arXiv subjects

E. I. Kats

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

At least 19 recordsLinked to original sources

arXiv2026

Scale dependent chirality in twist-bend liquid crystals

The discovery of new classes of lyotropic and thermotropic liquid crystals (e.g., twist-bend, splay, and ferroelectric phases), together with significant advances in experimental techniques for their investigation, has renewed interest in a number of physical phenomena that have been studied in classical liquid crystals (nematics, cholesterics, and smectics) for more than a century. In this paper, we revisit one such ''old--new'' problem, recently highlighted in the preprint by A. Ashkinazi, H. Chhabra, A. El Moumane, M. M. C. Tortora, and J. P. K. Doye, ''Chirality Transfer in Lyotropic Twist-Bend Nematics,'' arXiv:2508.03544v1 (2025), in which various mechanisms of chirality transfer from the molecular scale to the structural scale were discussed. Here we present a simple theoretical analysis of chirality transfer within a Landau theory describing the phase transition between cholesteric and chiral twist-bend liquid crystals. We demonstrate that the handedness of the heliconical structure is opposite to that of the parent cholesteric phase. This relationship originates from the orthogonality between the cholesteric director and the vector order parameter characterizing the phase.

cond-mat.soft↗

arXiv2026

Pattern formation in nonlinear dynamics of nematic liquid crystals above the flexoelectric instability threshold

For many decades, researchers have been studying various types of electro-hydrodynamic instabilities in liquid crystals. A significant amount of experimental data has been collected, however, the theoretical interpretations of the results typically rely on linear analysis. In response to this limitation, we investigate the nonlinear stage of the flexoelectric instability in nematics, focusing on liquid crystals with a negative anisotropy in their dielectric permittivity and electrical conductivity. We base our analysis on a comprehensive set of nonlinear electro-hydrodynamic equations for these nematics influenced by an external alternating electric field. The equations predict an instability that is driven by the flexoelectric effect. In order to examine the peculiarities of this phenomenon, we use a model that was proposed in our previous publications, Refs. [1,2], which allows us to perform numerical simulation of nonlinear dynamics. We examine patterns that are formed above the instability threshold. Through numerical simulations, we have identified static and dynamic patterns that occur over a timescale that is much longer than the period of the external electric field. The static patterns are one-dimensional structures and dynamic patterns are standing or traveling one-dimensional waves. The type of the realized pattern depends on the material and experimentally controlled parameters. We found that the standing waves are stable with respect to small transverse perturbations, whereas the propagating waves are unstable. We present a Ginzburg-Landau-like phenomenology that applies near the instability threshold. This approach allows us to rationalize our numerical findings with a few parameters.

cond-mat.soft↗

arXiv2024

Bird's-eye view to the realm of N_{TB} liquid crystals

In this work we start with an introductory review of the relatively recently discovered type of liquid crystals, twist-bend nematics N_{TB}. Then we describe a more detailed account of recent developments in the field. Namely: (i) Landau Theory of the easy axis N_{TB} nematics; (ii) Light scattering in the N_{TB} liquid crystals; (iii) Rheological behavior of the ordered N_{TB} samples; (iv) Shift of the N - N_{TB} phase transition point (where N stands for the conventional nematic liquid crystal) under actions of external fields. It is found that advocated in this work simple phenomenological approach successfully explains available experimental data. The paper integrates the input from publications of other researchers, and presents a personal view of the author formed partially by his own results and discussions with his collaborators.

