arXiv subjects

Markus Mueller

Publications and source records attributed to Markus Mueller.

At least 55 records · Page 3Linked to original sources

arXiv2009

Lossless Quantum Prefix Compression for Communication Channels that are Always Open

We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length of a quantum string is the maximal length in the superposition). This complements work by Schumacher and Westmoreland who calculated the corresponding rate for minimizing the output's average length. Our compressed code words are prefix-free indeterminate-length quantum bit strings which can be concatenated in the case of multiple sources. Therefore, we generalize the known theory of prefix-free quantum codes to the case of strings with indeterminate length. Moreover, we describe a communication model which allows the lossless transmission of the compressed code words. The benefit of compression is then the reduction of transmission errors in the presence of noise.

quant-ph↗

arXiv2008

Compensation driven superconductor-insulator transition

The superconductor-insulator transition in the presence of strong compensation of dopants was recently realized in La doped YBCO. The compensation of acceptors by donors makes it possible to change independently the concentration of holes n and the total concentration of charged impurities N. We propose a theory of the superconductor-insulator phase diagram in the (N,n) plane. It exhibits interesting new features in the case of strong coupling superconductivity, where Cooper pairs are compact, non-overlapping bosons. For compact Cooper pairs the transition occurs at a significantly higher density than in the case of spatially overlapping pairs. We establish the superconductor-insulator phase diagram by studying how the potential of randomly positioned charged impurities is screened by holes or by strongly bound Cooper pairs, both in isotropic and layered superconductors. In the resulting self-consistent potential the carriers are either delocalized or localized, which corresponds to the superconducting or insulating phase, respectively.

cond-mat.dis-nn↗

arXiv2008

Ising and Spin orders in Iron-based Superconductors

Motivated by recent neutron scattering experiments, we study the ordering of spins in the iron-based superconductors La(O_{1-x}F_x)FeAs, assuming them in proximity to a Mott insulator in the phase diagram. The ground state of the parent system with x = 0 is a spin density wave with ordering wave vector Q = (0, π) or (π, 0). Upon raising the temperature, we find the system to restore SU(2) symmetry, while an Ising symmetry remains broken, explaining the experimentally observed lattice distortion to a monoclinic crystal structure. Upon further temperature increase, the spins finally disorder at a second transition. The phase transition driven by doping with charge carriers similarly splits into an O(3) transition, and an Ising transition with z = 3 at larger doping.

cond-mat.str-el↗

arXiv2008

Effective Complexity and its Relation to Logical Depth

Effective complexity measures the information content of the regularities of an object. It has been introduced by M. Gell-Mann and S. Lloyd to avoid some of the disadvantages of Kolmogorov complexity, also known as algorithmic information content. In this paper, we give a precise formal definition of effective complexity and rigorous proofs of its basic properties. In particular, we show that incompressible binary strings are effectively simple, and we prove the existence of strings that have effective complexity close to their lengths. Furthermore, we show that effective complexity is related to Bennett's logical depth: If the effective complexity of a string $x$ exceeds a certain explicit threshold then that string must have astronomically large depth; otherwise, the depth can be arbitrarily small.

cs.IT↗

arXiv2008

Relativistic magnetotransport in graphene

We study the thermal and electric transport of a fluid of interacting Dirac fermions as they arise in single-layer graphene. We include Coulomb interactions, a dilute density of charged impurities and the presence of a magnetic field to describe both the static and the low frequency response as a function of temperature T and chemical potential mu. In the critical regime mu << T where both bands above and below the Dirac point contribute to transport we find pronounced deviations from Fermi liquid behavior, universal, collision-dominated values for transport coefficients and a cyclotron resonance of collective nature. In the collision-dominated high temperature regime the linear thermoelectric transport coefficients are shown to obey the constraints of relativistic magnetohydrodynamics which we derive microscopically from Boltzmann theory. The latter also allows us to describe the crossover to disorder-dominated Fermi liquid behavior at large doping and low temperatures, as well as the crossover to the ballistic regime at high fields.

cond-mat.mes-hall↗

arXiv2008

Quantum criticality and black holes

Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport co-efficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the AdS/CFT duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport co-efficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance.

cond-mat.str-el↗

arXiv2008

Collective cyclotron motion of the relativistic plasma in graphene

We present a theory of the finite temperature thermo-electric response functions of graphene, in the hydrodynamic regime induced by electron-electron collisions. In moderate magnetic fields, the Dirac particles undergo a collective cyclotron motion with a temperature-dependent relativistic cyclotron frequency proportional to the net charge density of the Dirac plasma. In contrast to the undamped cyclotron pole in Galilean-invariant systems (Kohn's theorem), here there is a finite damping induced by collisions between the counter-propagating particles and holes. This cyclotron motion shows up as a damped pole in the frequency dependent conductivities, and should be readily detectable in microwave measurements at room temperature. We also discuss the large Nernst effect to be expected in graphene.

