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Jana Tothova

Publications and source records attributed to Jana Tothova.

At least 19 recordsLinked to original sources
arXiv2025

Effect of Magnetic Field on Neutral Bath Containing Charged Brownian Particles

Based on the Zwanzig-Caldeira-Legget theory generalized to systems under the influence of a static magnetic field, we obtain equations of motion for the Brownian particle (BP) and oscillators constituting the bath in which the BP is embedded. The equations are of the type of a generalized Langevin equation, which accounts for the frictional memory of the system. The BP is assumed to be charged while the bath particles are neutral. They thus do not directly respond to the external field, but their interaction with the BP leads to changes in the bath state. Using the solution of the equations found, we calculate the average bath angular momentum and show that it persists for long times when the system is assumed to reach equilibrium. This indicates a possible violation of the Bohr-van Leeuwen theorem for baths consisting of charged particles. However, this must be confirmed by a substantial generalization of the presented model when the bath particles feel the external field, which affects the memory in the dynamics of the system.

cond-mat.soft↗
arXiv2025

Memory effects of a static magnetic field on Brownian motion and the question of the absence of classical magnetism

The Bohr-van Leeuwen (BvL) theorem, stating the absence of classical magnetization in equilibrium, a fundamental result in the field of magnetic phenomena, was originally proved for an electron gas. In the present work, we deal with the problem of whether this theorem applies to particles undergoing a non-Markovian Brownian motion in a static magnetic field. We consider a charged Brownian particle (BP) immersed in a bath of neutral particles. Generalizing the Zwanzig-Caldeira-Legget theory to the presence of a static external magnetic field, we come to the equation of motion for the BP in the form of a generalized Langevin equation that accounts for memory effects in the dynamics of the system. By using its solutions for the displacement and velocity of the BP, we calculate the angular momentum for the Ornstein-Uhlenbeck thermal noise. At long times, when the system should reach equilibrium, this momentum and, consequently, the classical magnetic moment of the BP are nonzero, in contrast to the BvL theorem. With the help of analytical and precise numerical calculations for different sets of system parameters, a simple formula for the angular momentum has been deduced.

cond-mat.soft↗
arXiv2024

Revisiting the work "Brownian motion with time-dependent friction and single-particle dynamics in liquids" by Lad, Patel, and Pratap [Phys. Rev. E 105, 064107 (2022)]

Recently, Lad, Patel, and Pratap (LP&P) [Phys. Rev. E 105, 064107 (2022)] revisited a microscopic theory of molecular motion in liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)]. Coming from this theory, LP&P derived a new equation of motion for the velocity autocorrelation function (VAF) and argued that the friction coefficient of particles in liquids should exponentially depend on time. The numerical solution of this equation was fitted to the results of molecular dynamics simulations on different liquids. In our Comment [Phys. Rev. E 108, 036107 (2023)], we showed that this solution, obtained under the condition of zero derivative of the VAF at time t = 0, is physically incorrect. This was evidenced by our exact analytical solution for the VAF, not found by LP&P, and numerically, by using the same method as in the commented work. In the Reply [Phys. Rev. E 108, 036108 (2023)], Lad, Patel, Pratap, and Pandya claimed that our solution does not satisfy all the necessary boundary conditions and is thus not appropriate for the description of atomic dynamics in liquids. Until and unless proven otherwise they do not find any reason for the reconsideration of their theory. Here we give a rebuttal to this Reply and, returning to the original work by LP&P, show that the presented there equation for the VAF is wrong. Due to errors in its derivation, it is, among other inconsistencies, incompatible precisely with the boundary conditions for the VAF which lie in the basis of their theory.

cond-mat.stat-mech↗
arXiv2021

Topology and Social Behaviour of Agents

In a social group its members are caled here agents. Any two agents from the group may interact. The interaction consists of the exchange of information and it costs some energy. There exist subgroups of interacting agents which are nonreducibile. The structure, configuration of interactions between agents in the group, forms a macroscopic structure. The statistical equilibrium due to microreversibility is characterised by the maximum of entropy and by the minimum of energy, costs of information exchange. Thus we have a structure which is equivalent to random cellular networks /N. Rivier, Physica 23D (1986) 129-137/. We will use methods described by Rivier to study social behaviour of agents. Their social behaviour is discussed. The social behaviour is discussed. Three empiricaly observed dependences of personal radius dependence on some factors enabled us to characterise the quantitz which characterises verification of information.

