arXiv subjects
Publications and source records attributed to Markus Mueller.
In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.
We study mean field systems whose free energy landscape is dominated by marginally stable states. We review and develop various techniques to describe such states, elucidating their physical meaning and the interrelation between them. In particular, we give a physical interpretation of the two-group replica symmetry breaking scheme and confirm it by establishing the relation to the cavity method and to the counting of solutions of the Thouless-Anderson-Palmer equations. We show how these methods all incorporate the presence of a soft mode in the free energy landscape and interpret the occurring order parameter functions in terms of correlations between the soft mode and the local magnetizations. The general formalism is applied to the prototypical case of the Sherrington-Kirkpatrick-model where we re-examine the physical properties of marginal states under a new perspective.
We study the magnetic hysteresis in the random field Ising model in 3D. We discuss the disorder dependence of the coercive field H_c, and obtain an analytical description of the smooth part of the hysteresis below and above H_c, by identifying the disorder configurations (instantons) that are the most probable to trigger local avalanches. We estimate the critical disorder strength at which the hysteresis curve becomes continuous. From an instanton analysis at zero field we obtain a description of local two-level systems in the ferromagnetic phase.
We present a theory for the memory effect in electron glasses. In fast gate voltage sweeps it is manifested as a dip in the conductivity around the equilibration gate voltage. We show that this feature, also known as anomalous field effect, arises from the long-time persistence of correlations in the electronic configuration. We argue that the gate voltage at which the memory dip saturates is related to an instability caused by the injection of a critical number of excess carriers. This saturation threshold naturally increases with temperature. On the other hand, we argue that the gate voltage beyond which memory is erased, is temperature independent. Using standard percolation arguments, we calculate the anomalous field effect as a function of gate voltage, temperature, carrier density and disorder. Our results are consistent with experiments, and in particular, they reproduce the observed scaling of the width of the memory dip with various parameters.
We discuss the history dependence and memory effects which are observed in the out-of-equilibrium conductivity of electron glasses. The experiments can be understood by assuming that the local density of states retains a memory of the sample history. We provide analytical arguments for the consistency of this assumption, and discuss the saturation of the memory effect with increasing gate voltage change. This picture is bolstered by numerical simulations at zero temperature, which moreover demonstrate the incompressibility of the Coulomb glass on short timescales.