5,370 research outputs found
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 ÏÏâ singlet (S1) states of tropolone are developed in terms of the localized OH...O fragment model and ab initio threeâdimensional 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 6â31G 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 S1âS0 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 2âD 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 tropoloneâOH. 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 twoâdimensional stretching model, which includes O...O and OâH 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
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 of
the control parameter globally over the whole energy range of the spectrum. All
states act cooperatively.Comment: 28 pages, 22 Postscript figure
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