The Experts below are selected from a list of 63 Experts worldwide ranked by ideXlab platform

Stephen Wiggins - One of the best experts on this subject based on the ideXlab platform.

  • Periodic-Orbit Formula for quantum reactions through transition states
    Physical Review A, 2010
    Co-Authors: Roman Schubert, Holger Waalkens, Arseni Goussev, Stephen Wiggins
    Abstract:

    Transition state theory forms the basis of computing reaction rates in chemical and other systems. Recently, it has been shown how transition state theory can rigorously be realized in phase space by using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this paper, these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic Orbits contained in the transition state.

  • A Periodic Orbit Formula for Quantum Reactions Through Transition States
    2010
    Co-Authors: Arseni Goussev, Roman Schubert, Holger Waalkens, Stephen Wiggins
    Abstract:

    Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov‐Siegert resonances. These results are used here to derive a Formula which expresses the cumulative reaction probability as an absolutely convergent sum over periodic Orbits contained in the transition state.

Roman Schubert - One of the best experts on this subject based on the ideXlab platform.

  • Periodic-Orbit Formula for quantum reactions through transition states
    Physical Review A, 2010
    Co-Authors: Roman Schubert, Holger Waalkens, Arseni Goussev, Stephen Wiggins
    Abstract:

    Transition state theory forms the basis of computing reaction rates in chemical and other systems. Recently, it has been shown how transition state theory can rigorously be realized in phase space by using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this paper, these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic Orbits contained in the transition state.

  • A Periodic Orbit Formula for Quantum Reactions Through Transition States
    2010
    Co-Authors: Arseni Goussev, Roman Schubert, Holger Waalkens, Stephen Wiggins
    Abstract:

    Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov‐Siegert resonances. These results are used here to derive a Formula which expresses the cumulative reaction probability as an absolutely convergent sum over periodic Orbits contained in the transition state.

D Biswas - One of the best experts on this subject based on the ideXlab platform.

  • Arbitrary trajectory quantization method.
    Physical review. E Statistical nonlinear and soft matter physics, 2000
    Co-Authors: D Biswas
    Abstract:

    The arbitrary trajectory quantization method (ATQM) is a time dependent approach to quasiclassical quantization based on the approximate dual relationship that exists between the quantum energy spectra and classical periodic Orbits. It has recently been shown however, that, for polygonal billiards, the periodicity criterion must be relaxed to include closed almost-periodic (CAP) Orbit families in this relationship. In light of this result, we reinvestigate the ATQM and show that at finite energies, a smoothened quasiclassical kernel corresponds to the modified Formula that includes CAP families while the delta function kernel corresponding to the periodic Orbit Formula is recovered as E-->infinity. Several clarifications are also provided.

  • Arbitrary trajectory quantization method.
    Physical Review E, 2000
    Co-Authors: D Biswas
    Abstract:

    The arbitrary trajectory quantization method (ATQM) is a time dependent approach to quasiclassical quantization based on the approximate dual relationship that exists between the quantum energy spectra and classical periodic Orbits. It has recently been shown however, that, for polygonal billiards, the periodicity criterion must be relaxed to include closed almost-periodic (CAP) Orbit families in this relationship. In light of this result, we reinvestigate the ATQM and show that at finite energies, a smoothened quasiclassical kernel corresponds to the modified Formula that includes CAP families while the $\ensuremath{\delta}$ function kernel corresponding to the periodic Orbit Formula is recovered as $\stackrel{\ensuremath{\rightarrow}}{E}\ensuremath{\infty}.$ Several clarifications are also provided.

Arseni Goussev - One of the best experts on this subject based on the ideXlab platform.

  • Periodic-Orbit Formula for quantum reactions through transition states
    Physical Review A, 2010
    Co-Authors: Roman Schubert, Holger Waalkens, Arseni Goussev, Stephen Wiggins
    Abstract:

    Transition state theory forms the basis of computing reaction rates in chemical and other systems. Recently, it has been shown how transition state theory can rigorously be realized in phase space by using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this paper, these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic Orbits contained in the transition state.

  • A Periodic Orbit Formula for Quantum Reactions Through Transition States
    2010
    Co-Authors: Arseni Goussev, Roman Schubert, Holger Waalkens, Stephen Wiggins
    Abstract:

    Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov‐Siegert resonances. These results are used here to derive a Formula which expresses the cumulative reaction probability as an absolutely convergent sum over periodic Orbits contained in the transition state.

Salma Nasrin - One of the best experts on this subject based on the ideXlab platform.

  • Corwin–Greenleaf multiplicity functions for complex semisimple symmetric spaces
    International Journal of Mathematics, 2015
    Co-Authors: Salma Nasrin
    Abstract:

    Let Gℂ be a complex simple Lie group, GU a compact real form, and [Formula: see text] the natural projection between the dual of the Lie algebras. We prove that, for any coadjoint Orbit [Formula: see text] of GU, the intersection of [Formula: see text] with a coadjoint Orbit [Formula: see text] of Gℂ is either an empty set or a single Orbit of GU if [Formula: see text] is isomorphic to a complex symmetric space.

  • CORWIN–GREENLEAF MULTIPLICITY FUNCTIONS FOR HERMITIAN SYMMETRIC SPACES AND MULTIPLICITY-ONE THEOREM IN THE Orbit METHOD
    International Journal of Mathematics, 2010
    Co-Authors: Salma Nasrin
    Abstract:

    Kobayashi's multiplicity-free theorem asserts that irreducible unitary highest-weight representations π are multiplicity-free when restricted to every symmetric pair if π is of scalar type. The aim of this paper is to find the "classical limit" of this multiplicity-free theorem in terms of the geometry of two coadjoint Orbits, for which the correspondence is predicted by the Kirillov–Kostant–Duflo Orbit method.For this, we study the Corwin–Greenleaf multiplicity function [Formula: see text] for Hermitian symmetric spaces G/K. First, we prove that [Formula: see text] for any G-coadjoint Orbit [Formula: see text] and any K-coadjoint Orbit [Formula: see text] if [Formula: see text]. Here,