarch formula. Our technique provides an explicit dimension formula and, most important, provides a formalism well suited for the multifractal analysis of this measure, as we will show in a forthcoming paper. 相似文献
16.
I. Kurkova 《Journal of statistical physics》2003,111(1-2):35-56
We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution
N
i=1
i
i
/N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D
0
0+D
1
1, with random weights D
0, D
1, while for the second one it is
0. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N. 相似文献
17.
We consider the usual one-dimensional tight-binding Anderson model with the random potential taking only two values, 0 and, with probabilityp and 1–p, 0<p<1. We show that the Liapunov exponent
(E), E R. diverges as uniformly in the energyE. Using a result of Carmona, Klein, and Martinelli, this proves that for large enough, the integrated density of states is singular continuous. We also compute explicitly the exact asymptotics for a dense set of energies and we compare the results with numerical simulations. 相似文献
18.
In the Laguerre ensembleof n xN Hermitian matrices, it is of interest both theoretically and for applications to quantum transport problems to compute the variance of a linear statistic, denoted varN
f, asN . Furthermore, this statistic often contains an additional parameter a for which the limit is most interesting and most difficult to compute numerically. We derive exact expressions for both limN varN
f and lim , limN varN
f. 相似文献
19.
Matsuta K. Minamisono T. Tanigaki M. Fukuda M. Nojiri Y. Mihara M. Onishi T. Yamaguchi T. Harada A. Sasaki M. Miyake T. Minamisono K. Fukao T. Sato K. Matsumoto Y. Ohtsubo T. Fukuda S. Momota S. Yoshida K. Ozawa A. Kobayashi T. Tanihata I. Alonso J. R. Krebs G. F. Symons T. J. M. 《Hyperfine Interactions》1996,97(1):519-526
The magnetic moments of the proton drip-line nuclei13O(I
= 3/2–,T
1/2 = 8.6 ms) and 9C(I
= 3/2–,T
1/2 = 126 ms) have been determined for the first time through the combined techniques of polarized radioactive nuclear beams and-NMR detection. The observed magnetic moments are ¦(13O)¦ = 1.3891 ±0.0003
N and ¦(9C)¦ = 1.3914 ±0.0005
N. Spin expectation values are deduced to be 0.76 and 1.44 for13O and9C, respectively. While the of13O is consistent with the systematics from isospinT= 1/2 mirror pairs, the of9C is unusually large, even far larger than the single particle value, = 1. 相似文献
20.
Basab B. Dasgupta 《Zeitschrift für Physik B Condensed Matter》1978,29(3):245-249
Using the random phase approximation and analytical calculation we show that a higher surface plasma mode can exist near a plane metal-vacuum interface provided the oscillation is sufficiently localized. This conclusion is confirmed for the infinite potential barrier model of the surface where a mode with long-wavelength frequency
p in sodium is predicted. 相似文献