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1.
It is shown that the experimentally investigated structural ion-sound plasma turbulence is a self-similar stationary random
process. The self-similarity parameter is determined by two temporal laws: the nonrandom character of the appearance of nonlinear
structures (nonlinear ion-sound solitons) in the plasma, and the nonlinear interaction between them. As the distance from
the threshold of the ion-sound current instability increases, the self-similar random process approaches a Gaussian random
process, but this limit has not been attained experimentally. The possibility of recording superlong time series of the fluctuations
of the signal of the plasma process and processing of the time series by the R/S analysis method has made it possible to prove self-similarity of the plasma structural turbulence.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 203–208 (10 August 1999) 相似文献
2.
We show that infinite variety of Poincaré bialgebras with nontrivial classicalr-matrices generate nonsymmetric nonlinear composition laws for the fourmomenta. We also present the problem of lifting the
Poincaré bialgebras to quantum Poincaré groups by using e.g. Drinfeld twist, what permits to provide the nonlinear composition
law in any order of dimensionfull deformation parameterλ (from physical reasons we can putλ=λ
p whereλ
p is the Planck length). The second infinite variety of composition laws for fourmomentum is obtained by nonlinear change of
basis in Poincaré algebra, which can be performed for any choice of coalgebraic sector, with classical or quantum coproduct.
In last Section we propose some modification of Hopf algebra scheme with Casimir-dependent deformation parameter, which can
help to resolve the problem of consistent passage to macroscopic classical limit.
Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.
Supported by KBN grant 5PO3B05620 相似文献
3.
The issue of whether teleparallel nonlinear connections exist is resolved by their explicit construction on Finslerian metrics
that arise in the Robertson test theory of special relativity (RTTSR), and on the Minkowski metric in particular. The method
is an adaptation to the Finsler bundle of a similar construction for teleparallel linear connections. It suggests the existence
of a concept of metric compatibility alternative toω
μλ
+ω
λμ
= 0 for teleparallel nonlinear connections. A sophisticated system of partial differential equations whose solutions have
been discussed in the computing literature is interpreted in geometric terms. The characteristics of the solutions are checked
against compliance with the conditionω
μλ
+ω
λμ
= 0, an issue whose relevance for this theory derives from the fact that nonantisymmetric connections repeatedly appear in
teleparallel geometry. 相似文献
4.
C.M. Horowitz E.V. Albano 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(4):563-569
The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's
evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the
corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on
p in the following way: ν(p) = νp and λ(p) = λp
3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation
can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp
2. It is expected that these results will help to find a framework for the development of stochastic equations starting from
microscopic details of growth models.
Received 26 August 2002 / Received in final form 20 November 2002 Published online 6 March 2003
RID="a"
ID="a"e-mail: ealbano@inifta.unlp.edu.ar 相似文献
5.
Jens Marklof 《Communications in Mathematical Physics》1998,199(1):169-202
The Berry–Tabor conjecture asserts that local statistical measures of the eigenvalues λ
j
of a “generic” integrable quantum system coincide with those of a Poisson process. We prove that, in the case of a rectangle
billiard with random ratio of sides, the sum behaves for τ random and N large like a random walk in the complex plane with a non-Gaussian limit distribution. The expectation value of the distribution
is zero; its variance, which is essentially the average pair correlation function, is one, in accordance with the Berry–Tabor
conjecture, but all higher moments (≥ 4) diverge. The proof of the existence of the limit distribution uses the mixing property
of a dynamical system defined on a product of hyperbolic surfaces. The Berry–Tabor conjecture and the existence of the limit
distribution for a fixed generic rectangle are related to an equidistribution conjecture for long horocycles on this product space.
Received: 16 February 1998 / Accepted: 24 April 1998 相似文献
6.
