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991.
Let m
, 0 m+ in Kato's class. We investigate the spectral function s( + m) where s( + m) denotes the upper bound of the spectrum of the Schrödinger operator + m. In particular, we determine its derivative at 0. If m- is sufficiently large, we show that there exists a unique 1 > 0 such that s( + 1m) = 0. Under suitable conditions on m+ it follows that 0 is an eigenvalue of + 1m with positive eigenfunction. 相似文献
992.
Using a multidimensional analogue of Vinogradov's inequality for a trigonometric integral, the upper bounds are constructed for the moduli of the characteristic functions both of the system of monomials in components of a random vector with an absolutely continuous distribution in
and of the system
where
is uniformly distributed in [0, l]s. 相似文献
993.
Hans-Gerd Leopold Elmar Schrohe 《Proceedings of the American Mathematical Society》1997,125(12):3679-3687
We show that the spectra of the -realizations for a class of hypoelliptic (pseudo-)differential operators are independent of in an interval around depending on the growth properties of the symbol. For elliptic operators we obtain the classical boundedness interval of Fefferman; in the general case we obtain a smaller interval which is as large as one can possibly expect it to be.
994.
Spectral properties of the polar operator depending on the smoothness of the periodic coefficient are studied. The width of the far gaps in the Bloch spectrum is shown to grow for piecewise continuous coefficients, to be asymptotically constant if the coefficient derivative is piecewise continuous, and to decrease in the more smooth cases. The high energy asymptotics of the Lyapunov function, of the quasimomentum and of effective masses are obtained. The spectral identities for the corresponding classical string equation are derived. 相似文献
995.
Zeta Function on a Generalised Cone 总被引:2,自引:0,他引:2
The analytic properties of the -function for a Laplace operator on a generalised cone
are studied in some detail using Cheeger's approach and explicit expressions are given. In the compact case, the -function of the Laplace operator turns out to be singular at the origin. As a result, strictly speaking, the -function regularisation does not regularise and a further subtraction is required for the related one-loop effective potential. 相似文献
996.
We consider the homotopy type of classifying spaces , where is a finite -group, and we study the question whether or not the mod cohomology of , as an algebra over the Steenrod algebra together with the associated Bockstein spectral sequence, determine the homotopy type of . This article is devoted to producing some families of finite 2-groups where cohomological information determines the homotopy type of .
997.
An algorithm is presented for the efficient and accurate computation of the coefficients of the characteristic polynomial of a general square matrix. The algorithm is especially suited for the evaluation of canonical traces in determinant quantum Monte-Carlo methods. 相似文献
998.
Nobuo Yoshida 《Journal of statistical physics》1998,90(3-4):1015-1035
We consider Glauber dynamics on a finite cube in d-dimensional lattice (d2), which is associated with basic Ising model at temperature T=1/1 under a magnetic field h > 0. We prove that if the effective magnetic field is positive, then the relaxation of the Glauber dynamics in the uniform norm is exponentially fast, uniformly over the size of underlying cube. The result covers the case of the free-boundary condition with arbitrarily small positive magnetic field. This paper is a continuation of an attempt initiated earlier by Schonmann and Yoshida to shed more light on the relaxation of the finite-volume Glauber dynamics when the thermodynamic parameter (, h) is so near the phase transition line, (, h);
c
< &h = 0, that the Dobrushin–Shlosman mixing condition is no longer available. 相似文献
999.
Remco van der Hofstad 《Journal of statistical physics》1998,90(5-6):1295-1310
The Edwards model in one dimension is a transformed path measure for one-dimensional Brownian motion discouraging self-intersections. We study the constants appearing in the central limit theorem (CLT) for the endpoint of the path (which represent the mean and the variance) and the exponential rate of the normalizing constant. The same constants appear in the weak-interaction limit of the one-dimensional Domb–Joyce model. The Domb–Joyce model is the discrete analogue of the Edwards model based on simple random walk, where each self-intersection of the random walk path recieves a penalty e
–2. We prove that the variance is strictly smaller than 1, which shows that the weak interaction limits of the variances in both CLTs are singular. The proofs are based on bounds for the eigenvalues of a certain one-parameter family of Sturm–Liouville differential operators, obtained by using monotonicity of the zeros of the eigen-functions in combination with computer plots. 相似文献
1000.
We derive a probabilistic expression for the symbol of the generator of a Feller process. 相似文献