Temporally stable coherent states for infinite well and Poschl-Teller potentials
- J. Antoine, J. Gazeau, P. Monceau, J. Klauder, K. Penson
- Mathematics, Physics
- 27 December 2000
This article is a direct illustration of a construction of coherent states which has been recently proposed by two of us (JPG and JK). We have chosen the example of a particle trapped in an infinite…
Generating random density matrices
- K. Życzkowski, K. Penson, I. Nechita, B. Collins
- Mathematics
- 18 October 2010
We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states,…
Product of Ginibre matrices: Fuss-Catalan and Raney distributions.
- K. Penson, K. Życzkowski
- MathematicsPhysical review. E, Statistical, nonlinear, and…
- 17 March 2011
Using similar techniques, involving the Mellin transform and the Meijer G function, it is found exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers.
Exact and explicit probability densities for one-sided Lévy stable distributions.
All the known results given by k ≤ 4 are reproduced and many new exact solutions for k > 4 are presented, all expressed in terms of known functions, to allow a "fine-tuning" of α in order to adapt gα(x) to a given experimental situation.
Constructing coherent states through solutions of Stieltjes and Hausdorff moment problems
- J. Klauder, K. Penson, J. Sixdeniers
- Mathematics
- 13 June 2001
PROBABILITY DISTRIBUTIONS WITH BINOMIAL MOMENTS
- W. Mlotkowski, K. Penson
- Mathematics
- 3 September 2013
We prove that if $p\geq 1$ and $-1\leq r\leq p-1$ then the binomial sequence $\binom{np+r}{n}$, $n=0,1,...$, is positive definite and is the moment sequence of a probability measure $\nu(p,r)$, whose…
Coherent States from Combinatorial Sequences
- K. Penson, A. Solomon
- Mathematics
- 28 November 2001
We construct coherent states using sequences of combinatorial numbers such as various binomial and trinomial numbers, and Bell and Catalan numbers. We show that these states satisfy the condition of…
Combinatorics and Boson normal ordering: A gentle introduction
- P. Blasiak, A. Horzela, U. Paris
- Mathematics
- 24 April 2007
We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the…
Integral Representations of Catalan and Related Numbers
- K. Penson, J. Sixdeniers
- Mathematics
- 1 October 2001
ONE-PARAMETER GROUPS AND COMBINATORIAL PHYSICS
- G. Duchamp, K. Penson, Poland
- Mathematics
- 20 January 2004
In this communication, we consider the normal ordering of sums of elements of the form (a*^r a a*^s), where a* and a are boson creation and annihilation operators. We discuss the integration of the…
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