共查询到20条相似文献,搜索用时 15 毫秒
1.
Fabian Schwarzenberger 《Journal of statistical physics》2012,146(6):1156-1183
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely
generated amenable group. We prove that the integrated density of states (IDS) or spectral distribution function can be approximated
uniformly in the energy variable. This result is already new for percolation on ℤ
d
. Using this, we are able to characterize the set of discontinuities of the IDS. 相似文献
2.
Felix Pogorzelski Fabian Schwarzenberger Christian Seifert 《Letters in Mathematical Physics》2013,103(9):1009-1028
Given an arbitrary, finitely generated, amenable group we consider ergodic Schrödinger operators on a metric Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume parts converge uniformly. The integrated density of states (IDS) as the limit can be expressed by a Pastur-Shubin formula. The spectrum supports the corresponding measure and discontinuities correspond to the existence of compactly supported eigenfunctions. In this context, the present work generalises the hitherto known uniform IDS approximation results for operators on the d-dimensional metric lattice to a very large class of geometries. 相似文献
3.
4.
Daniel Lenz Norbert Peyerimhoff Olaf Post Ivan Veseli? 《Mathematical Physics, Analysis and Geometry》2009,12(3):219-254
We establish several properties of the integrated density of states for random quantum graphs: Under appropriate ergodicity
and amenability assumptions, the integrated density of states can be defined using an exhaustion procedure by compact subgraphs.
A trace per unit volume formula holds, similarly as in the Euclidean case. Our setting includes periodic graphs. For a model
where the edge lengths are random and vary independently in a smooth way we prove a Wegner estimate and related regularity
results for the integrated density of states. These results are illustrated for an example based on the Kagome lattice. In
the periodic case we characterise all compactly supported eigenfunctions and calculate the position and size of discontinuities
of the integrated density of states.
相似文献
5.
C. Alves M. R. Hilário B. N. B. De Lima D. Valesin 《Journal of statistical physics》2017,169(5):972-980
We consider oriented long-range percolation on a graph with vertex set \({\mathbb {Z}}^d \times {\mathbb {Z}}_+\) and directed edges of the form \(\langle (x,t), (x+y,t+1)\rangle \), for x, y in \({\mathbb {Z}}^d\) and \(t \in {\mathbb {Z}}_+\). Any edge of this form is open with probability \(p_y\), independently for all edges. Under the assumption that the values \(p_y\) do not vanish at infinity, we show that there is percolation even if all edges of length more than k are deleted, for k large enough. We also state the analogous result for a long-range contact process on \({\mathbb {Z}}^d\). 相似文献
6.
Roberto H. Schonmann 《Communications in Mathematical Physics》2002,225(3):453-463
The critical exponents β, γ, δ and Δ are proved to exist and to take their mean-field values for independent percolation
on the following classes of infinite, locally finite, connected transitive graphs: (1) Non-amenable planar with one end. (2)
Unimodular with infinitely many ends.
Received: 4 April 2001 / Accepted: 4 October 2001 相似文献
7.
Steffen Klassert Daniel Lenz Peter Stollmann 《Communications in Mathematical Physics》2003,241(2-3):235-243
Despite all the analogies with usual random models, tight binding operators for quasicrystals exhibit a feature that clearly distinguishes them from the former: the integrated density of states may be discontinuous. This phenomenon is identified as a local effect, due to the occurrence of eigenfunctions with bounded support.Research partly supported by the DFG in the priority program Quasicrystals 相似文献
8.
Ivan Veselić 《Letters in Mathematical Physics》2011,97(1):25-27
The integrated density of states of a Schrödinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive mean, is locally uniformly Lipschitz-continuous. This is proven using a Wegner estimate. 相似文献
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11.
We analyse the density of states of the random graph Laplacian in the percolating regime. A symmetry argument and knowledge
of the density of states in the nonpercolating regime allows us to isolate the density of states of the percolating cluster
(DSPC) alone, thereby eliminating trivially localised states due to finite subgraphs. We derive a nonlinear integral equation
for the integrated DSPC and solve it with a population dynamics algorithm. We discuss the possible existence of a mobility
edge and give strong evidence for the existence of discrete eigenvalues in the whole range of the spectrum. 相似文献
12.
Given two weighted graphs (X, bk, mk), k =?1,2 with b1 ~ b2 and m1 ~ m2, we prove a weighted L1-criterion for the existence and completeness of the wave operators W±(H2, H1, I1,2), where Hk denotes the natural Laplacian in ?2(X, mk) w.r.t. (X, bk, mk) and I1,2 the trivial identification of ?2(X, m1) with ?2(X, m2). In particular, this entails a general criterion for the absolutely continuous spectra of H1 and H2 to be equal. 相似文献
13.
