Preface to Illinois Classical Studies v.18 1993: Studies in Honor of Miroslav Marcovich

published or submitted for publicatio

Getting excited: Challenges in quantum-classical studies of excitons in polymeric systems

A combination of classical molecular dynamics (MM/MD) and quantum chemical calculations based on the density functional theory (DFT) was performed to describe conformational properties of diphenylethyne (DPE), methylated-DPE and poly para phenylene ethynylene (PPE). DFT calculations were employed to improve and develop force field parameters for MM/MD simulations. Many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation were utilized to describe excited states of the systems. Reliability of the excitation energies based on the MM/MD conformations was examined and compared to the excitation energies from DFT conformations. The results show an overall agreement between the optical excitations based on MM/MD conformations and DFT conformations. This allows for calculation of excitation energies based on MM/MD conformations

Fragment Rotational Distributions From The Dissociation Of NeBr2: Experimental And Classical Trajectory Studies

The Br-2 fragment rotational distributions that result from the vibrational predissociation of NeBr2 in the B electronic state have been measured for several initial vibrational levels. In each case, the rotational distributions extend to the effective energetic Limit determined by the amount of energy available (E(av1)) for disposal into the fragment rotational and translational degrees of freedom. Analysis of the data allows refinement of the NeBr2 dissociation energy; we find that D-0=70.0 +/- 1.1 cm(-1) for the X electronic state, v = 0. Both Delta v = - 1 and -2 dissociation events have been examined. For dissociation pathways with approximately the same value of E(av1) the Delta v = -2 pathways are observed to have a higher fraction of the fragment energy in rotational excitation. The overall shape of the Delta v = -1 distributions are insensitive to the value of E(av1), suggesting that a Franck-Condon model for the dissociation may have some validity, though quantitative quantum mechanical calculations demonstrate that this model does not reproduce the large degree of fragment rotational excitation. Two classical models for the dissociation also fail to reproduce the extent of fragment rotational distribution. This result is discussed in light of previous experimental and theoretical investigations, focusing on the apparent agreement of classical models with the IBr fragment rotational distributions that result from the dissociation of NeIBr. (C) 1997 American Institute of Physics

Boundary Terms for Massless Fermionic Fields

Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal to the boundary and a pair of independent spinor fields. This paper studies the corresponding classical properties, i.e. the classical boundary-value problem and boundary terms in the variational problem. Interestingly, a link is found with the classical boundary-value problem when spectral boundary conditions are imposed on a 3-sphere in the massless case. Moreover, the boundary term in the action functional is derived.Comment: 8 pages, plain-tex, recently appearing in Foundations of Physics Letters, volume 7, pages 303-308, year 199

Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization

In this work we study the competition and correspondence between the classical and quantum routes to intramolecular vibrational energy redistribution (IVR) in a three degrees of freedom model effective Hamiltonian. Specifically, we focus on the classical and the quantum dynamics near the resonance junctions on the Arnold web that are formed by intersection of independent resonances. The regime of interest models the IVR dynamics from highly excited initial states near dissociation thresholds of molecular systems wherein both classical and purely quantum, involving dynamical tunneling, routes to IVR coexist. In the vicinity of a resonance junction classical chaos is inevitably present and hence one expects the quantum IVR pathways to have a strong classical component as well. We show that with increasing resonant coupling strengths the classical component of IVR leads to a transition from coherent dynamical tunneling to incoherent dynamical tunneling. Furthermore, we establish that the quantum IVR dynamics can be predicted based on the structures on the classical Arnold web. In addition, we investigate the nature of the highly excited eigenstates in order to identify the quantum signatures of the multiplicity-2 junctions. For the parameter regimes studies herein, by projecting the eigenstates onto the Arnold web, we find that eigenstates in the vicinity of the junctions are primarily delocalized due to dynamical tunneling.Comment: 17 pages, 9 figures (reduced size), Accepted in J. Phys. Chem. A (2018) for William P. Reinhardt Festschrif

Quantum and Classical Superballistic Transport in a Relativistic Kicked-Rotor System

As an unusual type of anomalous diffusion behavior, superballistic transport is not well known but has been experimentally simulated recently. Quantum superballistic transport models to date are mainly based on connected sublattices which are constructed to have different properties. In this work, we show that both quantum and classical superballistic transport in the momentum space can occur in a simple periodically driven Hamiltonian system, namely, a relativistic kicked-rotor system with a nonzero mass term. The nonzero mass term essentially realizes a junction-like scenario: regimes with low or high momentum values have different dispersion relations and hence different transport properties. It is further shown that the quantum and classical superballistic transport should occur under much different choices of the system parameters. The results are of interest to studies of anomalous transport, quantum and classical chaos, and the issue of quantum-classical correspondence.Comment: 10 pages, 8 figure

Geometric Phase and Classical-Quantum Correspondence

We study the geometric phase factors underlying the classical and the corresponding quantum dynamics of a driven nonlinear oscillator exhibiting chaotic dynamics. For the classical problem, we compute the geometric phase factors associated with the phase space trajectories using Frenet-Serret formulation. For the corresponding quantum problem, the geometric phase associated with the time evolution of the wave function is computed. Our studies suggest that the classical geometric phase may be related to the the difference in the quantum geometric phases between two neighboring eigenstates.Comment: Copy with higher resolution figures can be obtained from http://physics.gmu.edu/~isatija by clicking on publications. to appear in the Yukawa Institute conference proceedings, {\it Quantum Mechanics and Chaos: From Fundamental Problems through Nano-Science} (2003