共查询到20条相似文献,搜索用时 15 毫秒
1.
G. A. Mezincescu 《Communications in Mathematical Physics》1986,103(1):167-176
The integrated density of states has C-like singularities, ln|k(E)–k(E
c
)|=–|E–E
c
|–v/2
c
(E), with
c
>0, a milder function at the edges of the spectral gaps which appear when the distribution function of the potentiald has a sufficiently large gap. The behaviour of
c
nearE
c
is determined by the local continuity properties ofd near the relevant edge:
c
(E)=O(1) ifd has an atom and =O(ln|E–E
c
|) if is (absolutely) continuous and power bounded. 相似文献
2.
We prove for small and satisfying a certain Diophantine condition the operator
相似文献
3.
We provide lower bounds on the eigenvalue splitting for ?d 2/dx 2+V(x) depending only on qualitative properties ofV. For example, ifV is C∝ on [a, b] andE n ,E n?1 are two successive eigenvalues of ?d 2/dx 2+V withu(a)=u(b)=0 boundary conditions, and if \(\lambda = \mathop {\max }\limits_{E \in (E_{n - 1} ,E_n );x \in (a,b)} |E - V(x)|^{1/2} \) , then $$E_n - E_{n - 1} \geqq \pi \lambda ^2 \exp \left[ { - \lambda (b - a)} \right]$$ . The exponential factor in such bounds are saturated precisely in tunneling examples. Our results arenot restricted toV's of compact support, but only require \(E_n< \mathop {\lim }\limits_{\overline {x \to \infty } } V(x)\) . 相似文献
4.
LetS ?=??Δ+V, withV smooth. If 0<E 2
5.
We studyH=–d
2/dx
2+V(x) withV(x) limit periodic, e.g.V(x)=a
n
cos(x/2
n
) with a
n
<. We prove that for a genericV (and for generica
n
in the explicit example), (H) is a Cantor ( nowhere dense, perfect) set. For a dense set, the spectrum is both Cantor and purely absolutely continuous and therefore purely recurrent absolutely continuous.Research partially supported by NSF Grant MCS78-01885On leave from Department of Physics, Princeton UniversityOn leave from Departments of Mathematics and Physics, Princeton University; during 1980–81 Sherman Fairchild Visiting Scholar at Caltech 相似文献
6.
We give new examples of discrete Schrödinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hullX of the potential is strictly ergodic, then the existence of just one potentialx inX for which the operator has no eigenvalues implies that there is a generic set inX for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such anx is that there is azX that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset inX. The class includes well-known substitutions like Fibonacci, Thue-Morse, Period Doubling, binary non-Pisot and ternary non-Pisot. We also show that the operator has no absolutely continuous spectrum for allxX ifX derives from a primitive substitution. For potentials defined by circle maps,x
n
=1
J
(0+n), we show that the operator has purely singular continuous spectrum for a generic subset inX for all irrational and every half-open intervalJ.Work partially supported by NSERC.This material is based upon work supported by the National Science Foundation under Grant No. DMS-91-1715. The Government has certain rights in this material. 相似文献
7.
Frédéric Klopp 《Communications in Mathematical Physics》1995,167(3):553-569
We study the spectrum of random Schrödinger operators acting onL
2(R
d
) of the following type
. The
are i.i.d. random variables. Under weak assumptions onV, we prove exponential localization forH at the lower edge of its spectrum. In order to do this, we give a new proof of the Wegner estimate that works without sign assumptions onV.
Résumé Dans ce travail, nous étudions le spectre d'opérateurs de Schrödinger aléatoires agissant surL 2(R d ) du type suivant . Les sont des variables aléatoires i.i.d. Sous de faibles hypothèses surV, nous démontrons que le bord inférieur du spectre deH n'est composé que de spectre purement ponctuel et, que les fonctions propres associées sont exponentiellement décroissantes. Pour ce faire nous donnons une nouvelle preuve de l'estimée de Wegner valable sans hypothèses de signe surV. U.R.A. 760 C.N.R.S. 相似文献 8.
9.
10.
We prove localization at high disorder or low energy for lattice Schrödinger operators with random potentials whose values at different lattice sites are correlated over large distances. The class of admissible random potentials for our multiscale analysis includes potentials with a stationary Gaussian distribution whose covariance functionC(x,y) decays as |x–y|–, where >0 can be arbitrarily small, and potentials whose probability distribution is a completely analytical Gibbs measure. The result for Gaussian potentials depends on a multivariable form of Nelson's best possible hypercontractive estimate.Partially supported by the NSF under grant PHY8515288Partially supported by the NSF under grant DMS8905627 相似文献
11.
12.
E. Balslev 《Communications in Mathematical Physics》1977,52(2):127-146
The complex-dilated many-body Schrödinger operatorH(z) is decomposed on invariant subspaces associated with the cuts {+z
–2
R
+}, where is any threshold, and isolated spectral points. The interactions are dilation-analytic multiplicative two-body potentials, decaying asr
–1+ atr=0 and asr
–1+ atr=. 相似文献
13.
Theq=0 combinatorics for
is studied in connection with solvable lattice models. Crystal bases of highest weight representations of
are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors atq=0. It is shown that the crystal graphs for finite tensor products ofl-th symmetric tensor representations of
approximate the crystal graphs of levell representations of
. The identification is made between restricted paths for the RSOS models and highest weight vectors in the crystal graphs of tensor modules for
.Partially supported by NSF grant MDA904-90-H-4039 相似文献
14.
A. Angeletti 《Letters in Mathematical Physics》1980,4(6):495-504
Let (x) be the Dirac's delta,q(x)L
1
(R)L
2
(R) be a real valued function, and , R; we will consider the following class of one-dimensional formal Schrödinger operators on
. It is known that to the formal operator
may be associated a selfadjoint operatorH(,) onL
2(R). Ifq is of finite range, for >0 and || is small enough, we prove thatH(,) has an antibound state; that is the resolvent ofH(,) has a pole on the negative real axis on the second Riemann sheet.Work done while the author was supported by an undergraduate fellowship of the (Italian) National Research Council (CNR). 相似文献
15.
Walter Craig 《Communications in Mathematical Physics》1983,88(1):113-131
The finite difference Schrödinger operator on ? m is considered $$Hu_j = \left( {\sum\limits_{v = 1}^m { D_v^2 } } \right)u_j + \frac{1}{\varepsilon }q_j u_j ,u \in \ell ^2 (\mathbb{Z}^m ),$$ where \(\sum\limits_{v = 1}^m { D_v^2 } \) is the difference Laplacian inm dimensions. For ? sufficiently small almost periodic potentialsq j are constructed such that the operatorH has only pure point spectrum. The method is an inverse spectral procedure, which is a modification of the Kolmogorov-Arnol'd-Moser technique. 相似文献
16.
Walter Craig 《Communications in Mathematical Physics》1989,126(2):379-407
This paper discusses certain aspects of the spectral and inverse spectral problems for the Schrödinger operator
, for q(x)C(), the space of bounded continuous functions. The trace formula of the title is the relation
|