arXiv subjects

E. I. Kats

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

At least 37 records · Page 2Linked to original sources

arXiv2013

Twisted quasiperiodic textures of biaxial nematics

Textures (i.e., smooth space non-uniform distributions of the order parameter) in biaxial nematics turned out to be much more difficult and interesting than expected. Scanning the literature we find only a very few publications on this topic. Thus, the immediate motivation of the present paper is to develop a systematic procedure to study, classify and visualize possible textures in biaxial nematics. Based on the elastic energy of a biaxial nematic (written in the most simple form that involves the least number of phenomenological parameters) we derive and solve numerically the Lagrange equations of the first kind. It allows one to visualize the solutions and offers a deep insight into their geometrical and topological features. Performing Fourier analysis we find some particular textures possessing two or more characteristic space periods (we term such solutions quasiperiodic ones because the periods are not necessarily commensurate). The problem is not only of intellectual interest but also of relevance to optical characteristics of the liquid-crystalline textures.

cond-mat.soft↗

arXiv2013

Vibrational energy transport in molecular wires

Motivated by recent experimental observation (see e.g., I.V.Rubtsov, Acc. Chem. Res., v. 42, 1385 (2009)) of vibrational energy transport in CH_2O_N and CF_2_N molecular chains (N = 4 - 12), in this paper we present and solve analytically a simple one dimensional model to describe theoretically these data. To mimic multiple conformations of the molecular chains, our model includes random off-diagonal couplings between neighboring sites. For the sake of simplicity we assume Gaussian distribution with dispersion sigma for these coupling matrix elements. Within the model we find that initially locally excited vibrational state can propagate along the chain. However the propagation is neither ballistic nor diffusion like. The time T_m for the first passage of the excitation along the chain, scales linearly with N in the agreement with the experimental data. Distribution of the excitation energies over the chain fragments (sites in the model) remains random, and the vibrational energy, transported to the chain end at $t=T_m$ is dramatically decreased when sigma is larger than characteristic interlevel spacing in the chain vibrational spectrum. We do believe that the problem we have solved is not only of intellectual interest (or to rationalize mentioned above experimental data) but also of relevance to design optimal molecular wires providing fast energy transport in various chemical and biological reactions.

cond-mat.mes-hall↗

arXiv2012

Revivals in Caldeira - Leggett Hamiltonian Dynamics

In this work we reconsider the problem discussed by Caldeira and Leggett (CL), and generalize their results for a quantum oscillator coupled bilinearly to a reservoir with dense discrete spectrum of harmonic oscillators. We show that for such systems dynamic evolution of any state of the CL Hamiltonian consists of recurrence cycles with partial revivals of the initial state amplitude. This revival or Loschmidt echo appears in each cycle due to reverse (from the reservoir) transitions (not existing in the limit of a macroscopic bath). Width and number of the Loschmidt echo components increase with the recurrence cycle number, eventually leading to irregular, stochastic-like time evolution. Standard for continuous spectrum thermal bath CL dynamics dissipative dynamics (exponential decay) takes place only within the initial cycle. In terms of the effective CL Hamiltonian, where the reservoir degrees of freedom are integrated out, our results mean oscillatory (time periodic) behavior of the effective mass. Only in the initial cycle, we found the known for CL Hamiltonian exponential in time increase of the effective mass. We do believe that the basic ideas inspiring our work can be applied to a large variety of interesting nano-systems and molecular complexes.