cond-mat.str-el↗

arXiv2008

Quantum-critical relativistic magnetotransport in graphene

We study the thermal and electric transport of a fluid of interacting Dirac fermions using a Boltzmann approach. We include Coulomb interactions, a dilute density of charged impurities and the presence of a magnetic field to describe both the static and the low frequency response as a function of temperature T and chemical potential mu. In the quantum-critical regime mu << T we find pronounced deviations from Fermi liquid behavior, such as a collective cyclotron resonance with an intrinsic, collision-broadened width, and significant enhancements of the Mott and Wiedemann-Franz ratio. Some of these results have been anticipated by a relativistic hydrodynamic theory, whose precise range of validity and failure at large fields and frequencies we determine. The Boltzmann approach allows us to go beyond the hydrodynamic regime, and to quantitatively describe the deviations from magnetohydrodynamics, the crossover to disorder dominated Fermi liquid behavior at large doping and low temperatures, as well as the crossover to the ballistic regime at high fields. Finally, we obtain the full frequency and doping dependence of the single universal conductivity sigma_Q which parametrizes the hydrodynamic response.

cond-mat.str-el↗

arXiv2008

Quantum Bit Strings and Prefix-Free Hilbert Spaces

We give a mathematical framework for manipulating indeterminate-length quantum bit strings. In particular, we define prefixes, fragments, tensor products and concatenation of such strings of qubits, and study their properties and relationships. The results are then used to define prefix-free Hilbert spaces in a more general way than in previous work, without assuming the existence of a basis of length eigenstates. We prove a quantum analogue of the Kraft inequality, illustrate the results with some examples and discuss the relevance of prefix-free Hilbert spaces for lossless compression.

quant-ph↗

arXiv2008

Quantum critical transport in clean graphene

We describe electrical transport in ideal single-layer graphene at zero applied bias. There is a crossover from collisionless transport at frequencies larger than k_B T/hbar (T is the temperature) to collision-dominated transport at lower frequencies. The d.c. conductivity is computed by the solution of a quantum Boltzmann equation. Due to a logarithmic singularity in the collinear scattering amplitude (a consequence of relativistic dispersion in two dimensions) quasi-particles and -holes moving in the same direction tend to an effective equilibrium distribution whose parameters depend on the direction of motion. This property allows us to find the non-equilibrium distribution functions and the quantum critical conductivity exactly to leading order in 1/|ln(alpha)| where alpha is the coupling constant characterizing the Coulomb interactions.

cond-mat.mes-hall↗

arXiv2008

Infinite randomness fixed point of the superconductor-metal quantum phase transition

We examine the influence of quenched disorder on the superconductor-metal transition, as described by a theory of overdamped Cooper pairs which repel each other. The self-consistent pairing eigenmodes of a quasi-one dimensional wire are determined numerically. Our results support the recent proposal by Hoyos et al. (arXiv:0705.1865) that the transition is characterized by the same strong disorder fixed point describing the onset of ferromagnetism in the random quantum Ising chain in a transverse field.

cond-mat.dis-nn↗

arXiv2008

Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together

We compute the Functional Renormalization Group (FRG) disorder- correlator function R(v) for d-dimensional elastic manifolds pinned by a random potential in the limit of infinite embedding space dimension N. It measures the equilibrium response of the manifold in a quadratic potential well as the center of the well is varied from 0 to v. We find two distinct scaling regimes: (i) a "single shock" regime, v^2 ~ 1/L^d where L^d is the system volume and (ii) a "thermodynamic" regime, v^2 ~ N. In regime (i) all the equivalent replica symmetry breaking (RSB) saddle points within the Gaussian variational approximation contribute, while in regime (ii) the effect of RSB enters only through a single anomaly. When the RSB is continuous (e.g., for short-range disorder, in dimension 2 <= d <= 4), we prove that regime (ii) yields the large-N FRG function obtained previously. In that case, the disorder correlator exhibits a cusp in both regimes, though with different amplitudes and of different physical origin. When the RSB solution is 1-step and non- marginal (e.g., d < 2 for SR disorder), the correlator R(v) in regime (ii) is considerably reduced, and exhibits no cusp. Solutions of the FRG flow corresponding to non-equilibrium states are discussed as well. In all cases the regime (i) exhibits a cusp non-analyticity at T=0, whose form and thermal rounding at finite T is obtained exactly and interpreted in terms of shocks. The results are compared with previous work, and consequences for manifolds at finite N, as well as extensions to spin glasses and related models are discussed.

