Scattered wave packet formalism for the energy-resolved reaction probability

The scattered wave packet formalism developed for a quantum subsystem interacting with reservoirs through open boundaries is utilized to calculate the energy-resolved transmission probability. The total wave function is split into incident and scattered components. Markovian outgoing wave boundary conditions are imposed on the scattered or total wave function by the polynomial method. The wave packet correlation function approach is employed to compute the energy-resolved transmission probability for a one-dimensional potential barrier and a one-dimensional model chemical reaction exhibiting a quantum resonance. Accurate results demonstrate that this formalism can significantly reduce the number of grid points required in a dynamical calculation for the reaction probability.     

Generalized Weyl–Wigner–Moyal–Ville Formalism and Topological Groups

Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal, and Ville. We analyze the relationship between this formalism and geometry of the Galilei group, classical momentum mapping, theory of unitary projective representations of groups, and theory of groups algebras. Later on, we present some generalization to quantum mechanics on locally compact Abelian groups. It is based on Pontryagin duality. Indicated are certain physical aspects in quantum dynamics of crystal lattices, including the phenomenon of ‘Umklapp–Prozessen’. Copyright © 2011 John Wiley & Sons, Ltd.     

The bending triad of the quasi-spherical top molecule SO2F2 in the 550 cm region

The analysis of the ν₃/ν₇/ν₉ bending triad of SO₂F₂ has been recently performed with the Watson’s Hamiltonian up to octic terms employing 79 rovibrational parameters but including only the first order Coriolis interaction terms, fixed to ab initio values [H. Bürger, J. Demaison, F. Hegelund, L. Margulès, I. Merke, J. Mol. Struct. 612 (2002) 133-141]. Since SO₂F₂ is a quasi-spherical top, it can also be considered as derived from the sulfate ion. We have thus developed a new tensorial formalism in the O (3) ⊃ T_d ⊃ C_2v group chain [M. Rotger, V. Boudon, M. Loëte, J. Mol. Spectrosc. 216 (2002) 297-307]. This approach allows a systematic development of rovibrational interactions and makes global analyses easier to perform even for complex polyad systems. We present here an application of this model to the analysis of the bending triad, with the same set of microwave assignments and almost the same set of infrared assignments as in the previous study of Bürger et al. It appears that we need to expand our Hamiltonian to a lower degree than the “classical” one (six instead of eight) when including also the second order Coriolis interactions. Our fit does not include more parameters. Furthermore, all of them are determined and the standard deviation of the rotational transitions is twice smaller. The analysis has been performed thanks to the C_2v TDS program suite, which is freely available at the URL: http://www.u-bourgogne.fr/LPUB/c2vTDS.html.     

The BV Formalization of Chern-Simons Theory on Deformed Superspace

In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-Simons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky (BV) formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.     

Fermionic solutions of chiral Gross–Neveu and Bogoliubov–de Gennes systems in nonlinear Schrödinger hierarchy

The chiral Gross–Neveu model or equivalently the linearized Bogoliubov–de Gennes equation has been mapped to the nonlinear Schrödinger (NLS) hierarchy in the Ablowitz–Kaup–Newell–Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n  -th NLS hierarchy generally has n+1$n+1$ gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.     

Mueller-Stokes polarimetric characterization of transmissive liquid crystal spatial light modulator

In the twisted nematic liquid crystal spatial light modulators (TN-LCSLM), distortion of uniform twist and decrease in tilt angle of liquid crystal molecules on application of an electric field lead to amplitude and phase modulations of the transmitted or reflected wavefront, respectively. The amplitude and phase modulation characterization of TN-LCSLM using Jones calculi is simple and extensively used but does not give any information about important polarimetric parameters such as diattenuation and depolarizance. On the other hand, the characterization using Mueller calculi provides all information in terms of polarimetric properties such as diattenuation, retardance (birefringence) and depolarization. In this paper, polarimetric properties of the transmissive TN-LCSLM (HOLOEYE LC2002) are characterized measuring 17 different Mueller matrices at different addressed gray scale through Mueller Matrix Imaging Polarimeter (MMIP) at 530 nm wavelength. Lu-Chipman polar decomposition for Mueller matrix is utilized to separate out three independent Mueller matrices for diattenuation, depolarization and retardance as a function of addressed gray scale. Further, Mueller-Stokes combined formulation is used to examine the effect of depolarization present in the TN-LCSLM on six different states of polarization and evaluation of eigenpolarization states for the TN-LCSLM has been presented.     

Quantifier elimination on some pseudo-algebraically closed valued fields

In this article, some theories of pseudo-algebraically closed non-trivially valued fields are shown to admit quantifier elimination in the language obtained by adjoining to the language of rings the function symbols for splitting coefficients, the function symbols for relative p-coordinate functions, and the division predicate for a valuation.     

Parameter Invariance in Field Theory and the Hamiltonian Formalism

The deparametrization problem for parameter‐invariant Lagrangian densities defined over J¹(N, F), is solved in terms of a projection onto a suitable jet bundle. The Hamilton‐Cartan formalism for such Lagrangians is then introduced and the pre‐symplectic structure of such variational problems is proved to be projectable through the aforementioned projection. Specific examples with physical meaning are also analyzed. 1998 PACS codes. 02.20.Tw Infinite‐dimensional Lie groups, 02.30.Wd Calculus of variations and optimal control, 02.40.Ky Riemannian geometries, 02.40.Ma Global differential geometry, 02.40.Vh Global analysis and analysis on manifolds, 04.20.Fy Canonical formalism, Lagrangians, and variational principles, 11.10.Ef Lagrangian and Hamiltonian approach, 11.10.Kk Field theories in dimensions other than four, 11.25.Sq Nonperturbative techniques; string field theory. 1991 Mathematics Subject Classification. Primary: 58E30 Variational principles; Secondary: 53B20 Local Riemannian geometry, 58A20 Jets, 58E12 Applications to minimal surfaces (problems in two independent variables), 58G35 Invariance and symmetry properties, 81S10 Geometric quantization, symplectic methods, 83E30 String and superstring theories.