Classical lattice systems with random Hamiltonians $$\frac{1}{2}\sum\limits_{x_1 \ne x_2 } {\frac{{\varepsilon (x_1 ,x_2 )\varphi (x_1 )\varphi (x_2 )}}{{\left| {x_1 - x_2 } \right|^{\alpha d} }}}$$ are considered, whered is the dimension, andε(x 1,x 2) are independent random variables for different pairs (x 1,x 2),Eε(x 1,x 2) = 0. It is shown that the free energy for such a system exiists with probability 1 and does not depend on the boundary conditions, providedα > 1/2. 相似文献
14.
Daniel Lenz Norbert Peyerimhoff Ivan Veselić 《Mathematical Physics, Analysis and Geometry》2007,10(1):1-41
We study spectral properties of random operators in the general setting of groupoids and von Neumann algebras. In particular, we establish an explicit formula for the canonical trace of the von Neumann algebra of random operators and define an abstract density of states. While the treatment applies to a general framework we lay special emphasis on three particular examples: random Schrödinger operators on manifolds, quantum percolation and quasi–crystal Hamiltonians. For these examples we show that the distribution function of the abstract density of states coincides with the integrated density of states defined via an exhaustion procedure. 相似文献
15.
Wen-Xin Qin 《Communications in Mathematical Physics》2012,311(2):513-538
In this paper we are mainly concerned with existence and modulation of uniform sliding states for particle chains with damping
γ and external driving force F. If the on-site potential vanishes, then for each F > 0 there exist trivial uniform sliding states x
n
(t) = n
ω + ν
t + α for which the particles are uniformly spaced with spacing ω > 0, the sliding velocity of each particle is ν = F/γ, and the phase α is arbitrary. If the particle chain with convex interaction potential is placed in a periodic on-site potential,
we show under some conditions the existence of modulated uniform sliding states of the form
xn(t)=nw+nt+a+u(nw+nt+a),x_n(t)=n\omega+\nu t+\alpha+u(n\omega+\nu t+\alpha), 相似文献
16.
17.
Journal of Statistical Physics - We consider some kinds of graphs obtained by generalizing the pre-Sierpinski carpet, which is one of well known fractal lattices. Here, we deal with not only some... 相似文献
18.
D.V. Georgievskii 《Russian Journal of Mathematical Physics》2018,25(4):492-499
In the system formed by a heavy elastic layer (lithosphere) and a half-space filled by an ideal incompressible fluid (asthenosphere), the possibility of the existence of equilibrium states with curved boundaries near an equilibrium of a system with rectilinear boundaries is investigated. Using an analysis of the characteristic equation, we obtain a relationship between the wave number of the desired static perturbation and the dimensionless parameters of the problem, namely, the dimensionless shear modulus, Poisson’s ratio, and the decompression. The assumption that the deformations are small imposes conditions on the ranges of modification of the quantities. For example, for a moderately compressible elastic material, the equilibrium which is called tectonic waves in geophysical applications is possible only in the long-wavelength range in the presence of the inversion of density and very strong decompression. The stability problem with respect to small dynamical perturbations of an (obtained) equilibrium with curved boundaries is stated. A wave dispersion relation connecting the complex frequency of oscillations with the wave number of perturbations and with the above dimensionless parameters of the system is derived. 相似文献
19.
Wilhelm Schlag 《Communications in Mathematical Physics》2001,223(1):47-65
In this paper we consider discrete Schr?dinger operators on the lattice ℤ2 with quasi periodic potential. We establish new regularity results for the integrated density of states, as well as a quantitative
version of a “Thouless formula”, as previously considered by Craig and Simon, for real energies and with rates of convergence.
The main ingredient is a large deviation theorem for the Green's function that was recently established by Bourgain, Goldstein,
and the author. For the integrated density of states an argument of Bourgain is used. Finally, we establish certain fine properties
of separately subharmonic functions of two variables that might be of independent interest.
Received: 13 February 2001 / Accepted: 21 May 2001 相似文献
20.
Hubert Lacoin 《Journal of statistical physics》2014,154(6):1461-1482
Let $Z_N$ be the number of self-avoiding paths of length $N$ starting from the origin on the infinite cluster obtained after performing Bernoulli percolation on ${\mathbb Z} ^d$ with parameter $p>p_c({\mathbb Z} ^d)$ . The object of this paper is to study the connective constant of the dilute lattice $\limsup _{N\rightarrow \infty } Z_N^{1/N}$ , which is a non-random quantity. We want to investigate if the inequality $\limsup _{N\rightarrow \infty } (Z_N)^{1/N} \le \lim _{N\rightarrow \infty } {\mathbb E} [Z_N]^{1/N}$ obtained with the Borel–Cantelli Lemma is strict or not. In other words, we want to know if the quenched and annealed versions of the connective constant are equal. On a heuristic level, this indicates whether or not localization of the trajectories occurs. We prove that when $d$ is sufficiently large there exists $p^{(2)}_c>p_c$ such that the inequality is strict for $p\in (p_c,p^{(2)}_c)$ . 相似文献
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