Anisotropic glass-like properties in tetragonal disordered crystals

The low temperature acoustic and thermal properties of amorphous, glassy materials are remarkably similar. All these properties are described theoretically with reasonable quantitative accuracy by assuming that the amorphous solid contains dynamical defects that can be described at low temperatures as an ensemble of two-level systems (TLS), but the deep nature of these TLSs is not clarified yet. Moreover, glassy properties were found also in disordered crystals, quasicrystals, and even perfect crystals with a large number of atoms in the unit cell. In crystals, the glassy properties are not universal, like in amorphous materials, and also exhibit anisotropy. Recently it was proposed a model for the interaction of two-level systems with arbitrary strain fields (Phys. Rev. B 75, 64202, 2007), which was used to calculate the thermal properties of nanoscopic membranes at low temperatures. The model is also suitable for the description of anisotropic crystals. We describe here the results of the calculation of anisotropic glass-like properties in crystals of various lattice symmetries, emphasizing the tetragonal symmetry.Comment: 5 pages, no figure

Quantization of the elastic modes in an isotropic plate

We quantize the elastic modes in a plate. For this, we find a complete, orthogonal set of eigenfunctions of the elastic equations and we normalize them. These are the phonon modes in the plate and their specific forms and dispersion relations are manifested in low temperature experiments in ultra-thin membranes.Comment: 14 pages, 2 figure

Scattering of phonons on two-level systems in disordered crystals

We calculate the scattering rates of phonons on two-level systems in disordered trigonal and hexagonal crystals. We apply a model in which the two-level system, characterized by a direction in space, is coupled to the strain field of the phonon via a tensor of coupling constants. The structure of the tensor of coupling constants is similar to the structure of the tensor of elastic stiffness constants, in the sense that they are determined by the same symmetry transformations. In this way, we emphasize the anisotropy of the interaction of elastic waves with the ensemble of two-level systems in disordered crystals. We also point to the fact that the ratio $\gamma_l/\gamma_t$ has a much broader range of allowed values in disordered crystals than in isotropic solids.Comment: 5 pages, no figure

Anisotropic interaction of two-level systems with acoustic waves in disordered crystals

We apply the model introduced in Phys. Rev. B 75, 064202 (2007), cond-mat/0610469, to calculate the anisotropy effect in the interaction of two level systems with phonons in disordered crystals. We particularize our calculations to cubic crystals and compare them with the available experimental data to extract the parameters of the model. With these parameters we calculate the interaction of the dynamical defects in the disordered crystal with phonons (or sound waves) propagating along other crystalographic directions, providing in this way a method to investigate if the anisotropy comes from the two-level systems being preferably oriented in a certain direction or solely from the lattice anisotropy with the two-level systems being isotropically oriented.Comment: 10 page

Universal behaviour of ideal and interacting quantum gases in two dimensions

I discuss ideal and interacting quantum gases obeying general fractional exclusion statistics. For systems with constant density of single-particle states, described in the mean field approximation, the entropy depends neither on the microscopic exclusion statistics, nor on the interaction. Such systems are called {\em thermodynamically equivalent} and I show that the microscopic reason for this equivalence is a one-to-one correspondence between the excited states of these systems. This provides a method, different from the bosonisation technique, to transform between systems of different exclusion statistics. In the last section the macroscopic aspects of this method are discussed. In Appendix A I calculate the fluctuation of the ground state population of a condensed Bose gas in grandcanonical ensemble and mean field approximation, while in Appendix B I show a situation where although the system exhibits fractional exclusion properties on microscopic energy intervals, a rigorous calculation of the population of single particle states reveals a condensation phenomenon. This also implies a malfunction of the usual and simplified calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same content, with slight rephrasing. Apendices are new. In the original submission I just mentioned the condensation, which is now detailed in Appendix B. They were intended for a separate paper. Reason for changes: rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge

The thermodynamic limit for fractional exclusion statistics

I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev. Lett. {\bf 67}, 937, 1991) and I show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These inconsistencies appear when mutual exclusion statistics is manifested between different subspecies of particles in the system. In order to eliminate these inconsistencies, I introduce new mutual exclusion statistics parameters, which are proportional to the dimension of the Hilbert sub-space on which they act. These new definitions lead to properly defined particle distributions and thermodynamic properties. In another paper (arXiv:0710.0728) I show that fractional exclusion statistics manifested in general systems with interaction have these, physically consistent, statistics parameters.Comment: 8 page

Interaction of Lamb modes with two-level systems in amorphous nanoscopic membranes

Using a generalized model of interaction between a two-level system (TLS) and an arbitrary deformation of the material, we calculate the interaction of Lamb modes with TLSs in amorphous nanoscopic membranes. We compare the mean free paths of the Lamb modes with different symmetries and calculate the heat conductivity $\kappa$. In the limit of an infinitely wide membrane, the heat conductivity is divergent. Nevertheless, the finite size of the membrane imposes a lower cut-off for the phonons frequencies, which leads to the temperature dependence $\kappa\propto T(a+b\ln T)$. This temperature dependence is a hallmark of the TLS-limited heat conductance at low temperature.Comment: 9 pages, 2 figure

Heat transport in ultra-thin dielectric membranes and bridges

Phonon modes and their dispersion relations in ultrathin homogenous dielectric membranes are calculated using elasticity theory. The approach differs from the previous ones by a rigorous account of the effect of the film surfaces on the modes with different polarizations. We compute the heat capacity of membranes and the heat conductivity of narrow bridges cut out of such membranes, in a temperature range where the dimensions have a strong influence on the results. In the high temperature regime we recover the three-dimensional bulk results. However, in the low temperature limit the heat capacity, $C_V$, is proportional with $T$ (temperature), while the heat conductivity, $\kappa$, of narrow bridges is proportional to $T^{3/2}$, leading to a thermal cut-off frequency $f_c=\kappa/C_V\propto T^{1/2}$.Comment: 6 pages and 6 figure