共查询到20条相似文献,搜索用时 27 毫秒
1.
K. A. Bronnikov B. E. Meierovich 《Journal of Experimental and Theoretical Physics》2008,106(2):247-264
We consider (d
0 + 2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d
0 dimensions, endowed with a warp factor e
2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp
factor and the extradimensional circular radius r(l). Solutions with r → ∞ and r → const > 0 as l → ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l
c > 0, i.e., those with a second center, are interpreted as either multibrane systems (which are appropriate for large enough
distances l
c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the
case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (ɛ, Γ) parameter plane,
where ɛ acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties
of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for
models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading
to matter particle mass spectra that seem promising from the standpoint of hierarchy problems.
The text was submitted by the authors in English. 相似文献
2.
Ricardo Weder 《Communications in Mathematical Physics》1999,208(2):507-520
We prove that the wave operators for the Schr?dinger equation on the line are continuous on the Sobolev spaces W
k, p
, 1 < p < ∞. Moreover, if the potential is exceptional and , where f
1(x, 0) is a Jost solution at zero energy, the wave operators are continuous on W
k
,1 and on W
k
,∞.
Received: 21 April 1999 / Accepted: 15 July 1999 相似文献
3.
Remco van der Hofstad Frank den Hollander Gordon Slade 《Communications in Mathematical Physics》2002,231(3):435-461
We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ
d
× ℤ+, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ
n
(E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n) ℤ
d
× ℤ+, summing this probability over x ℤ
d
, and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation
to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n
−1, we prove existence of a limiting measure ℚ∞, with ℚ∞ = ℙ∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension
of the cluster of the origin, under ℙ∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented
percolation to super-Brownian motion, for d+1 > 4+1.
Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002
RID="*"
ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513,
5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl 相似文献
4.
We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having
anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r
2, u=4πξr
2, v
r=4πp
r
r
2, v
⊥=4πp
⊥
r
2[ρ, ξ(=−(1/2)F
14
F
14), p
r, p
⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas
ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field],
we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following
assumptions to solve the field equations (i) u=v
r=(a
2/2κ)r
n+2, v
⊥=k
1
v
r, w=k
2
v
r; a
2, n(>0), k
1, k
2 being constants with κ=((k
1+2)/3+k
2) and (ii) w+u=(b
2/2)r
n+2, u=v
r, v
⊥−v
r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as
well as physical variables for all values of n>0. Even though the second solution contains terms like k/r
2 since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing
it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior
Reissner-Nordstrom solution over a fixed boundary.
Dedicated to Prof. F A E Pirani. 相似文献
5.
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However,
the research is focused on systems with only one type of links, connectivity links. We review a recently developed mathematical
framework for analyzing percolation properties of realistic scenarios of networks having links of two types, connectivity
and dependency links. This formalism was applied to study Erdős-Rényi (ER) networks that include also dependency links. For
an ER network with average degree [`(k)]\bar{k} that is composed of dependency clusters of size s, the fraction of nodes that belong to the giant component, P
∞, is given by P¥=ps-1[1-exp(-[`(k)]pP¥) ]sP_{\infty}=p^{s-1}[1-\exp{(-\bar{k}pP_{\infty})} ]^{s} where 1−p is the initial fraction of randomly removed nodes. Here, we apply the formalism to the study of random-regular (RR) networks
and find a formula for the size of the giant component in the percolation process: P
∞=p
s−1(1−r
k
)
s
where r is the solution of r=p
s
(r
k−1−1)(1−r
k
)+1, and k is the degree of the nodes. These general results coincide, for s=1, with the known equations for percolation in ER and RR networks respectively without dependency links. In contrast to s=1, where the percolation transition is second order, for s>1 it is of first order. Comparing the percolation behavior of ER and RR networks we find a remarkable difference regarding
their resilience. We show, analytically and numerically, that in ER networks with low connectivity degree or large dependency
clusters, removal of even a finite number (zero fraction) of the infinite network nodes will trigger a cascade of failures
that fragments the whole network. Specifically, for any given s there exists a critical degree value, [`(k)]min\bar{k}_{\min}, such that an ER network with [`(k)] £ [`(k)]min\bar{k}\leq \bar{k}_{\min} is unstable and collapse when removing even a single node. This result is in contrast to RR networks where such cascades
and full fragmentation can be triggered only by removal of a finite fraction of nodes in the network. 相似文献
6.
