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We demonstrate that certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem and using principles of quantum mechanics. For simplicity we illustrate the method by exploring the problem of a particle in a box. Twofold calculation of the mean value of energy for the polynomial wave function inside the well yields even argument $p$ ($p>2$) of Riemann zeta and related functions. This method can be applied to a wide class of exactly solvable quantum mechanical problems which may lead to different infinite sums. Besides, the analysis performed here provides deeper understanding of superposition principle and presents useful exercise for physics students., 6 pages, 1 figure

Recently, there has been an increased interest in studying quantum entanglement and quantum coherence. Since both of these properties are attributed to the existence of quantum superposition, it would be useful to determine if some type of correlation between them exists. Hence, the purpose of this paper is to explore the type of the correlation in several systems with different types of anisotropy. The focus will be on the XY spin chains with the Dzyaloshinskii-Moriya interaction and the type of the mentioned bond will be explored using the quantum renormalization group method., 11 pages, 4 figures

The response function and largest Lyapunov exponent analysis were applied to the driven overdamped Frenkel-Kontorova model with two types of anharmonic convex interparticle potentials. In both cases model reduces to a single particle model for integer values of winding number. It is shown that the mirror image of the amplitude dependence of critical depinning force and largest Lyapunov exponent observed recently in the standard Frenkel-Kontorova model [Commun. Nonlinear Sci. Numer. Simul. 47, 100 (2017)] is not retained generally. Behaviour of systems with relatively strong interparticle force was examined and evidence for the appearance of mode-locking phenomenon in both directions of particles' motion is presented., 10 pages, 10 figures

We demonstrate on the example of the dc+ac driven overdamped Frenkel-Kontorova model that an easily calculable measure of complexity can be used for the examination of Shapiro steps in presence of thermal noise. In real systems, thermal noise causes melting or even disappearance of Shapiro steps, which makes their analysis in the standard way from the response function difficult. Unlike in the conventional approach, here, by calculating the Kolmogorov complexity of certain areas in the response function we were able to detect Shapiro steps, measure their size with desired precision and examine their temperature dependence. The aim of this work is to provide scientists, particularly experimentalists, an unconventional but a practical and easy tool for examination of Shapiro steps in real systems., 6 pages, 5 figures, References and text edited

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., 10 pages, 8 figures

We study the magnetic properties of the two-dimensional anisotropic antiferromagnetic spin-1/2 Heisenberg model with Dzyaloshinskii-Moriya interaction and in-plane frustration included. The method of spin Green functions within the framework of Tyablikov's random-phase-approximation decoupling scheme is used in order to derive expressions for the spin-wave spectrum, sublattice magnetization and transition temperature. Based on these expressions we perform a detailed analysis of the influence of varying values of model parameters on its magnetic properties. The model is also applied to the high-Tc superconducting parent compound La2Cuo4 and our results compared to available experimental data., 7 pages, 12 figues

The exciton dispersion is examined in the case of four selected prototypical molecular solids: pentacene,tetracene,picene,chrysene. The model parameters are determined by fitting to experimental data obtained by inelastic electron scattering. Within the picture that relies on Frenkel-type excitons we obtain that theoretical dispersion curves along different directions in the Brillouin zone are in good agreement with the experimental data, suggesting that the influence of charge-transfer excitons on exciton dispersion of the analyzed organic solids is not as large as proposed. In reciprocal space directions where Davydov splitting is observed we employ the upgraded version of Hamiltonian used in Materials 11, 2219 (2018)., Comment: 6 pages, 8 figures, 2 tables

In Serbia, one of the former republics of Socialist Federal Republic of Yugoslavia, men and women have equal access to higher education and professional employment. However, in practice, this equality is not always realized. In this paper we describe the status of women in physics in Serbia, focusing on student gender ratios and on positions held. The financial contributions of the Serbian government to the scientific sector are not sufficient. Many young physicists enter the information technology sector, where they can earn higher salaries. In addition, the lack of career opportunities motivates scientists to go abroad, so each year, more and more young people leave Serbia. Today, many young Serbian physicists plan their departure during their studies and leave the country immediately after graduation. We present statis- tical data for the last several years, reviewing the percentage of women who are pursuing physics as a subject of study or a profession. We report gender ratios at various career stages. Teaching at the primary and high-school level is the main professional activity for female physicists in Serbia. Even though a large percentage (about 50%) of Serbian physicists are female, few women hold positions in which decisions about scientific and educational policy are made. When women achieve leadership positions, their educational attainments often outstrip those required for the positions. Only six women have a high-level management position.

The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.