cond-mat.soft↗

arXiv2024

Dynamic flexoelectric instabilities in nematic liquid crystals

Electro-hydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of physical community to out-of-equilibrium systems. Nematic liquid crystals (NLCs) are ideally representative for such investigations. Our article aims to study theoretically the linear NLCs dynamics. We include into consideration orientation elastic energy, hydrodynamic motion, external alternating electric field, electric conductivity and flexoelectric polarization. We analyze the linear stability of the NLC film, determining dynamics of perturbations with respect to the homogeneous initial state of the NLC. For the purpose we compute eigen-values of the evolution matrix for a period of the external alternating electric field. These eigen-values determine the amplification factors for the modes during the period. The instability occurs when the principal eigen-value of the evolution matrix becomes unity by its absolute value. The condition determines the threshold (critical field) for the instability of the uniform state. It turns out that one might expect various types of the instability, only partially known and investigated in the literature. Particularly, we find that the flexoelectric instability may lead to two-dimensionally space modulated patterns exhibiting time oscillations. This type of the structures was somehow overlooked in the previous works.

cond-mat.soft↗

arXiv2022

Nonlinear electro-hydrodynamics of liquid crystals

We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is expressed as a sum of external electric field and the fields originating from feedback of liquid crystal order parameter, and a field, created by charged impurities. The system tends to decrease the total electric field, because it lowers the energy density. This basically nonlinear problem is not a pure academic interest. In the realm of liquid crystals and their applications, utilized nowadays modern experimental techniques have progressed to the point where even small deviations from the linear behavior can be observed and measured with a high accuracy. Hydrodynamics is the macroscopic description of condensed matter systems in the low frequency, long wavelength limit. Nonlinear hydrodynamic equations are well established to describe simple fluids. Similar approaches (with degrees of freedom related to the broken orientational or translational symmetry included) have been used also for liquid crystals. However to study behavior of strongly perturbed well above the thresholds of various electro-hydrodynamic instabilities of liquid crystals the nonlinear equations should include soft electromagnetic degrees of freedom as well. The self-consistent derivation of the complete set of the nonlinear electro-hydrodynamic equations for liquid crystals became an actual task. The aim of our work is to present these equations, which is a mandatory step to handle any nonlinear phenomenon in liquid crystals.

cond-mat.soft↗

arXiv2022

Non-Newtonian rheology in twist-bend nematic liquid crystals

In this work we present a simple qualitative model to describe shear rheological behavior of the twist-bend nematic liquid crystals. We find that at relatively low shear rate the effective viscosity decreases with the shear rate manifesting so-called shear-thinning phenomenon. At intermediate shear rate the stress is almost independent of the shear rate (a sort of plateau), and at large shear rate Newtonian rheology takes place. Within our theory we estimate the critical values of the shear rate in terms of coarse grained shear viscosity coefficients of the effective smectics equivalent to the twist-bend phase at large scales. The results of our work are in the agreement with recent experimental studies.

cond-mat.soft↗

arXiv2022

Long-range interactions between membrane inclusions: Electric field induced giant amplification of the pairwise potential

The aim of this work is to revisit the phenomenological theory of the interaction between membrane inclusions, mediated by the membrane fluctuations. We consider the case where the inclusions are separated by distances larger than their characteristic size. Within our macroscopic approach a physical nature of such inclusions is not essential, however we have always in mind two prototypes of such inclusions: proteins and RNA macromolecules. Because the interaction is driven by the membrane fluctuations, and the coupling between inclusions and the membrane, it is possible to change the interaction potential by external actions affecting these factors. As an example of such external action we consider an electric field. Under external electric field (both dc or ac), we propose a new coupling mechanism between inclusions possessing dipole moments (as it is the case for most protein macromolecules) and the membrane. We found, quite unexpected and presumably for the first time, that the new coupling mechanism yields to giant enhancement of the pairwise potential of the inclusions. This result opens up a way to handle purposefully the interaction energy, and as well to test of the theory set forth in our article.