cond-mat.stat-mech↗
arXiv2021

Topology and Behaviour of Agents: Capital Markets

On a capital market the social group is formed from traders. Individual behaviour of agents is influenced by the need to associate with other agents and to obtain the approval of other agents in the group. Making decisions an individual equates own needs with those of the other agents. Any two agents from the group may interact. The interaction consists of the exchange of information and it costs some money. We assume that agents give reference to the origin of the information if asked by other agents. Thus the agent may verify obtained private information. Hudak recently used methods described by Rivier to study social behaviour of such agents. He characterized the quantity which corresponds to verification of information. Quantity which characterizes verification of information contributes to an aversion of an agent with respect to a risk. The mix of investments of an agent in a given cell with an average measure A of risk aversion in the cell is found from minimum of the average per cell aim function $ $. Absolute minimum corresponds to such a state in which there is an optimal mix of the exchange of information for a given expectations about the capital market. The crowd and personal /$\approx $/ contributions to the risk aversion of an agent are present in the aversion constant A. We have discussed a stable and metastable states of the market for different values of E, an expected return for a given investment period, of EV, an expected risk for a given investment period, and of b, a constant which characterizes contribution of the quantity $ $ to the risk aversion. Variance of n for the distribution of nonreducibile subgroups is found. Our model describes intermediary process effects.

cond-mat.other↗
arXiv2021

Automated Trading Systems: Developed and Emerging Capital Markets

Automated trading systems on developed and emerging capital markets are studied in this paper. The standard for developed market is automated trading system with 40-days simple moving average. We tested it for the index SIX Industrial for 1000 and 730 trading days of the slovak emerging capital market. The Buy and Hold trading system was 7.80 times more profitable than this etalon trading system for active trading. Taking of profitable standard trading system from a developed capital market does not lead to optimal results on the emerging capital markets. We then studied optimized standard trading system based on the simple moving average. The parameter of optimization was the number of weeks. An optimal system was that with 5 weeks. This trading system has some of its characteristics comparable with the etalon trading system on the NYSE Composite Index. The emerging market is more risky than the developed market. The profit on the emerging market is also higher. The range of optimized system parameter is quite robust. Observed was increase of number of trades in the range from the 21 weeks to the 25 weeks. This indicates creation of a new optimal middle range trading system. Results of testing for liquid shares are quantitatively similar.

physics.soc-ph↗
arXiv2021

Social Behaviour of Agents: Capital Markets and Their Small Perturbations

We study social behaviour of agents on capital markets when these are perturbed by small perturbations. We use the mean field method. Social behaviour of agents on capital markets is described: volatility of the market, aversion constant and equilibrium states are discussed. Relaxation behaviour of agents on the capital market is studied. Equation of motion for the agent average number is of the relaxation type. Development of the group of agents in the states corresponding to minimum of the aim function is either linear either exponentially damped. There exist characteristic volatility constants $ V_{c3} $ and $ V_{c3} $. The constant b of verification of information contribution to the aversion constant A and the $ A_{0} $ constant of aversion are distinguishing three types of dependencies of the minimum of the aim function on the expected volatility EV and on the expected returns E. Arbitrage trades and group forces lead the group into the equilibrium state. Verification of information intensity influences return back to the equilibrium state. The linear in time damping to the equilibrium state is characterized with the characteristic time $ T_{3}$ and $ T_{6} $, the exponential with a characteristic time $ τ$. Their dependence on the expected volatility, on the expected profit and characteristics of agents is discussed.

physics.soc-ph↗
arXiv2020

Generalized Langevin equations and fluctuation-dissipation theorem for particle-bath systems in electric and magnetic fields