Parallel magnetic susceptibility temperature dependence of the high-TC superconducting parent compound La2CuO4 is calculated in both antiferromagnetic (AFM) and paramagnetic phase. By making use of the quantum Heisenberg three-dimensional AFM model including the in-plane spin anisotropy, the calculation is performed within the framework of three different theories: Green’s function theory in random-phase approximation (RPA), linear spinwave (LSW) theory and mean-field (MF) theory. The results suggest that at low temperatures quantum spin fluctuations play an important role, while at the temperatures above the critical one short-range correlations have a great impact on the behavior of the system. This leads to the discrepancy between RPA and MF results, since the later neglects the above phenomena. Further, LSW theory expectedly agrees with RPA results only at low temperatures where the magnon interactions are negligible. Comparison to the theoretical and experimental results quoted in literature confirms that RPA method presents the most appropriate method among the applied ones, suggesting that this approach is satisfactory in the case of the parallel magnetic susceptibility, while in order to reproduce the transversal one, spin-orbit coupling must be included.

We present the perturbation theory for lattice magnon fields of $D$-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 effective Lagrangian. Feynman diagrams for lattice scalar fields with derivative couplings are introduced, on 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 the low-temperature series for the free energy by examining magnon-magnon interactions and internal symmetry of the effective Hamiltonian (Lagrangian)., Comment: 20 pages, 8 figures

The double-time temperature-dependent Green’s function method is used to determine the Neel temperature of a Heisenberg antiferromagnet with easy axis X X Z anisotropy on a D -dimensional bcc lattice. Exact equations within the random phase approximation (RPA) and Callen approximation (CA) in terms of generalized hypergeometric functions valid for arbitrary D , S , and η ≥ 1 are given. Analytical and numerical results presented here strongly suggest that, for D ≥ 2 , the CA gives a higher critical temperature. It is also shown that the RPA set of self-consistent equations yields a Neel temperature closer to the experimental value for compound (CH3NH3)2MnCl4.

Bulk and surface magnetic excitations of the semi-infinite ferromagnetic semiconductor (FMS) superlattices and thin films described by Heisenberg and s – d model are analyzed using the transfer matrix method, developed in our previous work. Results are discussed in the narrow-band limit. The spin-wave frequencies for the semi-infinite narrow-band semiconductors are analyzed in both low- and high-frequency regions. Energies of localized excitations are compared to the bulk and the results of Green function formalism. Depending on the parameters of the system, the surface spin waves appear as “acoustical” and “optical”, and there are only some quantitative difference in the high-frequency region, comparing our method and the Green function method. In the framework of the same methodology, bulk and surface magnetic excitations of more complicated superlattices and thin films made of the FMS superlattices are analyzed in terms of dependence of the system parameters. It is shown that the s – d interaction governs the behavior of the systems. Dependence on bulk and surface parameters is discussed.

We calculate the temperature dependence of the magnon contribution to specific heat of the high- T C superconducting parent compounds La2CuO4 and Y Ba2Cu3O6 using the Green’s function (GF) method within the Tyablikov’s approximation (RPA). By making use of quantum Heisenberg S = 1 2 three-dimensional antiferromagnetic model, we obtain the specific heat temperature dependence in the whole temperature range from absolute zero to the Neel temperature. The analysis performed for La2CuO4 suggests that the magnon contribution to the total specific heat measured in the experiment is small, but not negligible as predicted by the simplified two-dimensional model often used within the linear spin-wave (LSW) theory. This discrepancy originates from the renormalization of the magnon energies due to the RPA in GF approach. Further, we discuss the influence of the in-plane frustration and the three-dimensionality of the system on the magnon specific heat in La2CuO4. We study the low-temperature behavior of the specific heat as well as the behavior in the vicinity of the Neel temperature which gives for the critical exponent α value α = − 1 2 . Finally, we tend to improve the LSW theory results found in the literature by applying that theory to the three-dimensional orthorhombic model with second- and third-neighbor exchange interaction.

The dispersion relation for noninteracting excitons and the influence of perturbative correction is examined in the case of pentacene structure. The values of exchange integrals are determined by the nonlinear fits to the experimental dispersion data obtained by inelastic electron scattering in Phys. Rev. Lett. \textbf{98}, 037402 (2007). We obtain theoretical dispersion curves along four different directions in the Brillouin zone which possess the same periodicity as the experimental data. We also showed that perturbative corrections are negligible since the exciton gap in dispersion relation is huge in comparison to exchange integrals., 7 pages, 9 figures

