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61.
This paper initiates a general study of the spectrum of two-particle bound states of transfer matrices for a fairly wide class of Gibbs fields at high temperature T. In the present first part of this study, a detailed statement of the problem is given and the existence of a so-called "isolated level" lying at a distance 1/T
2 from the boundary of the continuous spectrum is established for all values of the total quasimomentum of the system. In the concluding part of the paper, we prove that there are no other bound states provided that is far from certain singular values. In the second part, we will consider bound states for close to the singular values. The distance from these states (adjacent levels, in the authors' terminology) to the continuous spectrum is at most of the order of 1/T
4. 相似文献
62.
We study the relations between different determinants of the Dirac operator over a manifold with boundary considered as sections of a holomorphic line bundle over the Grassmannian of boundary conditions of Atiyah–Patodi–Singer type. 相似文献
63.
For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t
–(q)
when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1. 相似文献
64.
The Fredholm determinant asymptotics for self-adjoint convolution operators on finite intervals with real symbols vanishing on the real axis is studied. Explicit formulae are obtained in the case where the symbol satisfies the generalized zero index condition and has only two simple zeros of analytic type. These formulae are direct extensions of the Ahiezer–Kac–Szegö limit theorem which, in particular, take into account the oscillating character of the asymptotics. 相似文献
65.
Let 1 be an algebraic number with relatively small height. Recently, many authors, including Amoroso, Dubickas, Mignotte and Waldschmidt, stated sharp lower bounds for the quantity | – 1|. Here, we provide a p-adic analogue of their results. For instance, we give an upper bound for the absolute value of the norm of – 1, and we show that our estimate is rather sharp in terms of the degree of . Further, we discuss a generalization in several variables of our result. 相似文献
66.
Critical temperature of the classical O(N) spin model in two dimensions is investigated. We show that no phase transition exists in the system if the inverse temperature is less than c=c(N), where c(N) is a constant such that c(N) > const. N log N. 相似文献
67.
We consider the Hamiltonian , describing the motion of one quantum particle on a three-dimensional lattice in an external field. We investigate the number
of eigenvalues and their arrangement depending on the value of the interaction energy for μ ≥ 0 and λ ≥ 0.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 425–443, March, 2009. 相似文献
68.
建立了复正定矩阵的几个行列式不等式,将正定Hermite阵的Minkowski不等式、 Ostrowski-Taussky不等式推广到了复正定矩阵上,推广改进了一些文献的结果. 相似文献
69.
70.
THE OPPENHEIM-TYPE INEQUALITIES FOR THE HADAMARD PRODUCT OF M-MATRIX AND POSITIVE DEFINITE MATRIX 总被引:2,自引:0,他引:2
For the lower bound about the determinant of Hadamard product of A and B, where A is a n x n real positive definite matrix and B is a n x n M-matrix, Jianzhou Liu [SIAM J. Matrix Anal. Appl., 18(2)(1997).. 305-311] obtained the estimated inequality as follows 相似文献