In an addendum to the recent systematic Hermitization of certain N by N matrix Hamiltonians H
(N)(λ) (Znojil in J. Math. Phys. 50:122105, 2009) we propose an amendment H
(N)(λ,λ) of the model. The gain is threefold. Firstly, the updated model acquires a natural mathematical meaning of Runge-Kutta approximant
to a differential PT\mathcal{PT}-symmetric square well in which P\mathcal{P} is parity. Secondly, the appeal of the model in physics is enhanced since the related operator C\mathcal{C} of the so called “charge” (the requirement of observability of which defines the most popular Bender’s metric Q = PC\Theta=\mathcal{PC}) becomes also obtainable (and is constructed here) in an elementary antidiagonal matrix form at all N. Last but not least, the original phenomenological energy spectrum is not changed so that the domain of its reality (i.e.,
the interval of admissible couplings λ∈(−1,1)) remains the same. 相似文献
7.
Igor Loutsenko Oksana Yermolayeva Michel Zinsmeister 《Journal of statistical physics》2011,145(4):919-931
We introduce a competitive model of Laplacian growth in both stochastic and deterministic versions. This defines two different
aggregation laws with probabilities λ and 1−λ. The parameter λ varying from 0 to 1 is used to weight a ratio between the inner and outer harmonic measures that leads to a competition between
the Eden-like process and the DLA solved with site-sticking conditions. We perform numerical and qualitative analysis of the
competitive growth. 相似文献
8.
Here, we make an indirect phenomenological study of the possible presence of a CSB component in the λN interaction in medium and heavy hypernuclei using a semi-empirical formula for the difference in the ground stateB
λ of hypernuclear isobars. We find that light hypernuclei are better suited than heavier hypernuclei for such information. 相似文献
9.
We consider the families of entire transcendental maps given by F
λ,m
(z) = λz
m
exp(z), where m ≥ 2. All functions F
λ,m
have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin
of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin,
A
*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected.
For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A
*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of which serve as a model for F
λ,m
, in the sense that they are related by means of quasiconformal surgery to F
λ,m
.
Both authors were supported by MTM2005-02139/Consolider (including a FEDER contribution) and CIRIT 2005 SGR01028. The first
author was also supported by MTM2006-05849/Consolider (including a FEDER contribution). 相似文献
10.
We obtain relativistic solutions of a class of compact stars in hydrostatic equilibrium in higher dimensions by assuming a
pseudospheroidal geometry for the spacetime. The space-time geometry is assumed to be (D − 1) pseudospheroid immersed in a D-dimensional Euclidean space. The spheroidicity parameter (λ) plays an important role in determining the equation of state of the matter content and the maximum radius of such stars.
It is found that the core density of compact objects is approximately proportional to the square of the space-time dimensions
(D), i.e., core of the star is denser in higher dimensions than that in conventional four dimensions. The central density of
a compact star is also found to depend on the parameter λ. One obtains a physically interesting solution satisfying the acoustic condition when λ lies in the range λ > (D + 1)/(D − 3) for the space-time dimensions ranging from D = 4 to 8 and (D + 1)/(D − 3) < λ < (D
2 − 4D + 3)/(D
2 − 8D − 1) for space-time dimensions ≥9. The non-negativity of the energy density (ρ) constrains the parameter with a lower limit (λ > 1). We note that in the case of a superdense compact object the number of space-time dimensions cannot be taken infinitely
large, which is a different result from the braneworld model. 相似文献
11.
A phenomenological theory of the magnetic-field penetration-depth (λ
iα
) anisotropy in high-temperature superconductors is constructed taking account of the magnetic susceptibility (χ
ik
) anisotropy of the surface layer. The factor of 1.9 change in the anisotropy λ
c
/λ
ab
with 4% substitution of Co for Cu ions in YBa2Cu3O7 is virtually completely due to the increase in the magnetic susceptibility anisotropy. For Cu-Zn substitutions the change
in λ
c
/λ
ab
is characterized primarily by a change in the anisotropy of the tensor of the reciprocal effective masses of the charge carriers
(pairs).
