Quantum Charge Transport and Conformational Dynamics of Macromolecules

We study the dynamics of quantum excitations inside macromolecules which can undergo conformational transitions. In the first part of the paper, we use the path integral formalism to rigorously derive a set of coupled equations of motion which simultaneously describe the molecular and quantum transport dynamics, and obey the fluctuation/dissipation relationship. We also introduce an algorithm which yields the most probable molecular and quantum transport pathways in rare, thermally-activated reactions. In the second part of the paper, we apply this formalism to simulate the propagation of a charge during the collapse of a polymer from an initial stretched conformation to a final globular state. We find that the charge dynamics is quenched when the chain reaches a molten globule state. Using random matrix theory we show that this transition is due to an increase of quantum localization driven by dynamical disorder.Comment: 11 pages, 2 figure

Unitary relations in time-dependent harmonic oscillators

For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as well as operators. For a driven harmonic oscillator, it is also shown that, there are unitary transformations which give the driven system from the system of same mass and frequency without driving force. The transformation for a driven oscillator depends on the solution of classical equation of motion of the driven system. These transformations, thus, give a simple way of finding exact wave functions of a driven harmonic oscillator system, provided the quantum states of the corresponding system of unit mass are given.Comment: Submitted to J. Phys.

Frobenius theorem and invariants for Hamiltonian systems

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assurately restricted to a two-dimensional foliation. In some cases, Frobenius theorem allows the explicit construction of an associated invariant. It is proven the inverse result that, if an invariant is known, then it always can be furnished by Frobenius theorem

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

Polarization Energy Gradients in Combined Quantum Mechanics, Effective Fragment Potential, and Polarizable Continuum Model Calculations

A method that combines quantum mechanics (QM), typically a solute, the effective fragment potential (EFP) discrete solvent model, and the polarizable continuum model is described. The EFP induced dipoles and polarizable continuum model (PCM) induced surface charges are determined in a self-consistent fashion. The gradients of these two energies with respect to molecular coordinate changes are derived and implemented. In general, the gradients can be formulated as simple electrostatic forces and torques among the QM nuclei, electrons, EFP static multipoles, induced dipoles, and PCM induced charges. Molecular geometry optimizations can be performed efficiently with these gradients. The formulas derived for EFP∕PCM can be generally applied to other combined molecular mechanics and continuum methods that employ induced dipoles and charges

How long before the end of inflation were observable perturbations produced?

We reconsider the issue of the number of e-foldings before the end of inflation at which observable perturbations were generated. We determine a plausible upper limit on that number for the standard cosmology which is around 60, with the expectation that the actual value will be up to 10 below this. We also note a special property of the $\lambda \phi^4$ model which reduces the uncertainties in that case and favours a higher value, giving a fairly definite prediction of 64 e-foldings for that model. We note an extreme (and highly implausible) situation where the number of e-foldings can be even higher, possibly up to 100, and discuss the shortcomings of quantifying inflation by e-foldings rather than by the change in $aH$. Finally, we discuss the impact of non-standard evolution between the end of inflation and the present, showing that again the expected number of e-foldings can be modified, and in some cases significantly increased.Comment: 7 pages RevTeX4 file with one figure incorporated. Minor updates to match version accepted by Physical Review

Prevalence, patterns, and predictors of meditation use among US adults: A nationally representative survey

Emerging evidence suggests substantial health benefits from using meditation. While there are some indications that the popularity of meditation is increasing, little is known about the prevalence, patterns, and predictors of meditation use in the general population. In this secondary analysis of data from the 2012 US National Health Interview Survey (NHIS) (n = 34,525), lifetime and 12-month prevalence of meditation use were 5.2% and 4.1%, respectively. Compared to non-users, those who had used meditation in the past 12 months were more likely to be 40-64 years, female, non-Hispanic White, living in the West, at least college-educated, not in a relationship, diagnosed with one or more chronic conditions, smoking, consuming alcohol and physically active. Meditation was mainly used for general wellness (76.2%), improving energy (60.0%), and aiding memory or concentration (50.0%). Anxiety (29.2%), stress (21.6%), and depression (17.8%) were the top health problems for which people used meditation; 63.6% reported that meditation had helped a great deal with these conditions. Only 34.8% disclosed their use of meditation with a health provider. These findings indicate that about 9.3 million US adults have used meditation in the past 12 months; and that mental health problems were the most important reason for meditation use

A dynamical system approach to higher order gravity

The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review the main results and I give brief comments on the perspectives for further developments.Comment: 6 pages, 1 figure, 2 tables, talk given at IRGAC 2006, July 200

Sparrows can't sing : East End kith and kinship in the 1960s

Sparrows Can’t Sing (1963) was the only feature film directed by the late and much lamented Joan Littlewood. Set and filmed in the East End, where she worked for many years, the film deserves more attention than it has hitherto received. Littlewood’s career spanned documentary (radio recordings made with Ewan MacColl in the North of England in the 1930s) to directing for the stage and the running of the Theatre Royal in London’s Stratford East, often selecting material which aroused memories in local audiences (Leach 2006: 142). Many of the actors trained in her Theatre Workshop subsequently became better known for their appearances on film and television. Littlewood herself directed hardly any material for the screen: Sparrows Can’t Sing and a 1964 series of television commercials for the British Egg Marketing Board, starring Theatre Workshop’s Avis Bunnage, were rare excursions into an area of practice which she found constraining and unamenable (Gable 1980: 32). The hybridity and singularity of Littlewood’s feature may answer, in some degree, for its subsequent neglect. However, Sparrows Can’t Sing makes a significant contribution to a group of films made in Britain in the 1960s which comment generally on changes in the urban and social fabric. It is especially worthy of consideration, I shall argue, for the use which Littlewood made of a particular community’s attitudes – sentimental and critical – to such changes and for its amalgamation of an attachment to documentary techniques (recording an aural landscape on location) with a preference for nonnaturalistic delivery in performance