Łukasz A. Turski

Quantum motion of electrons in topologically distorted crystals

For the description of the long-wavelength quantum states of electrons in crystals with topological defects we establish a general framework on the basis of the continuum theory of defects. The resulting one-particle Schrodinger equation lives on a Riemann-Cartan manifold, representing the distorted crystal, and consists of two parts. All effects due to the topology of the defects are contained in the first part which has a covariant form and describes the purely geometric particle motion. The second part is non-covariant and derives from deformation-dependent tunneling rates of the particle which e.g. are responsible for the existence of bound states to edge dislocations.

Spreading of step-like density profiles in interacting lattice gas on a hexagonal lattice

Abstract Diffusion in a single-layer adsorbate on a crystalline surface with a hexagonal lattice site symmetry is studied by Monte Carlo simulations. A step-like density profile of the adsorbate is allowed to spread. From the evolution of this density profile the diffusion coefficient is obtained by use of standard Boltzmann–Matano analysis. Results are compared with those obtained from the harmonic profile evolution studies undertaken by us previously. Agreement between both approaches is found at high and low temperatures. We show results for systems with two different activated state energies. For the first model the diffusion coefficient increases smoothly with the density, and for the second one the diffusion coefficient reaches a maximum for a half-occupied lattice. For this density the step profile forms a long flat terrace. No increase of the diffusion constant for densities where perfect ordering happens was observed.

Collective diffusion on hexagonal lattices – repulsive interactions

DiVusion of interacting particle on a hexagonal lattice is studied by use of Monte Carlo simulations for a range of densities and temperatures including ordered and disordered phases. The decay of the initially prepared density perturbation is analyzed. Fast, local ordering happens at the beginning of system relaxation and clearly separates as a function of time the much slower global diVusion process. Locally equilibrated density perturbation decays according to the macroscopic diVusion equation, which allows a collective diVusion coeYcient to be calculated. The density dependence of the collective diVusion coeYcient is shown for several temperatures above and below the critical temperature.

Examples of the Dirac approach to dynamics of systems with constraints

The Dirac brackets approach to description of the dynamics of dynamical systems in presence of the phase-space constraints is illustrated here on few examples taken from classical and continuum mechanics course.

On the Dirac approach to constrained dissipative dynamics

In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for constrained dissipative systems through an extension of the Dirac brackets concept, and we present a new formula for calculating Dirac brackets. This formula is particularly useful in the description of dynamical systems with many second-class constraints. After presenting the necessary formal background we illustrate our method on several examples taken from particle dynamics, continuum media physics and wave mechanics.

Gauge theory of sound propagation in crystals with dislocations

Within the framework of gauge field theory a general scheme for describing sound propagation in harmonic crystals with dislocations is worked out. As an application the theory confirms the appearance of local elastic vibrations in the strain field of edge dislocations and their absence in the case of screw dislocations. When the theory is applied to the scattering of sound waves on a screw dislocation, one recovers the appearance of Aharonov–Bohm interferences.

Possible Freezing Scenarios for Classical Liquids

This paper contains a discussion of the orientational order model of the freezing transition for a classical, monoatomic liquid. It is argued that the orientational ordering is a more fundamental notion than the usually assumed periodic translational ordering. The model discussed allows then for a scenario of freezing in which liquids can freeze either into a crystal (with both translational and orientational long range correlations) or into a quasicrystal (with only orientational long range order). Possible extensions of the model as well as its relation to other models and theories of freezing are also discussed.

Recursive properties of Dirac and metriplectic Dirac brackets with applications

In this article, we prove that Dirac brackets for Hamiltonian and non-Hamiltonian constrained systems can be derived recursively. We then study the applicability of that formulation in analysis of some interesting physical models. Particular attention is paid to the feasibility of implementation code for Dirac brackets in Computer Algebra System.

The Bose–Einstein condensation in random box

The Bose–Einstein condensation in the presence of quenched disorder due to random boundary conditions is considered. We have shown that for bosons confined in a box with volume Ld and for random L the Bose condensation temperature is lowered by the presence of disorder and the onset of condensation may even be completely prohibited. Similar results hold for bosons confined in a harmonic oscillator potential well, the geometry used in recent experiments on Bose–Einstein condensation in atomic traps. Comments on possible consequences of quenched disorder in boundary conditions for many fermion systems are also given.

Diffusion and desorption in weakly interacting adsorbate

Abstract Using a properly chosen master equation describing combined desorption and surface diffusion processes in interacting adsorbate layers, we analyze the coverage evolution and calculate the dynamical structure factor for the adsorbate in the weak intra-adsorbate interaction limit. The connection with formerly analyzed desorption-diffusion processes in noninteracting adsorbate is made. For a simplified one-dimensional model the analytically derived expression for the dynamical structure factor permits discussion of its dependence on sign of the interactions and value of the desorption rate.