Fiz. Tverd. Tela (St. Petersburg) 41, 1552–1555 (September 1999) 相似文献
12.
I. M. Dremin A. V. Leonidov V. A. Nechitailo 《Bulletin of the Lebedev Physics Institute》2011,38(10):287-290
By the example of the asymptotically free theory λϕ
63 with random constant λ, the process of cascade multiplication of particles with random intensity of elementary decay is considered. The dependence
of the characteristics of the cascade particle multiplicity distribution on the parameters of the probabilistic distribution
over the elementary decay intensity is studied. 相似文献
13.
We study spectral properties of
the discrete Laplacian H on the half-space
with random boundary condition ;
the V(n) are independent random variables on a
probability
space and λ is the coupling constant.
It is known that if the
V(n) have densities, then on the interval
[-2(d+1), 2(d+1)] (=σ(H
0),
the spectrum of the
Dirichlet Laplacian) the spectrum of H is P-a.s.
absolutely continuous for all λ [JL1].
Here we show that if the random potential P
satisfies the
assumption of Aizenman–Molchanov [AM], then there
are constants λ
d
and
Λ
d
such that for
|λ|<lambda;
d
and |λ|>
Λ
d
the spectrum of
H outside σ(H
0)
is P-a.s. pure point with exponentially decaying
eigenfunctions.
Received: 3 December 1998 / Accepted: 27 May 1999 相似文献
14.
L. Gao X. P. Yu 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(4):403-409
We derive expressions for the effective nonlinear susceptibility
tensors for both the second harmonic generation (SHG) and induced
third harmonic generation (THG) of nonlinear composite materials,
in which nondilute coated particles with radial dielectric
anisotropy are randomly embedded in the linear host. Two types of
coated particles are considered. The first is that the core
possesses a second order nonlinear susceptibility and the shell is
linear and radially anisotropic, while the second is that the
core is linear with radial anisotropy and the shell has a second
order nonlinear susceptibility. We observe greatly enhanced SHG
and THG susceptibilities at several surface plasmon resonant
frequencies. For the second model, due to the coating material
being metallic, there exists two fundamental resonant frequencies
ωc1 and ωc2, whose difference
ωc2-ωc1 is strongly dependent on the interfacial
parameter and the radial dielectric anisotropy. Furthermore, in
both systems, the adjustment of the dielectric anisotropy results
in larger enhancement of both SHG and induced THG susceptibilities
at surface plasmon resonant frequencies than the corresponding
isotropic systems. Therefore, both the core-shell structure and
the dielectric anisotropy play important roles in determining the
nonlinear enhancement and the surface resonant frequencies. 相似文献
15.
Given a complex number λ of modulus 1, we show that the bifurcation locus of the one parameter family {f
b
(z)=λz+b
z
2+z
3}
b
∈
ℂ contains quasi-conformal copies of the quadratic Julia set J(λz+z
2). As a corollary, we show that when the Julia set J(λz+z
2) is not locally connected (for example when z↦λz+z
2 has a Cremer point at 0), the bifurcation locus is not locally connected. To our knowledge, this is the first example of
complex analytic parameter space of dimension 1, with connected but non-locally connected bifurcation locus. We also show
that the set of complex numbers λ of modulus 1, for which at least one of the parameter rays has a non-trivial accumulation
set, contains a dense G
δ subset of S
1.
Received: 22 September 2000 / Accepted: 16 January 2001 相似文献
16.
H. Boos M. Jimbo T. Miwa F. Smirnov Y. Takeyama 《Communications in Mathematical Physics》2006,261(1):245-276
Correlation functions of the XXZ model in the massive and massless regimes are known to satisfy a system of linear equations.
The main relations among them are the difference equations obtained from the qKZ equation by specializing the variables (λ1, . . . ,λ2n) as (λ1, . . . ,λn,λn+1, . . . ,λ1+1). We call it the reduced qKZ equation. In this article we construct a special family of solutions to this system. They
can be written as linear combinations of products of two transcendental functions ,ω with coefficients being rational functions. We show that correlation functions of the XXZ model in the massive regime are
given by these formulas with an appropriate choice of ,ω. We also present a conjectural formula in the massless regime.