cond-mat.mes-hall↗

arXiv2011

Rupture of a Biomembrane under Dynamic Surface Tension

How long a fluid membrane vesicle stressed with a steady ramp of micropipette last before rupture? Or conversely, how high the surface tension should be to rupture a membrane? To answer these challenging questions we have developed a theoretical framework that allows description and reproduction of Dynamic Tension Spectroscopy (DTS) observations. The kinetics of the membrane rupture under ramps of surface tension is described as a combination of initial pore formation followed by Brownian process of the pore radius crossing the time-dependent energy barrier. We present the formalism and derive (formal) analytical expression of the survival probability describing the fate of the membrane under DTS conditions. Using numerical simulations for the membrane prepared in an initial state with a given distribution of times for pore nucleation, we have studied the membrane lifetime (or inverse of rupture rate) and distribution of membrane surface tension at rupture as a function of membrane characteristics like pore nucleation rate, the energy barrier to failure and tension loading rate. It is found that simulations reproduce main features of the experimental data, particularly, the pore nucleation and pore size diffusion controlled limits of membrane rupture dynamics. This approach can also be applied to processes of permeation and pore opening in membranes (electroporation, membrane disruption by antimicrobial peptides, vesicle fusion).

cond-mat.soft↗

arXiv2010

Dynamic and spectral mixing in nanosystems

In the framework of simple spin-boson Hamiltonian we study an interplay between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian describes an initial vibrational state coupled to discrete dense spectrum reservoir. The reservoir states are formed by three sequences with rationally independent periodicities typical for vibrational states in many nanosize systems. We show that quantum evolution of the system is determined by a dimensionless parameter which is characteristic number of the reservoir states relevant for the initial vibrational level dynamics. Our semi-quantitative analytic results are confirmed by numerical solution of the equation of motion. We anticipate that predicted in the paper both kinds of stochastic-like behavior (namely, due to spectral mixing and recurrence cycle dynamic mixing) can be observed by femtosecond spectroscopy methods in nanosystems.

cond-mat.mes-hall↗

arXiv2010

Liquid-Crystal Smectic with Six-Layer Periodic Structure

Recently Wang et al. [Phys. Rev. Lett. 104, 027801 (2010)] discovered a new polar smectic phase with six-layer period (SmC*d6). In this manuscript, we demonstrate that the theory [Phys. Rev. E 67, 041716 (2003)] based on the free energy expansion with a two-component order parameter predicted the six-layer phase, describes its structure and the phase sequence observed in experiment [Phys. Rev. Lett. 104, 027801 (2010)].

cond-mat.soft↗

arXiv2009

Soft modes and thermal transport in guest-host crystalline structures

We propose a simple phenomenological model describing vibrational dynamics in a class of materials (like clathrates), which are crystalline compounds with closed cavities in their structures. In the spirit of a minimalist approach, our model includes only the minimum of ingredients necessary to capture the generic features of this class of compounds as brought to light by experiments. We consider only two kinds of particles: strongly coupled host atoms, which form the structural cavities, and guest atoms confined in the cavities. In spite of the confinement, for relatively small amplitude vibrations of the guest atoms, their interaction with the host particles is assumed to be weaker than between the host atoms. We calculate self-consistently the vibrational mode (phonon) line broadenings for the empty and filled (by the guest atoms) cavities. We show that the soft phonon dispersion sheet, which appears for weakly bonded guest atoms, yields to large mode broadening via three waves anharmonic mode coupling. In turn the Umklapp part of this broadening reduces drastically the phonon thermoconductivity coefficient. We conclude that for a system with a soft mode component in the vibrational spectrum phonon broadening is always larger and thermal conductivity is always appreciably smaller than for a system without this soft mode (provided all other characteristics are the same). Although our model is minimal, in the sense of ignoring the complexity of actual guest-host structures, when properly interpreted, it can yield quite reasonable values for a variety of measurable quantities.

cond-mat.mtrl-sci↗

arXiv2009

New mechanism for non-trivial intra-molecular vibrational dynamics

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state, coupled to all other intra-molecular vibrational states of the same molecule, and also to its environment. Molecular states forming the first reservoir are characterised by a discrete dense spectrum, whereas the environment reservoir states form a continuous spectrum. Assuming the equidistant reservoir states we find the exact analytical solution of the quantum dynamic equations. System reservoirs couplings yield to spontaneous decay of the states, whereas system-reservoir exchange leads to recurrence cycles and Loschmidt echo and double resonances at the interlevel reservoir transitions. Due to these couplings the system $S$ time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are four possible dynamic regimes of the evolution: (i) - independent of the environment exponential decay suppressing backward transitions, (ii) Loschmidt echo regime, (iii) - incoherent dynamics with multicomponent Loschmidt echo, when the system state exchanges its energy with many states of the reservoir, (iv) - cycle mixing regime, when the long term system dynamics appear to be random. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.

