arXiv subjects

E. I. Kats

Publications and source records attributed to E. I. Kats.

50 records · Page 3Linked to original sources

arXiv2004

Quasistationary states and coherent versus incoherent transitions for crossing diabatic potentials

We investigate coherent and incoherent tunneling phenomena in conditions of crossing diabatic potentials. We consider a model of two crossing parabolic diabatic potentials with an independent of coordinates constant adiabatic coupling. As a result of the coupling and level crossing avoiding, we get the asymmetric double-well lower adiabatic potential with a variable shape. We show that the doublet structure of levels (generic for double-well potentials) is remained valid as long as the transition matrix element is smaller than characteristic inter-level spacings (the latter ones in own turn decrease upon increasing of a difference between the diabatic potential minima). In the adiabatic limit the tunneling transitions do not depend on the upper potential. In the over-barrier energy region there is an oscillating behavior due to the resonances between the states in the lower and in the upper adiabatic potentials. A new phenomenom emanated from this oscillating dependence namely, multiple coherent - incoherent regime transitions for the upper adiabatic potential state evolution, is our main concern in this paper. The problem is not only of intellectual interest but also of relevance to various molecular systems undergoing conversion of electronic states or isomerization reactions. Our model exhausts all cases practically relevant for spectroscopy of non-rigid molecules, and can capture many of the features exhibited by experiment.

cond-mat.stat-mech↗

arXiv2004

Semiclassical quantization of bound and quasi-stationary states beyond the adiabatic approximation

We examine one important (and overlooked in all previous investigations) aspect of well - known crossing diabatic potentials or Landau - Zener (LZ) problem. We derive the semiclassical quantization rules for the crossing diabatic potentials with localized initial and localized or delocalized final states, in the intermediate energy region, when all four adiabatic states are coupled and should be taken into account. In fact these situations exhaust all cases practically relevant for spectroscopy of non-rigid molecules (i.e. with more than one stable configuration).

cond-mat.stat-mech↗

arXiv2003

Instanton versus traditional WKB approach to Landau - Zener problem

Different theoretical approaches to the famous two state Landau - Zener problem are briefly discussed. Apart from traditional methods of the adiabatic perturbation theory, Born - Oppenheimer approximation with geometric phase effects, two-level approach, and momentum space representation, the problem is treated semiclassically also in the coordinate space. Within the framework of the instanton approach we present a full and unified description of 1D Landau-Zener problem of level crossing. The method enables us to treat accurately all four transition points (appearing at two levels crossing), while the standard WKB approach takes into account only two of them. The latter approximation is adequate for calculating of the transition probability or for studying of scattering processes, however it does not work for finding corresponding chemical reactions rates, where very often for typical range of parameters all four transition points can be relevant. Applications of the method and of the results may concern the various systems in physics, chemistry and biology.

cond-mat.stat-mech↗

arXiv2002

Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations

We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is therefore realized either along one trajectory or along two equivalent paths. Zero point fluctuations smear out the sharp transition between these two regimes and lead to a certain crossover behavior. When the two saddle points are inequivalent one can also have a first order transition related to the fact that one of the two trajectories becomes unstable. We illustrate these results by numerical investigations. Even though a specific model is investigated here, the approach is quite general and has potential applicability for various systems in physics and chemistry exhibiting multi-stability and tunneling phenomena.

cond-mat.stat-mech↗

arXiv2002

Disclination motion in hexatic and smectic-C films

We present theoretical study of a single disclination motion in a thin free standing hexatic (or smectic-C) film, driven by a large-scale inhomogeneity in the bond (or director) angle. Back-flow effects and own dynamics of the bond angle are included. We find the angle and hydrodynamic velocity distributions around the moving disclination, what allows us to relate the disclination velocity to the angle gradient far from the disclination. Different cases are examined depending on the ratio of the rotational and shear viscosity coefficients.

cond-mat.soft↗

arXiv2002

Sound modes in composite incommensurate crystals

We propose a simple phenomenological model describing composite crystals, constructed from two parallel sets of periodic inter-penetrating chains. In the harmonic approximation and neglecting thermal fluctuations we find the eigenmodes of the system. It is shown that at high frequencies there are two longitudinal sound modes with standard attenuation, while in the low frequency region there is one propagating sound mode and an over-damped phase mode. The crossover between these two regions is analyzed numerically and the dynamical structure factor is calculated. It is shown that the qualitative features of the experimentally observed spectra can be consistently described by our model.

cond-mat.mtrl-sci↗

arXiv2002

Base pair dynamic assisted charge transport in DNA

An 1d model with time-dependent random hopping is proposed to describe charge transport in DNA. It admits to investigate both diffusion of electrons and their tunneling between different sites in DNA. The tunneling appears to be strongly temperature-dependent. Observations of a strong (exponential) as well as a weak distance dependence of the charge transfer in DNA can be explained in the framework of our model.

