The anomalous low temperature properties of glasses are commonly believed to originate from localized quantum-mechanical two-level tunneling systems, which couple to phonons and other elementary excitations, as well as to external fields. Although a broad range of experimental observations can be explained in terms of this idea, the microscopic nature of these two-level systems is generally unknown. Therefore, another class of substances is often considered, namely mixed crystals. Here, the microscopic nature of the tunneling units is clear. A substitutional defect (e.g. a Li defect in a KCl host crystal) is located in one of several off-center positions, and the defect can move from one potential well to the other by quantum tunneling. Mixed crystals thus allow an immediate investigation of the physics of tunneling units.
Our research activities deal with different aspects of tunneling systems, in particular their microscopic characterisation, their interactions, and their coupling to heat baths or external fields. Our main emphasis has been on the study of microscopic models of amorphous materials, in which tunneling systems with a broad range of barrier heights and asymmetries are generated through interactions as a collective effect.
Cooperations exist with the experimental group of C. Enss, A. Fleischmann and S. Hunklinger at the KIP in Heidelberg, one of the leading experimental teams in this field, and with the theory groups of Annette Zippelius in Göttingen and Alois Würger at Bordeaux.
We present a quantum statistical analysis of a microscopic mean-field model of structural glasses at low temperatures. The model can be thought of as arising from a random Born von Karman expansion of the full interaction potential. The problem is reduced to a single-site theory formulated in terms of an imaginary-time path integral using replicas to deal with the disorder. We study the physical properties of the system in thermodynamic equilibrium and develop both perturbative and non-perturbative methods to solve the model. The perturbation theory is formulated as a loop expansion in terms of two-particle irreducible diagrams, and is carried to three-loop order in the effective action. The non-perturbative description is investigated in two ways, (i) using a static approximation, and (ii) via Quantum Monte Carlo simulations. Results for the Matsubara correlations at two-loop order perturbation theory are in good agreement with those of the Quantum Monte Carlo simulations. Characteristic low-temperature anomalies of the specific heat are reproduced, both in the non-perturbative static approximation, and from a three-loop perturbative evaluation of the free energy. In the latter case the result so far relies on using Matsubara correlations at two-loop order in the three-loop expressions for the free energy, as self-consistent Matsubara correlations at three-loop order are still unavailable. We propose to justify this by the good agreement of two-loop Matsubara correlations with those obtained non-perturbatively via Quantum Monte Carlo simulations.
We introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite-coordination effects on the low-temperature behavior of finite dimensional systems. Our models use a description in terms of small deviations of particle coordinates from a set of reference positions, particularly appropriate for the description of low-temperature phenomena. A Born-von-Karman type expansion with random coefficients is used to model effects of frozen heterogeneities. The key quantity appearing in the theoretical description is a full distribution of effective single-site potentials which needs to be determined self-consistently. If microscopic interactions are harmonic, the effective single-site potentials turn out to be harmonic as well, and the distribution of these single-site potentials is equivalent to a distribution of localization lengths used earlier in the description of chemical gels. For structural glasses characterized by frustration and anharmonicities in the microscopic interactions, the distribution of single-site potentials involves anharmonicities of all orders, and both single-well and double well potentials are observed, the latter with a broad spectrum of barrier heights. The appearance of glassy phases at low temperatures is marked by the appearance of asymmetries in the distribution of single-site potentials, as previously observed for fully connected systems. Double-well potentials with a broad spectrum of barrier heights and asymmetries would give rise to the well known universal glassy low temperature anomalies when quantum effects are taken into account.
We propose a microscopic translationally invariant glass model
which exhibits two level tunneling systems, and shows the salient low-temperature
anomalies of glassy systems. Results so far obtained are in good accord with
experiment. Qualitative universality is due to the collective origin of the
glassy potential energy landscape. However, we obtain a simple explanation
also for the mysterious so-called quantitative universality that manifests
itself e.g. in the in the unusually weak dependence of values for the internal
friction plateau on substance or system parameters.
We investigate effects of interactions between substitutional defects on the properties of defect crystals at low temperatures, where defect motion is governed by quantum effects. Both, thermal and dynamical properties are considered. The influence of interactions on defect motion is described via a collective effect. Our treatment is semiclassical in the sense that we analyze collective effects in a classical setting, and analyze the influence on quantized defect motion only thereafter. Our theory describes a crossover to glassy behavior at sufficiently high defect concentration. Our approach is meant to be general. For the sake of definiteness, we evaluate most of our results with parameters appropriate for Li-doped KCl crystals.
We report on a refined version of our spin-glass type approach to the low-temperature physics of structural glasses. Its key idea is based on a Born von Karman expansion of the interaction potential about a set of reference positions in which glassy aspects are modeled by taking the harmonic contribution within this expansion to be random. Within the present refined version the expansion at the harmonic level is reorganized so as to respect the principle of global translational invariance. By implementing this principle, we have for the first time a mechanism that fixes the distribution of the parameters characterizing the local potential energy configurations responsible for glassy low-temperature anomalies solely in terms of assumptions about interactions at a microscopic level.
We discuss a spin-glass type approach to the physics of structural glasses, which leads to a class of models that exhibit both glassy low-temperature phases and double- and single-well configurations in their potential energy landscape. The low-temperature anomalies characteristic of amorphous systems are reproduced, and within our model the universality issue can be illuminated. We consider the interaction between localized excitations and phonons, and we present a general expression for the dynamic susceptibility, from which dynamic properties such as the internal friction can be calculated.
We review a model-based rather than phenomenological approach to low-temperature anomalies in glasses. Specifically, we present a solvable model inspired by spin-glass theory that exhibits both, a glassy low-temperature phase, and a collection of double- and single-well configurations in its potential energy landscape. The distribution of parameters characterizing the local potential energy configurations can be computed , and is found to differ from those assumed in the standard tunneling model and its variants. Still, low temperature anomalies characteristic of amorphous materials are reproduced. More importantly perhaps, we obtain a clue to the universality issue. That is, we are able to distinguish between properties which can be expected to be universal and those which cannot. Our theory also predicts the existence, under suitable circumstances of amorphous phases without low-energy tunneling excitations.
A random matrix approach to glassy physics is introduced. It leads to a class of models which exhibit both, glassy low-temperature phases, and double- and single-well configurations in their potential energy. The distribution of parameters characterizing the local potential energy configurations can be computed, and differ from those assumed in the standard tunneling model and its variants. Still, the low-temperature anomalies characteristic of amorphous systems are reproduced, and we are able to distinguish properties which can be expected to be universal from those which cannot.
An analytically tractable model is introduced which exhibits both, a glass-like freezing transition, and a collection of double-well configurations in its zero-temperature potential energy landscape. The latter are generally believed to be responsible for the anomalous low-temperature properties of glass-like and amorphous systems via a tunneling mechanism that allows particles to move back and forth between adjacent potential energy minima. Using mean-field and replica methods, we are able to compute the distribution of asymmetries and barrier-heights of the double-well configurations analytically, and thereby check various assumptions of the standard tunneling model. We find, in particular, strong correlations between asymmetries and barrier-heights as well as a collection of single-well configurations in the potential energy landscape of the glass-forming system - in contrast to the assumptions of the standard model. Nevertheless, the specific heat scales linearly with temperature over a wide range of low temperatures.