Thermally activated breakdown in a simple polymer model

We consider the thermally activated fragmentation of a homopolymer chain. In our simple model the dynamics of the intact chain is a Rouse one until a bond breaks and bond breakdown is considered as a first passage problem over a barrier to an absorbing boundary. Using the framework of the Wilemski-Fixman approximation we calculate activation times of individual bonds for free and grafted chains. We show that these times crucially depend on the length of the chain and the location of the bond yielding a minimum at the free chain ends. Theoretical findings are qualitatively confirmed by Brownian dynamics simulations

Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals

We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.Comment: 4 pages, 3 eps figure

Interfering resonances in a quantum billiard

We present a method for numerically obtaining the positions, widths and wavefunctions of resonance states in a two dimensional billiard connected to a waveguide. For a rectangular billiard, we study the dynamics of three resonance poles lying separated from the other ones. As a function of increasing coupling strength between the waveguide and the billiard two of the states become trapped while the width of the third one continues to increase for all coupling strengths. This behavior of the resonance poles is reflected in the time delay function which can be studied experimentally.Comment: 2 pages, 3 figure

Pseudo-epsilon expansion and the two-dimensional Ising model

Starting from the five-loop renormalization-group expansions for the two-dimensional Euclidean scalar \phi^4 field theory (field-theoretical version of two-dimensional Ising model), pseudo-\epsilon expansions for the Wilson fixed point coordinate g*, critical exponents, and the sextic effective coupling constant g_6 are obtained. Pseudo-\epsilon expansions for g*, inverse susceptibility exponent \gamma, and g_6 are found to possess a remarkable property - higher-order terms in these expansions turn out to be so small that accurate enough numerical estimates can be obtained using simple Pade approximants, i. e. without addressing resummation procedures based upon the Borel transformation.Comment: 4 pages, 4 tables, few misprints avoide

Theoretical study of hydrogen bonding and proton transfer in the ground and lowest excited singlet states of tropolone

Theoretical models of hydrogen bonding and proton transfer in the ground (S0) and lowest excited ππ∗ singlet (S1) states of tropolone are developed in terms of the localized OH...O fragment model and ab initio three‐dimensional potential energy surfaces (PESs). The PESs for proton transfer in the S0 and S1 states are calculated using ab initio SCF and CIS methods, respectively, with a 6–31G basis set which includes polarization functions on the atoms involved in the internal H bond. The Schrödinger equation for nuclear vibrations is solved numerically using adiabatic separation of the variables. The calculated values for the S0 state (geometry, relaxed barrier height, vibrational frequencies, tunnel splittings and H/D isotope effects) agree fairly well with available experimental and theoretical data. The calculated data for the S1 state reproduce the principal experimental trends, established for S1←S0 excitation in tropolone, but are less successful with other features of the dynamics of the excited state, e.g., the comparatively large value of vibrationless level tunnel splitting and its irregular increase with O...O excitation in S1. In order to overcome these discrepancies, a model 2‐D PES is constructed by fitting an analytical approximation of the CIS calculation to the experimental vibrationless level tunnel splitting and O...O stretch frequency of tropolone–OH. It is found that the specifics of the proton transfer in the S1 state are determined by a relatively low barrier (only one doublet of the OH stretch lies under the barrier peak). Bending vibrations play a minor role in modulation of the proton transfer barrier, so correct description of tunnel splitting of the proton stretch levels in both electronic states can be obtained in terms of the two‐dimensional stretching model, which includes O...O and O–H stretching vibration coordinates only. © 1994 American Institute of Physics

Phase transitions in open quantum systems

We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $\alpha_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.Comment: 28 pages, 22 Postscript figure