cond-mat.soft↗

arXiv2001

Coherent oscillations and incoherent tunnelling in one - dimensional asymmetric double - well potential

For a model 1d asymmetric double-well potential we calculated so-called survival probability (i.e. the probability for a particle initially localised in one well to remain there). We use a semiclassical (WKB) solution of Schroedinger equation. It is shown that behaviour essentially depends on transition probability, and on dimensionless parameter which is a ratio of characteristic frequencies for low energy non-linear in-well oscillations and inter wells tunnelling. For the potential describing a finite motion (double-well) one has always a regular behaviour. For the small value of the parameter there is well defined resonance pairs of levels and the survival probability has coherent oscillations related to resonance splitting. However for the large value of the parameter no oscillations at all for the survival probability, and there is almost an exponential decay with the characteristic time determined by Fermi golden rule. In this case one may not restrict oneself to only resonance pair levels. The number of perturbed by tunnelling levels grows proportionally to the value of this parameter (by other words instead of isolated pairs there appear the resonance regions containing the sets of strongly coupled levels). In the region of intermediate values of the parameter one has a crossover between both limiting cases, namely the exponential decay with subsequent long period recurrent behaviour.

cond-mat.stat-mech↗

arXiv2001

Concerted motion of protons in hydrogen bonds of DNA-type molecules

We study the dynamical behaviour of the proton transfer in the hydrogen bonds in the base-pairs of the double helices of the DNA type. Under the assumption that the elastic and the tunnelling degrees of freedom may be coupled, we derive a non-linear and non-local Schrodinger equation (SNLNL) that describes the concerted motion of the proton tunnelling. Rough estimates of the solutions to the SNLNL show an intimate interplay between the concerted tunnelling of protons and the symmetry of double helix.

cond-mat.soft↗

arXiv2000

Novel Cholesteric Phase in Dispersions of Nucleic Acids due to Polymeric Chelate Bridges

We consider cholesteric liquid-crystalline DNA dispersions, and show that polymeric (Dau-Cu) complexes, the so-called bridges, between pairs of DNA molecules may generate a super liquid-crystalline structure (BR-phase). The latter could have a layered spatial structure and an abnormal optical activity that could have a bearing upon the intense CD-band observed in DNA-dispersions.

cond-mat.soft↗

arXiv2000

Network of Hydrogen Bonds as a Medium for DNA Interaction in Solvents

We suggest that the DNA molecules could form the cholesteric phase owing to an interaction mediated by the network of the hydrogen bonds (H-network) in the solvent. The model admits of the dependence of the optical activity of the solution on the concentration of the PEG, and the change in the sense of the cholesteric twist due to the intercalation by the daunomicyn. Using the experimental data for the cholesteric phase of the DNA dispersion, we obtain a rough estimate for the energy given by our model, and show that it should be taken into account as well as the energy due to the steric repulsion, van der Waals, and electrostatic forces, generally used for studying the DNA molecules. The elastic constant of the H-network generating the interaction between the DNA molecules is determined by the energy due to the proton's vibration in the hydrogen bonds.

cond-mat.soft↗

arXiv1999

Domain Structures of Smectic Films Formed by Bent-Shaped Molecules

We formulate a simple Landau type model describing macroscopic behaviour recently discovered new smectic phases composed of achiral bent-shaped molecules. Films of such smectics exhibit three types of ordering related to dipole polarization, molecular tilt, and chirality. However due to specific third order coupling of the order parameters these three types of symmetry-breaking are not independent ones, and this fact leads to specific domain structures really observed in experiments.

cond-mat.soft↗

arXiv1999

A Model for Double-Stranded Excitations of DNA

We calculate the spectrum of torsional vibrations of a double-stranded structure that models the double helix of the DNA. We come to the conclusion that within the framework of the model elementary excitations may display an asymmetry as regards their winding and direction of the propagation, depending on initial polarization. The asymmetry could have a bearing on processes that take place in molecules of the DNA.

cond-mat.soft↗

arXiv1997

Dynamic Fluctuation Phenomena in Double Membrane Films

Dynamics of double membrane films is investigated in the long-wavelength limit including the overdamped squeezing mode. We demonstrate that thermal fluctuations essentially modify the character of the mode due to its nonlinear coupling to the transversal shear hydrodynamic mode. The corresponding Green function acquires as a function of the frequency a cut along the imaginary semi-axis. Fluctuations lead to increasing the attenuation of the squeezing mode it becomes larger than the `bare' value.

cond-mat.soft↗