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1.
Letters in Mathematical Physics - We characterize quantum perfect state transfer on real-weighted graphs of the Johnson scheme $${\mathcal {J}}(n,k)$$ , which represent spin networks with... 相似文献
2.
The multivariate quantum q-Krawtchouk polynomials are shown to arise as matrix elements of “q-rotations” acting on the state vectors of many q-oscillators. The focus is put on the two-variable case. The algebraic interpretation is used to derive the main properties of the polynomials: orthogonality, duality, structure relations, difference equations, and recurrence relations. The extension to an arbitrary number of variables is presented. 相似文献
3.
The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the \({\mathfrak{su}(1,1)}\) algebra. The Hamiltonian of the 3-parameter system and the generators of its quadratic symmetry algebra are seen to correspond to the total and intermediate Casimir operators of the combination of three \({\mathfrak{su}(1,1)}\) algebras, respectively. The construction makes explicit the isomorphism between the Racah–Wilson algebra, which is the fundamental algebraic structure behind the Racah problem for \({\mathfrak{su}(1, 1)}\) , and the invariance algebra of the generic 3-parameter system. It also provides an explanation for the occurrence of the Racah polynomials as overlap coefficients in this context. The irreducible representations of the Racah–Wilson algebra are reviewed as well as their connection with the Askey scheme of classical orthogonal polynomials. 相似文献
4.
M. Hofheinz X. Jehl M. Sanquer G. Molas M. Vinet S. Deleonibus 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,54(3):299-307
We study anomalies in the Coulomb blockade spectrum of a quantum dot
formed in a silicon nanowire. These anomalies are attributed to electrostatic
interaction with charge traps in the device. A simple model reproduces these
anomalies accurately and we show how the capacitance matrices of the traps can
be obtained from the shape of the anomalies. From these capacitance matrices
we deduce that the traps are located near or inside the wire. Based on the
occurrence of the anomalies in wires with different doping levels we infer
that most of the traps are arsenic dopant states. In some cases the anomalies
are accompanied by a random telegraph signal which allows time resolved
monitoring of the occupation of the trap. The spin of the trap states is
determined via the Zeeman shift. 相似文献
5.
6.
Krall and Sheffer found in 1967 that there exists at most nine different types of two-dimensional orthogonal polynomials which are eigensolutions of a second-order linear differential operator with polynomial coefficients. We show that, for all these types, there correspond quantum mechanical systems on a Euclidean (pseudo-Eeuclidean) plane, two-dimensional sphere, or hyperboloid. 相似文献
7.
Roberto FloreaniniLuc Vinet 《Physics letters. A》1993,180(6):393-401
Certain automorphisms of the quantum oscillator algebra are shown to provide an algebraic interpretation for q-generalizations of the Charlier polynomials. 相似文献
8.
Using the factorization method, we construct finite-difference Schrödinger operators (Jacobi matrices) whose discrete spectra are composed from independent arithmetic, or geometric series. Such systems originate from the periodic, orq-periodic closure of a chain of corresponding Darboux transformations. The Charlier, Krawtchouk, Meixner orthogonal polynomials, theirq-analogs, and some other classical polynomials appear as the simplest examples forN = 1 andN = 2 (N is the period of closure). A natural generalization involves discrete versions of the Painlevé transcendents.On leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia. 相似文献
9.
Roberto Floreanini Javier Negro Luis Miguel Nieto Luc Vinet 《Letters in Mathematical Physics》1996,36(4):351-355
Discrete versions of the heat equation on two-dimensional uniform lattices are shown to possess the same symmetry algebra as their continuum limits. Solutions with definite symmetry properties are presented. 相似文献
10.
Formulas of Rodrigues-type for the Macdonald polynomials are presented. They involve creation operators, certain properties of which are proved and other conjectured. The limiting case of the Jack polynomials is discussed. 相似文献