cond-mat.soft↗

arXiv2021

Non-trivial dynamic regimes of small (nano-scale) quantum systems

Small (but still containing many atoms) quantum systems (traditionally termed nano-systems) are dramatically different from their macroscopic or genuine microscopic (atomic) cousins. Microscopic molecular systems (with a few atoms) obey a regular quantum dynamics (described by time dependent Schrodinger equation), whereas in macroscopic systems with continuous energy spectra, one can expect, also regular, although typically relaxation, dynamic behavior. The topic of our paper is in-between these limits. System behavior becomes non-trivial and manifests a sort of transitions between regular and chaotic dynamics. We show that such dynamic transitions occur when the Loschmidt echo time of life exceeds the typical recurrence cycle period. We illustrate this behavior in the frame work of a few versions of the exactly solvable quantum problem, proposed long ago by Zwanzig. It is based on the study of time evolution of the initially prepared vibrational state coupled to a reservoir with dense spectrum of its vibrational states. In the simplest version of the Zwanzig model, the reservoir has an equidistant spectrum, and the system - reservoir coupling matrix elements are independent of the reservoir states. We generalize the model to include into consideration the coupling of the initially prepared single state to system phonon excitations. The coupling results to temperature dependent broadening and decay of the echo components. Another generalization is to replace a single level by two states coupled to the Zwanzig reservoir. We anticipate that the basic ideas inspiring our work can be applied to a large variety of interesting for the applications nano-systems (e.g., dissipative free propagation of excitations along molecular chains, or as a model for exchange reactions).

quant-ph↗

arXiv2020

Flashing a look at the stability of the uniform ferroelectric nematic phase

Recent discovery of the ferroelectric nematic phase N_F resurrects a question about stability of the uniform N_F state with respect to the formation of either standard for solid ferroelectrics domain structure, or often occurring in liquid crystals space modulation of the polarization vector P (and naturally coupled to P nematic director. In this work within Landau mean-field theory we investigate the linear stability of the minimal model admitting the conventional paraelectric nematic N and N_F phases. Our minimal model, (besides the standard terms of the expansion over P and director gradients) includes, also standard for liquid crystals, director flexoelectric coupling term f and often overlooked in the literature (although similar by its symmetry to the director flexoelectric coupling) the flexo-dipolar coupling. We find that in the easy-plane anisotropy case the uniform N_F state loses its stability with respect to one-dimensional or two-dimensional modulation. For non-zero f the 2D modulation threshold is always higher than its 1D counterpart. No any instability at all if one neglects the dipole-flexoelectric coupling. In the easy-axis case the both instability thresholds are the same, and the instability can occur even without flexo-dipolr coupling. We speculate that the phases with 1D or 2D modulations can be identified with discussed in the literature [see M.P.Rosseto, J.V.Selinger, Physical Review E, volume 101, page 052707 (2020)] single splay or double splay nematics.

cond-mat.soft↗

arXiv2019

Landau theory for smectic-A -- hexatic-B coexistence in smectic films

We explain theoretically peculiarities of the smectic A -- hexatic B equilibrium phase coexistence in a finite temperature range recently observed experimentally in free standing smectic films [I.A.Zaluzhnyy et al., Physical Review E, volume 98, 052703 (2018)]. We quantitatively describe this unexpected phenomenon within Landau phase transitions theory assuming that the film state is close to a tricritical point. We found that the surface hexatic order leads to diminishing the phase coexistence range as the film thickness decreases shrinking it at some minimal film thickness, of the order of the hexatic correlation length. We established universal laws for the temperature width of the phase coexistence in terms of the reduced variables. Our theory is in agreement with the existing experimental data.

cond-mat.soft↗

arXiv2017

Simple analysis of scattering data with Ornstein-Zernike equation

In this paper we propose and explore a method of analysis of the scattering experimental data for uniform liquid-like systems. In our pragmatic approach we are not trying to introduce by hands an artificial small parameter to work out a perturbation theory with respect to the known results e.g., for hard spheres or sticky-hard spheres (all the more that in the agreement with the notorious Landau statement, there is no any physical small parameter for liquids). Instead of it guided by the experimental data we are solving the the Ornstein-Zernike equation with a trial (variational) form of the inter-particle interaction potential. To find all needed correlation functions this variational input is iterated numerically to satisfy the Ornstein-Zernike equation supplemented by a closure relation. We illustrate by a number of model and real experimental examples of the X-ray and neutron scattering data how the approach works.

cond-mat.soft↗

arXiv2016

Why the smectic A -- hexatic phase transition does not follow its universality class?