cond-mat.mes-hall↗

arXiv2008

Pyrophosphate Groups in Liquid Crystalline Phases of the DNA

We study electrostatic interaction between molecules of the DNA in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential $U$ of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of potential $U$ indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by potential $U$. The symmetries form a noncommutative group of 8-th order, ${\cal S}$. Using the group ${\cal S}$ we suggest a classification of liquid crystalline phases of the DNA, which allows of several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the part played by charges in its liquid crystalline phases, and make for experimental research, important for nano-technological and bio-medical applications.

cond-mat.soft↗

arXiv2008

Electromagnon excitations in modulated multiferroics

The phenomenological theory of ferroelectricity in spiral magnets presented in [M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006)] is generalized to describe consistently states with both uniform and modulated-in-space ferroelectric polarizations. A key point in this description is the symmetric part of the magnetoelectric coupling since, although being irrelevant for the uniform component, it plays an essential role for the non-uniform part of the polarization. We illustrate this importance in generic examples of modulated magnetic systems: longitudinal and transverse spin-density wave states and planar cycloidal phase. We show that even in the cases with no uniform ferroelectricity induced, polarization correlation functions follow to the soft magnetic behavior of the system due to the magnetoelectric effect. Our results can be easily generalized for more complicated types of magnetic ordering, and the applications may concern various natural and artificial systems in condensed matter physics (e.g., magnon properties could be extracted from dynamic dielectric response measurements).

cond-mat.mtrl-sci↗

arXiv2007

Loschmidt echo and stochastic-like quantum dynamics of nano-particles

We investigate time evolution of prepared vibrational state (system) coupled to a reservoir with dense spectrum of its vibrational states. We assume that the reservoir has an equidistant spectrum, and the system - reservoir coupling matrix elements are independent of the reservoir states. The analytical solution manifests three regimes of the evolution for the system: (I) weakly damped oscillations; (II) multicomponent Loschmidt echo in recurrence cycles; (III) overlapping recurrence cycles. We find the characteristic critical values of the system - reservoir coupling constant for the transitions between these regimes. Stochastic dynamics occurs in the regime (III) due to inevoidably in any real system coarse graining of time or energy measurements, or initial condition uncertainty. Even though a specific toy model is investigated here, when properly interpreted it yields quite reasonable description for a variety of physically relevant phenomena.

cond-mat.stat-mech↗

arXiv2005

Structures and orientational transitions in thin films of tilted hexatic smectics

We present detailed systematic studies of structural transformations in thin liquid crystal films with the smectic-C to hexatic phase transition. For the first time all possible structures reported in the literature are observed for one material (5 O.6) at the variation of temperature and thickness. In unusual modulated structures the equilibrium period of stripes is twice with respect to the domain size. We interpret these patterns in the frame work of phenomenological Landau type theory, as equilibrium phenomena produced by a natural geometric frustration in a system having spontaneous splay distortion.

cond-mat.soft↗

arXiv2005

A time lens for high resolution neutron time of flight spectrometers

We examine in analytic and numeric ways the imaging effects of temporal neutron lenses created by traveling magnetic fields. For fields of parabolic shape we derive the imaging equations, investigate the time-magnification, the evolution of the phase space element, the gain factor and the effect of finite beam size. The main aberration effects are calculated numerically. The system is technologically feasible and should convert neutron time of flight instruments from pinhole- to imaging configuration in time, thus enhancing intensity and/or time resolution. New fields of application for high resolution spectrometry may be opened.

