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101.
Carl M. Bender 《Czechoslovak Journal of Physics》2006,56(9):1047-1062
In this paper, two independent methods are used to show that the non-Hermitian
-symmetric wrong-sign quartic Hamiltonian H = (1/2m)p
2 − gx
4 is exactly equivalent to the conventional Hermitian Hamiltonian
. First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated
by using functional-integration methods. As the linear term in the Hermitian Hamiltonian
is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly
is a consequence of the broken parity symmetry of the original non-Hermitian
-symmetric Hamiltonian. The anomaly term in
remains unchanged if an x
2 term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in
are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states. 相似文献
102.
Mathematische Semesterberichte - We describe in the form of a dialogue a development of various reflections on the combinatorics of set partitions; among the topics we pursue are... 相似文献
103.
Carl Bender Fred Cooper L. M. Simmons Jr. Pinaki Roy Greg Kilcup 《Journal of statistical physics》1991,64(1-2):395-428
We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx
1+2. The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t(
n))
f
as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and. 相似文献
104.
105.
Balinski uses his signature method for the proof of the Hirsch-conjecture for dual transportation polyhedra to obtain an efficient
algorithm for the assignment problem. We will show how to extend this method to other primal transportation problems, including
transportation problems with unit demands. We then prove that Balinski's assignment algorithm is equivalent, cycle by cycle,
to that of Hung and Rom. We demonstrate that, under some assumptions for our probability model, a modification of the latter
algorithm has an average complexity of O(n
2logn) and present some computational results confirming this. We also present results that indicate that this modification compares
favorably with Balinski's algorithm and other codes.
Research of both authors supported, in part, by grants of the Alexander von Humboldt-Stiftung.
Supported, in part, by NSF grant DMS-8504050. 相似文献
106.
A controlled interference is proposed to reduce, by two orders of magnitude, the decoherence of a quantum gate for which the gate fidelity is limited by coupling to states other than the /0> and /1> qubit states. This phenomenon is demonstrated in an ultracold neutral atom implementation of a phase gate using qubits based on motional states in individual wells of an optical lattice. 相似文献
107.
The evaluation of matrix functions of the form f(A)v, where A is a large sparse or structured symmetric matrix, f is a nonlinear function, and v is a vector, is frequently subdivided into two steps: first an orthonormal basis of an extended Krylov subspace of fairly small dimension is determined, and then a projection onto this subspace is evaluated by a method designed for small problems. This paper derives short recursion relations for orthonormal bases of extended Krylov subspaces of the type Km,mi+1(A)=span{A-m+1v,…,A-1v,v,Av,…,Amiv}, m=1,2,3,…, with i a positive integer, and describes applications to the evaluation of matrix functions and the computation of rational Gauss quadrature rules. 相似文献
108.
Carl Bracken Eimear Byrne Gary McGuire Gabriele Nebe 《Designs, Codes and Cryptography》2011,61(3):261-272
Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show
that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation
for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main
result is that a quadratic function is CCZ-equivalent to the APN Gold function x2r+1{x^{2^r+1}} if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family
of APN functions that exist on finite fields of order 2
n
where n ≡ 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code
associated with such a function. 相似文献
109.
Carl H. FitzGerald Frederick Weening 《Transactions of the American Mathematical Society》2000,352(2):485-513
We consider a generalization of the parallel slit uniformization in which the angle of inclination of each image slit is assigned independently. Koebe proved that for domains of finite connectivity there is, up to a normalization, a unique rectilinear slit map achieving any given angle assignment. Koebe's theorem is partially extended to domains of infinite connectivity. A uniqueness result is shown for domains of countable connectivity and arbitrary angle assignments, and an existence result is proved for arbitrary domains under the assumption that the angle assignment is continuous and has finite range. In order to prove the existence result a new extremal length tool, called the crossing-module, is introduced. The crossing-module allows greater freedom in the family of admissible arcs than the classical module. Several results known for the module are extended to the crossing-module. A generalization of Jenkins' module condition for the parallel slit problem is given for the rectilinear slit problem in terms of the crossing-module and it is shown that rectilinear slit maps satisfying this crossing-module condition exist.
110.
Philip J. Everson Carl N. Morris 《Journal of computational and graphical statistics》2013,22(2):380-389
Abstract This article provides an efficient algorithm for generating a random matrix according to a Wishart distribution, but with eigenvalues constrained to be less than a given vector of positive values. The procedure of Odell and Feiveson provides a guide, but the modifications here ensure that the diagonal elements of a candidate matrix are less than the corresponding elements of the constraint vector, thus greatly improving the chances that the matrix will be acceptable. The Normal hierarchical model with vector outcomes and the multivariate random effects model provide motivating applications. 相似文献