Spectral analysis of electron transfer kinetics II

Electron transfer processes in Debye solvents are studied using a spectral analysis method recently proposed. Spectral structure of a nonadiabatic two-state diffusion equation is investigated to reveal various kinetic regimes characterized by a broad range of physical parameters; electronic coupling, energy bias, reorganization energy, and solvent relaxation rate. Within this unified framework, several kinetic behaviors of the electron transfer kinetics, including adiabatic Rabi oscillation, crossover from the nonadiabatic to adiabatic limits, transition from the incoherent to coherent kinetic limits, and dynamic bath effect, are demonstrated and compared with results from previous theoretical models. Dynamics of the electron transfer system is also calculated with the spectral analysis method. It is pointed out that in the large reorganization energy case the nonadiabatic diffusion equation exhibits a non-physical behavior, yielding a negative eigenvalue.Comment: submitted for a publication in Journal of Chemical Physic

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn't stationary under the flex.Comment: 10 pages, 2 Postscript figure

Polaron and bipolaron transport in a charge segregated state of doped strongly correlated 2D semiconductor

The 2D lattice gas model with competing short and long range interactions is appliedused for calculation of the incoherent charge transport in the classical strongly-correlated charge segregated polaronic state. We show, by means of Monte-Carlo simulations, that at high temperature the transport is dominated by hopping of the dissociated correlated polarons, where with thetheir mobility is inversely proportional to the temperature. At the temperatures below the clustering transition temperature the bipolaron transport becomes dominant. The energy barrier for the bipolaron hopping is determined by the Coulomb effects and is found to be lower than the barrier for the single-polaron hopping. This leads to drastically different temperature dependencies of mobilities for polarons and bipolarons at low temperatures

Emergent order in the spin-frustrated system DyxTb2-xTi2O7 studied by ac susceptibility measurements

We report the a.c. susceptibility study of Dy_xTb_{2-x}Ti_2O_7 with x in [0, 2]. In addition to the single-ion effect at Ts (single-ion effect peak temperature) corresponding to the Dy3+ spins as that in spin ice Dy_2Ti_2O_7 and a possible spin freezing peak at Tf (Tf < 3 K), a new peak associated with Tb^{3+} is observed in $\chi_{ac}(T)$ at nonzero magnetic field with a characteristic temperature T^* (Tf < T^* < Ts). T^* increases linearly with x in a wide composition range (0 < x < 1.5 at 5 kOe). Both application of a magnetic field and increasing doping with Dy3+ enhance T^*. The T^* peak is found to be thermally driven with an unusually large energy barrier as indicated from its frequency dependence. These effects are closely related to the crystal field levels, and the underlying mechanism remains to be understood.Comment: 7 pages, 5 figure

Electron relaxation in metals: Theory and exact analytical solutions

The non-equilibrium dynamics of electrons is of a great experimental and theoretical value providing important microscopic parameters of the Coulomb and electron-phonon interactions in metals and other cold plasmas. Because of the mathematical complexity of collision integrals theories of electron relaxation often rely on the assumption that electrons are in a "quasi-equilibrium" (QE) with a time-dependent temperature, or on the numerical integration of the time-dependent Boltzmann equation. We transform the integral Boltzmann equation to a partial differential Schroedinger-like equation with imaginary time in a one-dimensional "coordinate" space reciprocal to energy which allows for exact analytical solutions in both cases of electron-electron and electron-phonon relaxation. The exact relaxation rates are compared with the QE relaxation rates at high and low temperatures.Comment: Citation list has been extended. The paper is submitted to the Physical Review

From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators

In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. An important feature of this group element is its simplicity: this is a group element of the Virasoro subalgebra of $gl(\infty)$. If proved, this conjecture would allow to derive the Virasoro constraints for the Hurwitz tau-function, which remain unknown in spite of existence of several matrix model representations, as well as to give an integrable operator description of the Kontsevich--Witten tau-function.Comment: 13 page