M. Pantić

Thermodynamical properties of ultrathin layered structures

Thermodynamical properties of ultrathin films were analysed using Greens function method. Mean-square of the molecular displacements, mean-square of the velocities and the phonon contribution to the specific heat of the thin films were calculated. A comparison with crystal bulk has shown that thermodynamical properties of thin films are strongly influenced both by the sample dimensions and boundary conditions. The results of the specific heat analyses make the validity of free surface model doubtful, because the specific heat calculated in this model becomes negative at very low temperature.

Green's function theory of free electrons in thin films

The electronic subsystem of ultrathin films was analysed using Greens function method including quantum size effect and the effect of boundaries to Hamiltonian parameters. Diagonal components of Greens functions were evaluated which enabled a complete insight into the thermodynamical properties of electrons. A comparison with crystal bulk has shown that electronic properties of the materials are strongly influenced both by the sample dimensions and boundary conditions. The numerical calculations show that the electron distribution may be manipulated by varying the surface parameters which is significant for the operation of devices based on thin films.

Phase diagram of spin-12 quantum Heisenberg J1–J2 antiferromagnet on the body-centered-cubic lattice in random phase approximation

Abstract Magnetic properties of spin 1 2 J 1 – J 2 Heisenberg antiferromagnet on the body centered cubic lattice are investigated. By using two-time temperature Greens functions, sublattice magnetization and critical temperature depending on the frustration ratio p = J 2 / J 1 are obtained in both stripe and Neel phases. The analysis of ground state sublattice magnetization and phase diagram indicates the critical end point at J 2 / J 1 = 0.714 , in agreement with previous studies.

Exciton concentrations in thin films

Excitons in thin films are analyzed using Greens function method within the framework of Tyablikovs version of random phase approximation. The spectra of surface and bulk excitons were determined and the distribution of exciton concentrations over film layers was evaluated. It was shown that high surface concentrations could be achieved by decreasing of the dipole-dipole interaction of the molecules in surface layers.

Free electron distribution in thin films

In this paper we analyze the electron states in metallic films. The first part of the paper is devoted to the study of the film where ion-ion interaction changes only in boundary layers. It was concluded that bulk states always appear in such film. Surface states appear only if the variation of the ion-ion interaction in the direction of the symmetry breaking in the boundary layer are neutralized. If the conditions for the creation of surface states are realized, one can obtain dense currents running along the film surface.

INFLUENCE OF TRANSLATIONAL SYMMETRY OF FERROMAGNETIC SUPERLATTICES IN THE STUDY OF ELEMENTARY EXCITATIONS

Elementary excitations in ferromagnetic superlattices are analyzed theoretically using the transfer matrix method. The method is extended to enable the study of the cases when the boundaries are not consisting of a single plane, but of a complete cell. In this way, semi-infinite superlattice, the interface between two superlattices and the film built of a superlattice are treated. However, it is shown that the choice of the transfer matrix strongly depends on the translational symmetry of the remaining part of the system. Energies of localized excitations are derived and compared both with bulk and the results of standard transfer matrix treatment proposed by Barnas. Also, a special Ansatz for spin amplitudes is proposed leading to identical results with the transfer matrix method and introducing large simplifications.

The Estimate of the Electron–Phonon Coupling Constant in the Thin Film

Hamiltonians of electron–phonon interaction for thin metallic films are formulated. This is the basis for the estimate of the superconductivity critical temperature for films and corresponding bulk structures. It is shown that the interaction of surface electrons in the film with bulk phonons could explain the experimental fact that critical temperatures of the films are higher than the corresponding ones in bulk (massive) structures. Since above fact is valid nearly for all pure metallic, one can conclude that the dominant form or the interaction in films is the interaction of surface electrons with bulk phonons.

Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces

Abstract Dynamics of driven dissipative Frenkel–Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of the system in the presence of external forces is studied by analyzing its dynamical response function, the largest Lyapunov exponent analysis can represent a very convenient tool to examine system dynamics. In the dc driven systems, the critical depinning force for particular structure could be estimated by computing the largest Lyapunov exponent. In the dc+ac driven systems, if the substrate potential is the standard sinusoidal one, calculation of the largest Lyapunov exponent offers a more sensitive way to detect the presence of Shapiro steps. When the amplitude of the ac force is varied the behavior of the largest Lyapunov exponent in the pinned regime completely reflects the behavior of Shapiro steps and the critical depinning force, in particular, it represents the mirror image of the amplitude dependence of critical depinning force. This points out an advantage of this technique since by calculating the largest Lyapunov exponent in the pinned regime we can get an insight into the dynamics of the system when driving forces are applied. Additionally, the system is shown to be not chaotic even in the case of incommensurate structures and large amplitudes of external force, which is a consequence of overdampness of the model and the Middleton’s no passing rule.

Magnon energy renormalization and low-temperature thermodynamics of O(3) Heisenberg ferromagnets

Abstract We present the perturbation theory for lattice magnon fields of the D -dimensional O(3) Heisenberg ferromagnet. The effective Hamiltonian for the lattice magnon fields is obtained starting from the effective Lagrangian, with two dominant contributions that describe magnon–magnon interactions identified as a usual gradient term for the unit vector field and a part originating in the Wess–Zumino–Witten term of the effective Lagrangian. Feynman diagrams for lattice scalar fields with derivative couplings are introduced, on the basis of which we investigate the influence of magnon–magnon interactions on magnon self-energy and ferromagnet free energy. We also comment appearance of spurious terms in low-temperature series for the free energy by examining magnon–magnon interactions and internal symmetry of the effective Hamiltonian (Lagrangian).

Some new characterizations of Hamiltonian cycles in triangular grid graphs

Abstract In the studies that have been devoted to the protein folding problem, which is one of the great unsolved problems of science, some specific graphs, like the so-called triangular grid graphs, have been used as a simplified lattice model. Generation and enumeration of Hamiltonian paths and Hamiltonian circuits (compact conformations of a chain) are needed to investigate the thermodynamics of protein folding. In this paper, we present new characterizations of the Hamiltonian cycles in labeled triangular grid graphs, which are graphs constructed from rectangular grids by adding a diagonal to each cell. By using these characterizations and implementing the computational method outlined here, we confirm the existing data, and obtain some new results that have not been published. A new interpretation of Catalan numbers is also included.