A. S. Ioselevich 《JETP Letters》1998,67(1):83-89
The hybridization-induced interaction of Anderson impurities with orbital angular momentum l is revisited. At short distances R<R
c
∝(l+1)/k
F
the interaction has antiferromagnetic sign and decays as (R
c
/R)4l
. At larger distances R>R
c
the RKKY-like oscillatory interaction sets in. As l increases, the system will sooner or later enter the “short-distance” domain, where the intersite magnetic interaction dominates
over the screening processes. This means that, contrary to previous expectations, the nonmagnetic state of the Anderson lattice
is unstable at l→∞.
Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 76–81 (10 January 1998)
Published in English in the original Russian journal. Edited by Steve Torstveit. 相似文献
7.
On the basis of the experimental data on diffractive processes in πp, pp and pˉp collisions at intermediate, moderately high and high energies, we restore the scattering amplitude related to the t-channel exchange by vacuum quantum numbers by taking account of the diffractive s-channel rescatterings. At intermediate and moderately high energies, the t-channel exchange amplitude turns, with a good accuracy, into an effective pomeron which renders the results of the additive
quark model. At superhigh energies the scattering amplitude provides a Froissart-type behaviour, with an asymptotic universality
of cross sections such as σtot
πp/σtot
pp→ 1 at s→∞. The quark structure of hadrons being taken into account at the level of constituent quarks, the cross sections of pion
and proton (antiproton) in the impact parameter space of quarks, σπ(r
1⊥, r
2⊥; s) and σp(r
1⊥, r
2⊥, r
3⊥; s), are found as functions of s. These cross sections implicate the phenomenon of colour screening: they tend to zero at |r
i⊥−r
k⊥|→ 0. The effective colour screening radius for pion (proton) is found for different s. The predictions for the diffractive cross sections at superhigh energies are presented.
Received: 15 December 1998 相似文献
8.
Antal A. Járai 《Communications in Mathematical Physics》2003,236(2):311-334
We establish two links between two-dimensional invasion percolation and Kesten's incipient infinite cluster (IIC). We first
prove that the k
th moment of the number of invaded sites within the box [−n, n]×[−n, n] is of order (n
2π
n
)
k
, for k≥1, where π
n
is the probability that the origin in critical percolation is connected to the boundary of a box of radius n. This improves a result of Y. Zhang. We show that the size of the invaded region, when scaled by n
2π
n
, is tight.
Secondly, we prove that the invasion cluster looks asymptotically like the IIC, when viewed from an invaded site v, in the limit |v|→∞. We also establish this when an invaded site v is chosen at random from a box of radius n, and n→∞.
Received: 3 December 2000 / Accepted: 3 December 2002
Published online: 18 February 2003
RID="⋆"
ID="⋆" Present address: CWI, PNA 3, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. E-mail:jarai@cwi.nl
Communicated by M. Aizenman 相似文献
9.
Gastão A. Braga Leandro M. Ciolleti Rémy Sanchis 《Journal of statistical physics》2007,129(3):587-591
In this short note we consider mixed short-long range independent bond percolation models on ℤ
k+d
. Let p
uv
be the probability that the edge (u,v) will be open. Allowing a x,y-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior
of the connectivity τ
xy
is governed by the probability p
xy
. The result holds up to the critical point. 相似文献
10.
