Convergence properties of the q-deformed binomial distribution

Zeiner, Martin

doi:10.2298/aadm100217016z

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Probability Distribution Of Total Change Of Spin Polarization1

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Cited by 5 publications

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“…Since its introduction [15], this distribution has been extensively studied. For example, its generating function is given in [15], and its mean can be expressed in terms of the q-Pochhammer symbols and q-binomial coefficients [19]. Mathematically, it is referred to as the q-Bernstein basis function, in connection with q-Bernstein polynomials [17,18].…”

Section: Probability Distribution Of Total Change Of Spin Polarizationmentioning

confidence: 99%

Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

Sun

Sinitsyn

2016

Phys. Rev. A

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We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and q-deformed binomial statistics.

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Section: Probability Distribution Of Total Change Of Spin Polarizationmentioning

confidence: 99%