Biomedical subjects

Andrey Pereverzev

Publications and source records attributed to Andrey Pereverzev.

6 recordsLinked to original sources

PubMed2006

Time-convolutionless master equation for mesoscopic electron-phonon systems.

The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number of normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers.

Journal Article↗

PubMed2006

Exactly solvable approximating models for Rabi Hamiltonian dynamics.

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonalizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By keeping only certain terms, we can achieve an excellent approximation to the exact dynamics within specified parameter ranges.

Biophysical Phenomena↗

PubMed2005

Quantum transport in chains with noisy off-diagonal couplings.

We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time evolution of the system reduces to the [Lindblad, Commun. Math. Phys. 48, 119 (1976)] equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfies discrete versions of the heat and diffusion equations. Transport coefficients are given in terms of model Hamiltonian parameters. We discuss conditions on the Hamiltonian under which the noise-averaged expectation value of the total energy remains constant. For chains placed between two heat reservoirs, the gradient of the energy density along the chain is linear.

Journal Article↗

PubMed2005

Competing elimination and substitution reactions of simple acyclic disulfides.

MP2/aug-cc-pVDZ and B3LYP/cc-pVDZ calculations of the reactions of CH3SSR (R = H or CH3) with fluoride, hydroxide or allyl anion in the gas-phase were performed to determine the mechanism for both elimination and substitution reactions. The elimination reactions were shown to follow the E2 mechanism. The substitution reactions with hydroxide and fluoride proceed by the addition-elimination mechanism, but those with allyl anion proceed by the SN2 mechanism. The elimination reactions with F- and HO- are preferred to the substitution reactions, while allyl anion prefers the substitution route.

Journal Article↗

PubMed2003

Fermi-Pasta-Ulam beta lattice: Peierls equation and anomalous heat conductivity.

The Peierls equation is considered for the Fermi-Pasta-Ulam beta lattice. Explicit form of the linearized collision operator is obtained. Using this form the decay rate of the normal-mode energy as a function of wave vector k is estimated to be proportional to k(5/3). This leads to the t(-3/5) long-time behavior of the current correlation function, and, therefore, to the divergent coefficient of heat conductivity. These results are in good agreement with the results of recent computer simulations. Compared to the results obtained through the mode coupling theory our estimations give the same k dependence of the decay rate but a different temperature dependence. Using our estimations we argue that adding a harmonic on-site potential to the Fermi-Pasta-Ulam beta lattice may lead to finite heat conductivity in this model.

Journal Article↗

PubMed2003

Damped harmonic oscillator: pure states of the bath and exact master equations.

Time evolution of a harmonic oscillator linearly coupled to a heat bath is compared for three classes of initial states for the bath modes-grand canonical ensemble, number states, and coherent states. It is shown that for a wide class of number states the behavior of the oscillator is similar to the case of the equilibrium bath. If the bath modes are initially in coherent states, then the variances of the oscillator coordinate and momentum, as well as its entanglement to the bath, asymptotically approach the same values as for the oscillator at zero temperature and the average coordinate and momentum show a Brownian-like behavior. We derive an exact master equation for the characteristic function of the oscillator valid for arbitrary factorized initial conditions. In the case of the equilibrium bath this equation reduces to an equation of the Hu-Paz-Zhang type, while for the coherent states bath it leads to an exact stochastic master equation with a multiplicative noise.

Journal Article↗