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51.
We study primitive theta functions, which were first introduced by Shintani, in a purely local setting. We investigate a metaplectic representation of U(1) acting on the space of local primitive theta functions and give its explicit irreducible decomposition. As a by-product, we give a new proof of epsilon dichotomy for (U(1),U(1)). 相似文献
52.
We introduce a class of non-commutative Heisenberg-like infinite-dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to be bounded. Brownian motion and the corresponding heat kernel measures, {νt}t>0, are also studied. We show that these heat kernel measures admit: (1) Gaussian like upper bounds, (2) Cameron-Martin type quasi-invariance results, (3) good Lp-bounds on the corresponding Radon-Nikodym derivatives, (4) integration by parts formulas, and (5) logarithmic Sobolev inequalities. The last three results heavily rely on the boundedness of the Ricci tensor. 相似文献
53.
In this paper we answer to a question raised by Ambrosio and Rigot [L. Ambrosio, S. Rigot, Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2) (2004) 261-301] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is absolutely continuous if one of the end-points is. Since our proof relies on the validity of the so-called Measure Contraction Property and on the fact that the optimal transport map exists and the Wasserstein geodesic is unique, the absolute continuity of Wasserstein geodesic also holds for Alexandrov spaces with curvature bounded from below. 相似文献
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55.
REN Jie ZHU Shi-Qun 《理论物理通讯》2008,49(6):1449-1452
The effects of anisotropy and magnetic field on multipartite entanglement of ground state in Heisenberg XY model are investigated. The multipartite entanglement increases as a function of the inverse strength of the external field when the degree of anisotropy is finite. There are two peaks when the degree of anisotropy is γ=±1. When the degree of anisotropy increases further, the multipartite entanglement will decrease and tend to a constant. The threshold of the inverse strength of the external field for generating multipartite entanglement generally decreases with the increasing of qubits. 相似文献
56.
Yongyang JIN 《数学年刊B辑(英文版)》2008,29(5):567-574
The author obtains some weighted Hardy-type inequalities on H-type groups and anisotropic Heisenberg groups. These inequalities generalize some recent results due to N. Garofalo, E. Lanconelli, I. Kombe and P. Niu et al. 相似文献
57.
Qiaohua Yang 《Journal of Mathematical Analysis and Applications》2008,341(2):998-1006
Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. We prove a refined version of the Sobolev inequality on N in presence of symmetry. 相似文献
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60.
R. Der 《Journal of statistical physics》1987,46(1-2):391-424
On a semiphenomenological level, generalized Langevin equations are usually obtained by adding a random force (RF) term to macroscopic deterministic equations assumed to be known. Here this procedure is made rigorous by conveniently redefining the RF, which is shown to be colored noise weakly correlated with the observables at earlier times due to the finite lifetime of microscopic events. Corresponding fluctuation-dissipation theorems are derived. Explicit expressions for the spectral density of the fluctuations are obtained in a particularly simple form, with the deviation of the line shape from the Lorentzian being related most explicitly to the spectral density of the RF. Well-known low-frequency expressions and the Einstein relation of (generalized) Brownian motion theory are modified so as to include lifetime effects. New sum rules are obtained relating dissipative quantities to contour integrals (in the complex frequency domain) over spectral densities or corresponding response functions. The Heisenberg dynamics of a complete set of macroobservables is shown to be equivalent to a generalized Orstein-Uhlenbeck stochastic process which is a non-Markovian process due to the lifetime effects. 相似文献