The Brownian motion of a particle immersed in a medium of charged particles is considered when the system is placed in magnetic or electric fields. Coming from the Zwanzig-Caldeira-Legget particle-bath model, we modify it so that not only the charged Brownian particle (BP) but also the bath particles respond to the external fields. For stationary systems the generalized Langevin equations are derived. Arbitrarily time-dependent electric fields do not affect the memory functions, the thermal noise force, and the BP velocity correlation functions. In the case of a constant magnetic field two equations with different memory functions are obtained for the BP motion in the plane perpendicular to the field. As distinct from the previous theories, the random thermal force depends on the field magnitude. Its time correlation function is connected with one of the found memory functions through the familiar second fluctuation-dissipation theorem.

cond-mat.stat-mech↗
arXiv2018

NMR measurements and all-time Brownian movement with memory

In the present work, by using the method of accumulation of phase shifts in the rotating frame, the attenuation function S(t) of the NMR signal from an ensemble of spin-bearing particles in a magnetic-field gradient is expressed through the particle mean square displacement in a form applicable for any kind of stationary stochastic dynamics of spins and for any times. S(t) is evaluated providing that the random motion of particles can be modeled by the generalized Langevin equation (GLE) with a colored random force driving the particles. The memory integral in this equation is the convolution of the particle velocity or its acceleration with a memory kernel related to the random force by the fluctuation-dissipation theorem. We consider three popular models of the BM with memory: the model of viscoelastic (Maxwell) fluids with the memory exponentially decaying in time, the fractional BM model, and the model of the hydrodynamic BM. In all the cases the solutions of the GLEs are obtained in an exceedingly simple way. The corresponding attenuation functions are then found for the free-induction NMR signal and the pulsed and steady-gradient spin-echo experiments. The results for the free-particle fractional BM compare favorably with experiments acquired in human neuronal tissues and with the observed subdiffusion dynamics in proteins.

cond-mat.stat-mech↗
arXiv2018

Nonlinear Dielectric Response of Microcomposite Ferroelectrics

A dielectric nonlinear response in model two-phase composites, prepared from a displacive ferroelectric material with a dominant dielectric response due to a single oscillator ferroelectric mode and a dielectric material, is characterized by the existence of new modes due to geometric resonances below the percolation threshold in the ferroelectric matrix. The geometric nature of oscilations depends on composition and geometric properties of the mixture. Generation of higher frequency modes is studied within our model and discussed for displacive ferroelectric materials of the $BaTiO_{3}$ type. The Bergman Representation of the effective dielectric function together with our model for spectral function recently introduced are used simultaneously with theory of absorption in finite displacive ferroelectric crystals in quasistatic approximation to describe the physics of the composite. The boundaries of the present study are within this quasistatic approximation. New ways how to optimize material properties for nonlinear optics is outlined.

cond-mat.mtrl-sci↗
arXiv2018

Inverse Scattering Method II.: Methodological part with an example: Breather solution of the Sine-Gordon Equation

Recently it was discussed the Inverse Scattering Method, Part I. (paper I.) . It was a methodological Part with an example - soliton (kink) solution of the Sine-Gordon Equation. The aim of the paper I. was to introduce the Inverse Scattering Method for later studies of some problems in nonlinear dynamics. As a methodological example we described how to solve the Sine-Gordon Equation using the Inverse Scattering Method to obtain a soliton. This soliton solution is well known. In this paper we discuss another methodological example: the solution of the Sine-Gordon Equation using the Inverse Scattering Method to obtain description of a breather. While this breather solution is also well known, we will discuss later breather solutions in some physical systems. Thus we will have in the Part I. and in this Part II. seeds for solving problems with the Inverse Scattering Method, and in case of the Sine-Gordon Equation solutions describing the soliton and the breather.

nlin.SI↗
arXiv2018

Social Behavior of Drivers and Traffic

Drivers are agents, they are members of the group of drivers. Human groupings have hierarchical structure. The civilization consists of societies, societies consist of groups, and groups consist of individuals. We will consider the group of drivers. Every social group has power to organize individuals and use them for its own purposes. This is true also for the group of drivers. An agent, a driver, we call a member of a social group of drivers, we assume that his-her special properties are defined: they are agents driving a car. A driver-s behavior is influenced to some degree by the need to associate with other drivers and to obtain the approval of other drivers in the group, this is a general property of agents in a group. A driver equates his-her needs with those of the other drivers from the group. From this we explain how three empirically observed dependencies of personal driver radius dependence on some factors enabled us to identify quantity which characterizes verification of information by a driver. The smaller personal radius the larger process of verification of verbal and non-verbal information about the other person in other to accept the risk that this person will be closer to us as a person (driver). We expect that this conclusion is a general conclusion.

