K. Kladko

Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices

Discrete breathers are time-periodic, spatially localized solutions of equations of motion for classical degrees of freedom interacting on a lattice. They come in one-parameter families. We report on studies of energy properties of breather families in one-, two-, and three-dimensional lattices. We show that breather energies have a positive lower bound if the lattice dimension of a given nonlinear lattice is greater than or equal to a certain critical value. These findings could be important for the experimental detection of discrete breathers.

Moving discrete breathers

Abstract We give definitions for different types of moving spatially localized objects in discrete nonlinear lattices. We derive general analytical relations connecting frequency, velocity and localization length of moving discrete breathers and kinks in nonlinear one-dimensional lattices. Then we propose a new numerical algorithm to find these solutions.

Universal Scaling of Wave Propagation Failure in Arrays of Coupled Nonlinear Cells

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular coupling. We find the universal scaling of the field throughout the range of couplings and show that the field becomes exponentially small for large couplings. Our method is generic and applicable to a wide class of cellular dynamics in chemical, biological, and engineering systems. We confirm our results by direct numerical simulations.

Perturbation analysis of weakly discrete kinks

We present a perturbation theory of static kink solutions of discrete Klein-Gordon chains. The unperturbed solutions correspond to the kinks of the adjoint partial differential equation. The perturbation theory is based on a reformulation of the discrete chain problem into a partial differential equation with spatially modulated mass density. The first-order corrections to the kink solutions are obtained analytically and are shown to agree with exact numerical results. We use these findings to reconsider the problem of calculating the Peierls-Nabarro barrier. \textcopyright{} 1996 The American Physical Society.

The weak-password problem: Chaos, criticality, and encrypted p-CAPTCHAs

Vulnerabilities related to weak passwords are a pressing global economic and security issue. We report a novel, simple, and effective approach to address the weak-password problem. Building upon chaotic dynamics, criticality at phase transitions, CAPTCHA recognition, and computational round-off errors, we design an algorithm that strengthens the security of passwords. The core idea of our simple method is to split a long and secure password into two components. The first component is memorized by the user. The second component is transformed into a CAPTCHA image and then protected using the evolution of a two-dimensional dynamical system close to a phase transition, in such a way that standard brute-force attacks become ineffective. We expect our approach to have wide applications for authentication and encryption technologies.

Cumulant expansion for systems with large spins

A method is proposed for obtaining a systematic expansion of thermodynamic functions of spin systems with large spin S in powers of 1/S. It uses the cumulant technique and a coherent-state representation of the partition function . The expansion of in terms of cumulants yields an effective classical Hamiltonian with temperature-dependent quantum corrections. For the Heisenberg quantum Hamiltonian, they have a non-Heisenberg form. The effective Hamiltonian can be solved by methods familiar for classical systems.

ON THE GROUND STATE OF SOLIDS WITH STRONG ELECTRON CORRELATIONS

Abstract We formulate the calculation of the ground-state wavefunction and energy of a system of strongly correlated electrons in terms of scattering matrices. A hierarchy of approximations is introduced which results in an incremental expansion of the energy. The present approach generalizes previous work designed for weakly correlated electronic systems.

On the correlation effect in Peierls-Hubbard chains

We reexamine the dimerization, the charge and the spin gaps of a half-filled Peierls–Hubbard chain by means of the incremental expansion technique combined with density matrix renormalization group...

Intrinsic localized modes in the charge-transfer solid PtCl

We report a theoretical analysis of intrinsic localized modes in a quasi-one-dimensional charge-transfer solid, [Pt(en)2][Pt(en)2Cl2](ClO4)4(PtCl). We discuss strongly non-linear features of resonant Raman overtone scattering measurements on PtCl, arising from quantum intrinsic localized (multiphonon) modes (ILMs) and ILM-plus-phonon states. We show that Raman scattering data display clear signs of a non-thermalization of the lattice degrees of freedom, manifested in a non-equilibrium density of intrinsic localized modes. Adiabatic lattice dynamics is used in a model two-band Peierls-Hubbard Hamiltonian, including a screened Coulomb interaction between neighbouring sites. The Hamiltonian is diagonalized on a finite chain. The calculated adiabatic potential for Peierls distortion of the Cl sublattice displays characteristic non-analytic points, related to a lattice-distortion-induced charge transfer. Possible non-adiabatic effects on ILMs are discussed.

Quasiclassical Hamiltonians for large-spin systems

Abstract:We extend and apply a previously developed method for a semiclassical treatment of a system with large spin S. A multisite Heisenberg Hamiltonian is transformed into an effective classical Hamilton function which can be treated by standard methods for classical systems. Quantum effects enter in form of multispin interactions in the Hamilton function. The latter is written in the form of an expansion in powers of J/(TS), where J is the coupling constant. Main ingredients of our method are spin coherent states and cumulants. Rules and diagrams are derived for computing cumulants of groups of operators entering the Hamiltonian. The theory is illustrated by calculating the quantum corrections to the free energy of a Heisenberg chain which were previously computed by a Wigner-Kirkwood expansion.