On leave of absence from the Institute for High Energy Physics, Protvino, 142281, Russia
Membre du CNRS 相似文献
17.
The most recently measured differential cross-section data forπ
−
p → η’n has been fitted by using a simple Regge pole model with phenomenological residue functions. It has also been observed that
this inelastic process has the scaling property. 相似文献
18.
A. S. Vshivtsev M. A. Vdovichenko K. G. Klimenko 《Journal of Experimental and Theoretical Physics》1998,87(2):229-238
The phase structure of the Nambu-Jona-Lasinio model in space-time with the topology R
3×S
1 (spatial coordinate compactified) and chemical potential μ is investigated. Phase portraits of the model are constructed in the μλ plane (λ=1/L, where L is the size of the dimension S
1) in the case with periodic boundary conditions. It is shown here for the first time that there exist in the model an infinite
number of both chirally symmetric massless phases and asymmetric massive phases, between which (as a rule) transitions are
second-order. Because of this phase structure, changes in the parameter λ induce oscillations in the particle density, fermion mass, and the critical curve on which chiral invariance is restored.
Zh. éksp. Teor. Fiz. 114, 418–436 (August 1998) 相似文献
19.
New experimental data on the binding energyB
λλ
ofλλ6He, reported very recently, come up with the valuesB
λλ
= 725 ±0.14 MeV and ΔBλλ = 101 ±0.2 MeV which are substantially lower than the old dataB
λλ
= 109 ±0.8 MeV and ΔBλλ = 4.7±10 MeV in use in literature since 1966. In view of the new data we decided to undertake a re-study of the
λλ
6
He hypernucleus using the same three-body model (α-λ-λ) with a simple coordinate space variational approach which was employed
earlier with the old data onλλ/6He. After fitting different λ-λ potentials to the new data of
λλ
6
He we have applied our method to study some double-λ hypernuclei in light, medium and heavy mass regions and have determined
the structural quantities like Bλλ, the r.m.s. values of core-λ (〈rcore-λ〉〉) and λ-λ (〈rλ-λ〉〉) distances theoretically. The core-λ interaction considered is of Woods-Saxon type. The strength and the range of the core-A
potential have been adjusted to reproduce the λ-binding energy(B
λ)
. These are in good agreement with the relativistic mean field (RMF) results. Our study shows that the λ-λ bonding energy
ΔBλλ decreases with increasing mass number from
λλ
10
Be to
λλ
210
Pb of a double-A hypernucleus 相似文献
20.
Claudio Dappiaggi Valter Moretti Nicola Pinamonti 《Communications in Mathematical Physics》2009,285(3):1129-1163
As a starting point, we state some relevant geometrical properties enjoyed by the cosmological horizon of a certain class
of Friedmann-Robertson-Walker backgrounds. Those properties are generalised to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon common to all co-moving observers. This structure is later exploited in order to recast, in a cosmological background, some
recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable
hypotheses on M, encompassing both the cosmological de Sitter background and a large class of other FRW spacetimes, the algebra of observables
for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables constructed on the cosmological horizon. There is exactly one pure quasifree state λ on which fulfills a suitable energy-positivity condition with respect to a generator related with the cosmological time displacements.
Furthermore λ induces a preferred physically meaningful quantum state λ
M
for the quantum theory in the bulk. If M admits a timelike Killing generator preserving , then the associated self-adjoint generator in the GNS representation of λ
M
has positive spectrum (i.e., energy). Moreover λ
M
turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of
an expanding de Sitter spacetime, λ
M
coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the
Hadamard property for λ
M
in more general spacetimes are presented.
Dedicated to Professor Klaus Fredenhagen on the occasion of his 60th birthday. 相似文献