S-matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient of a neutral gas. Here, we take another look at this approach, and discuss the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the 'pole' expansion and the physical significance of the 'higher' poles.Comment: 20 pages, 8 tables, submitted to J. Mol. Phy

Semiclassical interpretation of Wei–Norman factorization for SU(1,1) and its related integral transforms

J.G. thanks the Spanish Ministerio de Ciencia, Innovacion y Universidades for financial support (Grant Nos. FIS2017-84440-C2-2-P and PGC2018-097831-B-I00). M.B. acknowledges the hospitality of the University of Jaen and the Institute Carlos I of Theoretical and Computational Physics (University of Granada).We present an interpretation of the functions appearing in the Wei–Norman factorization of the evolution operator for a Hamiltonian belonging to the SU(1,1) algebra in terms of the classical solutions of the Generalized Caldirola–Kanai (GCK) oscillator (with time-dependent mass and frequency). Choosing P2, X2, and the dilation operator as a basis for the Lie algebra, we obtain that, out of the six possible orderings for the Wei–Norman factorization of the evolution operator for the GCK Hamiltonian, three of them can be expressed in terms of its classical solutions and the other three involve the classical solutions associated with a mirror Hamiltonian obtained by inverting the mass. In addition, we generalize the Wei–Norman procedure to compute the factorization of other operators, such as a generalized Fresnel transform and the Arnold transform (and its generalizations), obtaining also in these cases a semiclassical interpretation for the functions in the exponents of the Wei–Norman factorization. The singularities of the functions appearing in the Wei–Norman factorization are related to the caustic points of Morse theory, and the expression of the evolution operator at the caustics is obtained using a limiting procedure, where the Fourier transform of the initial state appears along with the Guoy phase.Spanish Ministerio de Ciencia, Innovacion y Universidades FIS2017-84440-C2-2-P PGC2018-097831-B-I0

Visualization 2: Vector fields in a tight laser focus: comparison of models

Animation of the Singh model for a tight focus Originally published in Optics Express on 26 June 2017 (oe-25-13-13990

Visualization 6: Vector fields in a tight laser focus: comparison of models

Animation of the Singh model for a loose focus Originally published in Optics Express on 26 June 2017 (oe-25-13-13990

Visualization 5: Vector fields in a tight laser focus: comparison of models

Animation of the Quesnel model Originally published in Optics Express on 26 June 2017 (oe-25-13-13990