We resolve the old riddle related to the critical behavior of the heat capacity near the smectic A -- hexatic second order phase transition. Experiment suggests a "large" positive specific heat critical exponent inconsistent with the universality class for this phase transition implying the very small negative exponent. We show that essential features of the heat capacity for the smectic A -- hexatic phase transition can be rationalized in the framework of a theoretical model treating jointly fluctuations of the hexatic orientational order and of the positional (translational) order parameters. Assuming that the positional (translational) correlation length is larger than the hexatic correlation length, we calculate a temperature dependence of the specific heat in the critical region near the smectic A -- hexatic phase transition. Our results are in a quantitative agreement with the calorimetric experimental data.

cond-mat.soft↗

arXiv2015

Non-linear fluctuation effects in dynamics of freely suspended film

Long-scale dynamic fluctuation phenomena in freely suspended films is analyzed. We consider isotropic films that, say, can be pulled from bulk smectic A liquid crystals. The key feature of such objects is possibility of bending deformations of the film. The bending (also known as flexular) mode turns out to be anomalously weakly attenuated. In the harmonic approximation there is no viscous-like damping of the bending mode, proportional to q^2 (q is the wave vector of the mode), since it is forbidden by the rotational symmetry. Therefore the bending mode is strongly affected by non-linear dynamic fluctuation effects. We calculate the dominant fluctuation contributions to the damping of the bending mode due to its coupling to the in-plane viscous mode, that restores the viscous-like q^2 damping of the bending mode. Our calculations are performed in the framework of the perturbation theory where the coupling of the modes is assumed to be small, then the bending mode damping is relatively weak. We discuss our results in the context of existing experiments and numeric simulations of the freely suspended films and propose possible experimental observations of our predictions.

cond-mat.soft↗

arXiv2014

Comment on "Thermodynamics of quantum crystalline membranes"

B. Amorim et al., (B.Amorim, R.Roldan, E.Cappelluti, A.Fasolino, F.Guinea, M.I.Katsnelson, Phys. Rev. B, v. 89, 224307 (2014)) reported the theoretical investigation of quantum crystalline membranes. In this comment we dismiss validity of their calculations based on a "natural" estimation of the ultra-violet (UV) divergent contributions into correlation functions. We claim that such calculations may not be performed correctly within the long-scale theory.

cond-mat.stat-mech↗

arXiv2014

Landau theory for helical nematic phases

We propose Landau phenomenology for describing the phase transition from the conventional nematic into the conical helical orientationally non-uniform structure recently identified in liquid crystals formed by "banana"-shaped molecules. The mean field predictions are mostly in agreement with experimental data. Based on the analogy with de Gennes model, we argue that fluctuations of the order parameter turn the transition to the first order phase transition rather than continuous one predicted by the mean-field theory. This conclusion is in agreement with experimental observations. We discuss the new Goldstone mode to be observed in the low-temperature phase.

cond-mat.soft↗

arXiv2013

Asymptotic freedom at zero temperature in crystalline membranes

We investigate effects of quantum (zero-temperature) long wavelength fluctuations of free standing crystalline membranes, that are two-dimensional objects embedded into three-dimensional space. The fluctuations produce logarithmic renormalization of elasticity and bending moduli of the membranes. We find one-loop RG-equations to demonstrate that the system is in the "asymptotic freedom" regime that is the quantum fluctuations destabilize the flat membrane phase.

cond-mat.stat-mech↗

arXiv2013

Topological metastability of textures in biaxial nematics

We consider textures of biaxial nematics confined between two parallel plates. The boundary conformations at the bordering plates are supposed to be identical, the gradients of the order parameter being generally nonzero. We claim that for any texture (including stable uniform order parameter alignment) there exists its counterpart texture which is also a minimum of the gradient elastic energy. Our arguments are based on the topological analysis of the conformation of the order parameter.

cond-mat.soft↗

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↗