L. G. Moyano A. P. Majtey C. Tsallis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(4):493-500
We introduce, and numerically study, a system of N symplectically and globally coupled
standard maps localized in a d=1 lattice array. The global coupling is modulated
through a factor r-α, being
r the distance between maps. Thus, interactions are long-range (nonintegrable) when
0≤α≤1, and short-range (integrable) when α>1.
We verify that the largest Lyapunov exponent λM scales as λM ∝
N-κ(α), where κ(α) is positive when interactions are
long-range, yielding weak chaos in the thermodynamic
limit N↦∞ (hence λM→0). In the short-range case,
κ(α) appears to vanish,
and the behaviour corresponds to strong chaos. We show that, for certain
values of the control parameters of the system, long-lasting metastable states
can be present. Their duration tc scales as tc ∝Nβ(α),
where β(α) appears to be numerically in agreement with the following
behavior: β>0 for 0 ≤α< 1, and zero for α≥1.
These results are consistent with features typically found in nonextensive statistical mechanics.
Moreover, they exhibit strong similarity between the present
discrete-time system, and the α-XY Hamiltonian ferromagnetic model. 相似文献
11.
By using the thermo entangled state representation we solve the master equation for a dissipative cavity with Kerr medium
to obtain density operators’ infinite operator-sum representation ρ(t)=∑
m,n,l=0∞
M
m,n,l
ρ
0ℳ
m,n,l
†
. It is noticeable that M
m,n,l
is not Hermite conjugate to ℳ
m,n,l
†
, nevertheless the normalization ∑
m,n,l=0∞ℳ
n,m,l
†
M
m,n,l
=1 still holds, i.e., they are trace-preserving in a general sense. This example may stimulate further studying if general
superoperator theory needs modification. 相似文献
12.
H. Chamati D.M. Dantchev 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,26(1):89-99
The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite
O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic
boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r
- (d + σ), where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs
to the short-range universality class it is shown that above the bulk critical temperature T
c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems.
Received 8 August 2001 相似文献
13.
On Noncommutative Multi-Solitons 总被引:2,自引:0,他引:2
Rajesh Gopakumar Matthew Headrick Marcus Spradlin 《Communications in Mathematical Physics》2003,233(2):355-381
We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The
existence of a non-trivial moduli space at leading order in 1/θ is a consequence of a Bogomolnyi bound obeyed by the kinetic
energy of the θ=∞ solitons. In two spatial dimensions, the parameter space for k solitons is a K?hler de-singularization of the symmetric product (ℝ2)
k
/S
k
. We exploit the existence of this moduli space to construct solitons on quotient spaces of the plane: ℝ2/ℤ
k
, cylinder, and T
2
. However, we show that tori of area less than or equal to 2πθ do not admit stable solitons. In four dimensions the moduli
space provides an explicit K?hler resolution of (ℝ4)
k
/S
k
. In general spatial dimension 2d, we show it is isomorphic to the Hilbert scheme of k points in ℂ
d
, which for d>2 (and k>3) is not smooth and can have multiple branches.
Received: 29 May 2001 / Accepted: 16 August 2002 Published online: 7 November 2002
Communicated by R.H. Dijkgraaf 相似文献
14.
B. Canals D.A. Garanin 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,26(4):439-447
Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are
studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances
smaller than the correlation length, r
ξ
c∝ exp(T
*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy
of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures,
spin CFs decay as <
>∝ 1/r
2 in the range a
0≪r≪ξ
c∝T
-1/2, where a0 is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with
MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard
lattice is a classical spin liquid.
Received 16 November 2001 and Received in final form 12 February 2002 相似文献
15.