Two-dimensional Heisenberg antiferromagnet with XXZ spin anisotropy Rb2MnCl4, is studied using the method of double-time-temperature Green’s functions (GF) with arbitrary spin S (in particular case S = 5/2) within random-phase approximation (RPA) and Callen approximation (CA). Exchange field and anisotropy field are extracted from experimental data on the magnon frequencies in Rb2MnCl4. They are used to calculate dispersion relation and the sublattice magnetization in the self-consistent way in the whole temperature range. The results obtained using RPA and CA are compared. The existence of a finite temperature transition is investigated, probably describing the low-temperature critical behavior experimentally observed in many layered compounds. The Neel temperature TN is calculated employing both methods. Calculated transition temperature within RPA agrees rather well with the measured values for the quasi two-dimensional antiferromagnet Rb2MnCl4 in zero magnetic field, while CA overestimates the critical temperature. The dependence of critical temperature on parameter of spin anisotropy η is also analysed. The good agreement found between our theoretical results and the experimental data relative to the real compound Rb2MnCl4 shows that the inclusion of this type of spin anisotropy with quantum effect properly taken into account, provides a quantitative description and explanation of the experimental data.

Theoretical analysis of the layered quasi-periodic Fibonacci structures (superlattices-sequence) is presented for the systems consisting of nA and nB ferromagnetically ordered planes within the layers with Sa and Sb spins, respectively, while the interfaces are coupled with bilinear and/or biquadratic exchange interaction, within the framework of localized spin model in the low-temperature limit. Transfer matrix method and direct diagonalization after the bosonization in Bloch's approximation resulted both in the same analytical expression for the magnon-excitation energy. The equivalence (at low-temperatures) of the transfer matrix (spin) and boson approach was discussed, as well as the role of the interlayer biquadratic coupling between different blocks constituting the Fibonacci sequences. Also, our approach allows the determination of the internal energy and calculation of the magnon contribution to the specific heat. It was clearly demonstrated that the magnon specific heat vanishes for T → 0. Our results are compared with the results of other authors.

The relevance of the quasi-two-dimensional spin-1/2 frustrated quantum antiferromagnet due to its possibility of modelling the high-temperature superconducting parent compounds has resulted in numerous theoretical and experimental studies. This paper presents a detailed research of the influence of the varying exchange interactions on the model magnetic properties within the framework of self-consistent spin-wave theory based on Dyson-Maleev representation. Beside the nearest neighbour interaction within the plane, the planar frustration up to the third nearest neighbours, cyclic interaction and the interlayer coupling are taken into account. The detailed description of the elementary spin excitations, staggered magnetization, spin-wave velocity renormalization factor and ground-state energy is given. The results are compared to the predictions of the linear spin-wave theory and when possible also to the second-order perturbative spin-wave expansion results. Finally, having at our disposal improved experimental results for the in-plane spin-wave dispersion in high-$T_c$ copper oxide $\mbox{La}_2\mbox{CuO}_4$, the self-consistent spin-wave theory is applied to that compound in order to correct earlier obtained set of exchange parameters and high temperature spin-wave dispersion., Comment: 19 pages, 8 figures

Magnetic properties of spin ½ J1-J2 quantum Heisenberg antiferromagnet on body centered cubic lattice are investigated in the paper. By using two-time temperature Green's functions, sublattice magnetization and critical temperature depending on the frustration ratio J2/ J1 are obtained in both stripe and Neel phase. The analysis of ground state sublattice magnetization and internal energy indicates the first order phase transition from Neel to stripe phase for 0.7 J2/ J1 0.8, which is in agreement with previous studies.

The energy of elementary excitations in the superlattice consisting of ferromagnetic planes interacting ferromagnetically described by the Heisenberg ferromagnet is discussed. Standard approach is to linearize the equations of motion for the particular spins and formulate the transfer matrix for the system. Its trace leads to the energy of the elementary excitations. We show that this linearization is completely equivalent to the substitution of spin operators with Bose‐operators in Bloch’s approximation. Then one can perform the diagonalization of the Hamiltonian using a simple unitary transformation, leading to the same energy of elementary excitations. This opens new possibilities for the calculation with superlattices.

Watson-like integrals for a d-dimensional bcc antiferromagnetic lattice I_d(\eta) and J_d(\eta) and another two similar integrals are evaluated in an exact way in terms of generalized hypergeometric functions. A simple formula connecting Id and Jd+1 is given along with the differential equations for I_d(\eta) and J_d(\eta). An application of I_d and J_d in the theory of the Heisenberg antiferromagnet is discussed, together with possible generalizations to non-integer values of d. Corresponding integrals for sc lattices are also briefly reviewed., Comment: 13 pages, 2 figures, Accepted for publication in Journal of Physics A: Mathematical & Theoretical 2010