physics.soc-ph↗
arXiv2018

NMR and the antiferromagnetic crystal phase regions in rapidly quenched ribbons and in alloys of the type $Cu-Mn-Al$

It was shown that anomalous resistivity behavior of the $Cu-Mn-Al$ ribbons is explained by the s-d interaction between conduction electrons and the clustered Mn atoms. While nuclear magnetic resonance measurements show the antiferromagnetic and ferromagnetic clusters of Mn atom coexisting without long-range order, it is an interesting problem to study magnetic resonance properties also for the antiferromagnetic crystal phase regions (which have long-range order for larger regions) and which may also occur in these ribbons. The Heusler Type $Cu-Mn-Al$ Alloy has a composition half way between $Cu_{2}MnAl$ and $Cu_{3}Al$. Electron microscopy of the premartensitic $βCu-Zn-Al$ alloy has shown that the $βCu-Zn-Al$ alloy quenched from high temperature has the electron diffraction patterns of this alloy well explained by the model with the existence of small particles with an orthorhombic structure. It was noted that an important aspect of improvement in the material properties is to create a nanostructured state in matrix, which has significant advantages in magnetic and mechanical characteristics in contrast to the bulk materials in crystalline or amorphous state. It is an interesting problem to study magnetic resonance properties not only for the Mn atoms and clusters without long-range order but also for the antiferromagnetic crystal phase regions (which have long-range order for larger regions) which may also occur in ribbons. This is the aim of our paper.

cond-mat.mtrl-sci↗
arXiv2018

Attenuation of the NMR signal due to hydrodynamic Brownian motion

Nuclear magnetic resonance (NMR) is a widely used nondestructive method to study random motion of spin-bearing particles in different systems. In the long-time limit the theoretical description of the NMR experiments is well developed and allows proper interpretation of measurements of normal and anomalous diffusion. The traditional description becomes, however, insufficient for the shorter-time dynamics of the particles. In the present paper, the all-time attenuation function of the NMR signal in a magnetic-field gradient due to the Brownian motion (BM) of particles in incompressible liquids is calculated by using the method of accumulation of phases by a precessing magnetic moment, without reference to a concrete model of the stochastic dynamics. The obtained expressions are then used to evaluate the attenuation within the hydrodynamic theory of the BM. It is shown that the well-known time behavior of the formulas corresponding to the Einstein theory of diffusion in the case of steady gradient and Hahn's echo experiments is reached at times much larger than the characteristic time of the loss of memory in the particle dynamics. At shorter times the attenuation function significantly differs from the classical formulas used to interpret these experiments.

cond-mat.stat-mech↗
arXiv2018

NMR signals within the generalized Langevin model for fractional Brownian motion

The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S(t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S(t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

cond-mat.stat-mech↗
arXiv2018

Displays and antiferroelectric liquid crystals

Recently we have formulated theory of bi-layer-dimerized chiral liquid antiferroelectric crystals. The spontaneous polarization has been increased owing to the strong interaction of the aromatic cores of the rod like liquid crystal molecules with the honey-comb pattern of the CNT walls The SmC*A ordering is improved around the CNTs. All relaxation modes in each phase are facilitated by dispersion of nanotubes whicg enhances the relaxation frequencies. This composite system with improvement in electro-optical properties can be exploited in modern display applications. SmC* LC were studied by one of t he authors (OH), namely their transition from the SmC phase. The role of disclinations in an applied electric field was studied by O. Hudak in the SmC* structure. While the role of fluctuations and of disclinations in the SmC* (FLC)was studied in the above papers, the role of fluctuations and disclinations in SmC*A and the role of addition of MWCNTs in SmC*A phaseis not well understood. Our theoretical description of (AFLC) including SmC*A introduced in may thus be used to study these effects.

cond-mat.soft↗