cond-mat.other↗

arXiv2005

Accuracy of Semiclassics: Comparative Analysis of WKB and Instanton Approaches

We analyze quantitatively the accuracy of eigenfunction and eigenvalue calculations in the frame work of WKB and instanton semiclassical methods. We show that to estimate the accuracy it is enough to compare two linearly independent (with the same quantum number) solutions to the Schrödinger equations with the potential under study, and with the approximating piecewise smooth potential. The main advantage of the approach is related to the appropriate choice of the approximating potential, providing absolutely convergent majorant series for the solutions. We test our method for a strongly anharmonic one dimensional potential, but the basic ideas inspiring our work and its results can be applied to a large variety of interesting chemical and physical problems which are of relevance to various molecular systems.

cond-mat.other↗

arXiv2005

Semiclassical model of ultrafast photoisomerization reactions

In this letter we propose a model which explains ultrafast and efficient photoisomerization reactions as driven by transitions between quasistationary states of one dimensional (1D) double well potential of an excited electronic state. This adiabatic potential is formed as a result of doubly crossing of a decay diabatic potential of the ground electronic state and a bound diabatic potential of the excited state. We calculate the eigenstates and eigenfunctions using the semiclassical connection matrices at the turning and crossing points and the shift matrices between these points. The transitions between the localized in the wells below the adiabatic barrier states are realized by the tunneling and by the double non-adiabatic transitions via the crossing points processes. Surprisingly the behavior with the maximum transition rate keeps going even for the states relatively far above the barrier (2 -4 times the barrier height). Even though a specific toy model is investigated here, when properly interpreted it yields quite reasonable values for a variety of measured quantities, such as a reaction quantum yield, and conversion time.

cond-mat.other↗

arXiv2005

Sound modes broadening for Fibonacci one dimensional quasicrystals

We investigate vibrational excitation broadening in one dimensional Fibonacci model of quasicrystals (QCs). The chain is constructed from particles with two masses following the Fibonacci inflation rule. The eigenmode spectrum depends crucially on the mass ratio. We calculate the eigenstates and eigenfunctions. All calculations performed self-consistently within the regular expansion over the three wave coupling constant. The approach can be extended to three dimensional systems. We find that in the intermediate range of mode coupling constants, three-wave broadening for the both types of systems (1D Fibonacci and 3D QCs) depends universally on frequency. Our general qualitative conclusion is that for a system with a non-simple elementary cell phonon spectrum broadening is always larger than for a system with a primitive cell (provided all other characteristics are the same).

cond-mat.stat-mech↗

arXiv2004

Casimir forces in modulated systems

For the first time we present analytical results for the contribution of electromagnetic fluctuations into thermodynamic properties of modulated systems, like cholesteric or smectic liquid crystalline films. In the case of small dielectric anisotropy we have derived explicit analytical expressions for the chemical potential of such systems. Two limiting cases were specifically considered: (i) the Van der Waals (VdW) limit, i.e., in the case when the retardation of the electromagnetic interactions can be neglected; and (ii) the Casimir limit, i.e. when the effects of retardation becomes considerable. It was shown that in the Casimir limit, the film chemical potential oscillates with the thickness of the film. This non-monotonic dependence of the chemical potential on the film thickness can lead to step-wise wetting phenomena, surface anchoring reorientation and other important effects. Applications of the results may concern the various systems in soft matter or condensed matter physics with multilayer or modulated structures.

cond-mat.soft↗

arXiv2004

Landau-Zener problem for energies close to potential crossing points

We examine one overlooked in previous investigations aspect of well - known Landau - Zener (LZ) problem, namely, the behavior in the intermediate, i.e. close to a crossing point, energy region, when all four LZ states are coupled and should be taken into account. We calculate the 4 x 4 connection matrix in this intermediate energy region, possessing the same block structure as the known connection matrices for the tunneling and in the over-barrier regions of the energy, and continously matching those in the corresponding energy regions.

cond-mat.stat-mech↗