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1 February 1, 2008 7:33 WSPC/Trim Size: 9in x 6in for Proceedings 1param2 2 In this communication, we consider the normal ordering of operators of the type â„¦ = Î±+Î²=e+1 c Î±,Î² (a +) Î± a(a +) Î² , whereâ€¦ (More)

We construct coherent states using sequences of combinatorial numbers such as various binomial and trinomial numbers, and Bell and Cata-lan numbers. We show that these states satisfy the condition ofâ€¦ (More)

- Karol A. Penson, Karol Zyczkowski
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2011

Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions P(s)(x), such that their moments are equal to the Fuss-Catalanâ€¦ (More)

For any function F (x) having a Taylor expansion we solve the boson normal ordering problem for F [ (aâ€ )ras ] , with r, s positive integers, [ a, aâ€ ] = 1, i.e. we provide exact and explicitâ€¦ (More)

The Heisenbergâ€“Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebraâ€¦ (More)

- K. GÃ³rska, Karol A. Penson, D. Babusci, Giuseppe Dattoli, G'erard Henry Edmond Duchamp
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2012

We obtain exact results for fractional equations of Fokker-Planck type using the evolution operator method. We employ exact forms of one-sided LÃ©vy stable distributions to generate a set ofâ€¦ (More)

We consider the numbers arising in the problem of normal ordering of expressions in boson creation a and annihilation a operators ([a, a] = 1). We treat a general form of a boson string (a)nanâ€¦ (More)

Abstract. The general normal ordering problem for boson strings is a combinatorial problem. In this talk we restrict ourselves to single-mode boson monomials. This problem leads to elegantâ€¦ (More)

Abstract. A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In thi s note we consider the normal ordering problem for aâ€¦ (More)

- Karol A. Penson, K. GÃ³rska
- Physical review letters
- 2010

We study functions gÎ±(x) which are one-sided, heavy-tailed LÃ©vy stable probability distributions of index Î±, 0<Î±<1, of fundamental importance in random systems, for anomalous diffusion and fractionalâ€¦ (More)