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1.
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
2.
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
3.
We investigate the spectrum of the following random Schrödinger operators:
相似文献
4.
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
5.
Y. A. Gordon V. Jakšić S. Molčanov B. Simon 《Communications in Mathematical Physics》1993,157(1):23-50
We investigate spectral properties of random Schrödinger operators H = - + n()(1 + |n|) acting onl
2(Z
d), where n are independent random variables uniformly distributed on [0, 1].Research partially supported by a Sloan Doctoral Dissertation Fellowship and NSERC under grant OGP-0007901Research partially supported by NSF grant DMS-9101716 相似文献
6.
Shu Nakamura 《Communications in Mathematical Physics》1994,161(1):63-76
Low energy behavior of Schrödinger operators with potentials which decay slowly at infinity is studied. It is shown that if the potential is positive then the zero energy is very regular and the resolvent is smooth near 0. This implies rapid local decay for the solutions of the Schrödinger equation. On the other hand, if the potential is negative then the resolvent has discontinuity at zero energy. Thus one cannot expect local decay faster than ordert
–1 ast. 相似文献
7.
We consider the Schrödinger operatorH = – +V(|x|) onR
3. Letn
denote the number of bound states with angular momentum (not counting the 2 + 1 degeneracy). We prove the following bounds onn
. LetV 0 and d/dr r
1-2p
(-V)1 –p
0 for somep [1/2, 1) then
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