Nariyuki Minami 《Communications in Mathematical Physics》2000,213(1):203-247
Let f(ϕ) be a positive continuous function on 0 ≤ϕ≤Θ, where Θ≤ 2 π, and let ξ be the number of two-dimensional lattice points in
the domain Π
R
(f) between the curves r=(R+c
1/R)f(ϕ) and r=(R+c
2/R)f(ϕ), where c
1<c
2 are fixed. Randomizing the function f according to a probability law P, and the parameter R according to the uniform distribution μ
L
on the interval [a
1
L,a
2
L], Sinai showed that the distribution of ξ under P×μ
L
converges to a mixture of the Poisson distributions as L→∞. Later Major showed that for P-almost all f, the distribution of ξ under μ
L
converges to a Poisson distribution as L→∞. In this note, we shall give shorter and more transparent proofs to these interesting theorems, at the same time extending
the class of P and strengthening the statement of Sinai.
Received: 15 June 1999 / Accepted: 11 February 2000 相似文献
16.
Tomoyuki Shirai 《Journal of statistical physics》2006,123(3):615-629
For the fermion point process on the whole complex plane associated with the exponential kernel , we show the central limit theorem for the random variable ξ(D
r
, the number of points inside the ball D
r
of radius r, as r → ∞ and we establish the large deviation principle for the random variables {r
−2ξ (D
r
), r > 0}. 相似文献
17.
Harry A. Mavromatis 《International Journal of Theoretical Physics》2001,40(9):1665-1670
A recursion relation is derived for the potential V(r) = Ar
p. Generally, this connects off-diagonal matrix elements of r
k–2, r
k+p, r
k, and r
k+2. The diagonal case is obtained by setting m = n in this relation. The relation is derived by elementary methods and without recourse to specific properties of the eigenstates. Finally, this relation is studied for the familiar potentials p = –1, 1, 2. 相似文献
18.
D. Dantchev 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(2):211-219
The behavior of the bulk two-point correlation function G(;T| d ) in d-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties
of the susceptibility in such finite systems with periodic boundary conditions is discussed within mean-spherical model which
is an example of Ornstein and Zernike type theory. The interaction is supposed to decay at large distances r as r
- (d + σ), with 2 < d < 4, 2 < σ < 4 and d + σ≤6. It is shown that G(;T| d ) decays as r
- (d - 2) for 1 ≪r≪ξ, exponentially for ξ≪r≪r
*, where r
* = (σ - 2)ξlnξ, and again in a power law as r
- (d + σ) for r≫r
*. The analytical form of the leading-order scaling function of G(;T| d ) in any of these regimes is derived.
Received 28 May 2001 相似文献
19.
E. -S. Zanoun 《Thermophysics and Aeromechanics》2010,17(1):21-38
Effects of the upstream conditions and the degree of the wall roughness on the mean velocity profiles and some integral flow
parameters in two dimensional zero-pressure-gradient boundary layer were characterized experimentally. The results were analyzed
utilizing conventional and recent scaling flow parameters for 245< Re
θ
≤ 11·103, where Re
θ
is the Reynolds number based on the free stream velocity (Ū
∞) and the momentum thickness (θ). Good correlation of the quantity ΔŪ
+ as a function of the roughness parameter k
+ was obtained for sand roughness of 1.7 < k
+ ≤ 172, revealing a universality of the roughness effect, where ΔŪ
+ = = (Ū
∞ − Ū)/u
τ and K
+ = ku
τ
/v.The mean flow structure of the outer flow was observed not to be influenced by the degree of the wall roughness, i. e., the
outer flow of either the smooth or the rough surfaces scales similarly with the various scaling parameters regardless the
degree of the wall roughness. However, it made flow confined to the wall region away from the classical universality, allowing
similarity hypothesis not to be identical in the wall region at least for the current range of the Reynolds number. 相似文献
20.
Yu Zhang 《Journal of statistical physics》1996,84(1-2):263-267
Consider the electrical resistancer
n
(p) of a hypercubic bond lattice [O,n]
d
inZ
d
, where the bonds have resistance 1 with probabilityp or with probability 1-p. Letp
n
(p)=n
2-d
r
n
(p) andp(p)=limnpn(p). It is well known thatp(p)< ifp>p
c
andp(p)= ifp<p
c
, wherep
c
is the percolation threshold. Here we show thatp(p
c
)=, and
. 相似文献