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181.
182.
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
183.
Massimo Campanino Abel Klein J. Fernando Perez 《Communications in Mathematical Physics》1991,135(3):499-515
We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z d, σ1, σ3 are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ3(x)σ3(y)〉 and prove:
- Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z d withC x h <∞.
- Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z d.
184.
Let
and
be independent sets of nonnegative i.i.d.r.v.'s, <x,y> denoting a pair of nearest neighbors inZ
d; let , >0. We consider the random systems: 1. A bond Bernoulli percolation model onZ
d+1 with random occupation probabilities 相似文献
185.
We consider two-dimensional Coulomb gases (standard or hard-core) with activityz, and prove that for any >8 the two-point external charges correlation function exhibits the power-law falloff characteristic of the Kosterlitz-Thouless phase at sufficiently low activity. 相似文献
186.
Ion‐Pair SN2 Reaction of OH− and CH3Cl: Activation Strain Analyses of Counterion and Solvent Effects
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Jalal Z. A. Laloo Dr. Lydia Rhyman Dr. Olatz Larrañaga Prof. Dr. Ponnadurai Ramasami Prof. Dr. F. Matthias Bickelhaupt Dr. Abel de Cózar 《化学:亚洲杂志》2018,13(9):1138-1147
We have theoretically studied the non‐identity SN2 reactions of MnOH(n?1)+CH3Cl (M+=Li+, Na+, K+, and MgCl+; n=0, 1) in the gas phase and in THF solution at the OLYP/6‐31++G(d,p) level using polarizable continuum model (PCM) implicit solvation. We want to explore and understand the effect of the metal counterion M+ and solvation on the reaction profile and the stereoselectivity of these processes. To this end, we have explored the potential energy surfaces of the backside (SN2‐b) and frontside (SN2‐f) pathways. To explain the computed trends, we have carried out analyses with an extended activation strain model (ASM) of chemical reactivity that includes the treatment of solvation effects. 相似文献
187.
188.
The necessary condition for the existence of a resolvable balanced incomplete block design on v points, with = 1 and k = 8, is that v 8 mod 56. With the exception of 66 values of v, this condition is shown to be sufficient. The largest exceptional value of v is 24480. 相似文献
189.
We show that at the special energiesE=2cosp/q, the invariant measure, the Lyapunov exponent, and the density of states can be extended to zero disorder as C functions in the disorder parameter. In particular, we obtain asymptotic series in the disorder parameter. This gives a rigorous proof of the existence of the anomalies originally discovered by Kappus and Wegner and studied by Derrida and Gardner and by Bovier and Klein.Partially supported by NSF grant DMS 87-02301 相似文献
190.
Domingos H. U. Marchetti Abel Klein J. Fernando Perez 《Journal of statistical physics》1990,60(1-2):137-166
We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have
, whereG
(x) is the two-point external charges correlation function,=dist(, Z), and
for
0$$
" align="middle" border="0">
. In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0. 相似文献