cond-mat.dis-nn↗

arXiv2007

Quantum Kolmogorov Complexity and the Quantum Turing Machine

The purpose of this thesis is to give a formal definition of quantum Kolmogorov complexity (QC), and rigorous mathematical proofs of its basic properties. The definition used here is similar to that by Berthiaume, van Dam, and Laplante. It defines the QC of some indeterminate-length qubit string ρas the minimum base length of any quantum input which makes a quantum Turing machine (QTM) halt and output ρ, up to some error tolerance. First, we prove that there is a QTM which is universal in the sense of input base length. Furthermore, we show several general properties of QTMs, including a result on mutually orthogonal ``halting spaces'', and a way to transform every almost-halting input into a deterministically-halting input by adding at most a constant number of qubits. Afterwards, we apply these results to QC. In particular, we show that QC is invariant, incompressible, agrees with classical Kolmogorov complexity for classical strings, and is closely related to von Neumann entropy for ergodic quantum information sources.

quant-ph↗

arXiv2007

Collective modes in quantum electron glasses and electron-assisted hopping

We study electronic transport in Anderson insulators with strong Coulomb interactions in dimensions d>=2. Close to the metal insulator transition where the single particle localization length is much larger than interparticle-distance, the interactions lead to a strongly correlated quantum glass phase. Even though single particle excitations are localized and the system is insulating, there are collective electronic modes which remain delocalized down to parametrically small energies. These collective excitations serve as a continuous bath which can provide the activation energy for variable range hopping transport. This circumvents the energy conservation problem arising when only discrete particle-hole excitations are present. In contrast to the weak and material-dependent phonon-assisted hopping mechanism, the activation by an electronic bath leads to a nearly universal prefactor e^2/h of the Efros-Shklovskii conductance, as is observed in many recent experiments.

cond-mat.str-el↗

arXiv2007

Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity

We show that there exists a universal quantum Turing machine (UQTM) that can simulate every other QTM until the other QTM has halted and then halt itself with probability one. This extends work by Bernstein and Vazirani who have shown that there is a UQTM that can simulate every other QTM for an arbitrary, but preassigned number of time steps. As a corollary to this result, we give a rigorous proof that quantum Kolmogorov complexity as defined by Berthiaume et al. is invariant, i.e. depends on the choice of the UQTM only up to an additive constant. Our proof is based on a new mathematical framework for QTMs, including a thorough analysis of their halting behaviour. We introduce the notion of mutually orthogonal halting spaces and show that the information encoded in an input qubit string can always be effectively decomposed into a classical and a quantum part.

quant-ph↗

arXiv2007

Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes

We present a general hydrodynamic theory of transport in the vicinity of superfluid-insulator transitions in two spatial dimensions described by "Lorentz"-invariant quantum critical points. We allow for a weak impurity scattering rate, a magnetic field B, and a deviation in the density, ρ, from that of the insulator. We show that the frequency-dependent thermal and electric linear response functions, including the Nernst coefficient, are fully determined by a single transport coefficient (a universal electrical conductivity), the impurity scattering rate, and a few thermodynamic state variables. With reasonable estimates for the parameters, our results predict a magnetic field and temperature dependence of the Nernst signal which resembles measurements in the cuprates, including the overall magnitude. Our theory predicts a "hydrodynamic cyclotron mode" which could be observable in ultrapure samples. We also present exact results for the zero frequency transport co-efficients of a supersymmetric conformal field theory (CFT), which is solvable by the AdS/CFT correspondence. This correspondence maps the ρand B perturbations of the 2+1 dimensional CFT to electric and magnetic charges of a black hole in the 3+1 dimensional anti-de Sitter space. These exact results are found to be in full agreement with the general predictions of our hydrodynamic analysis in the appropriate limiting regime. The mapping of the hydrodynamic and AdS/CFT results under particle-vortex duality is also described.

cond-mat.str-el↗

arXiv2007

Fractional Sums and Euler-like Identities

We introduce a natural definition for sums of the form \[ \sum_{ν=1}^x f(ν) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory includes the known interpolation of the factorial by the gamma function or Euler's little-known formula \sum_{ν=1}^{-1/2} \frac 1ν= -2\ln 2. Many classical identities like the geometric series and the binomial theorem nicely extend to this more general setting. Sums with a fractional number of terms are closely related to special functions, in particular the Riemann and Hurwitz zeta functions. A number of results about fractional sums can be interpreted as classical infinite sums or products or as limits, including identities like \[ \lim_{n\to\infty}[ e^{\frac n 4(4n+1)}n^{-\frac 1 8 - n(n+1)}(2π)^{-\frac n 2} \prod_{k=1}^{2n} Γ(1+\frac k 2)^{k(-1)^k} ] = \sqrt[12]{2} \exp({5/24} - \frac 3 2 ζ'(-1) -\frac{7ζ(3)}{16π^2}) \] some of which seem to be new.

math.CA↗

arXiv2007

Mean field theory for the three-dimensional Coulomb glass

We study the low temperature phase of the 3D Coulomb glass within a mean field approach which reduces the full problem to an effective single site model with a non-trivial replica structure. We predict a finite glass transition temperature $T_c$, and a glassy low temperature phase characterized by permanent criticality. The latter is shown to assure the saturation of the Efros-Shklovskii Coulomb gap in the density of states. We find this pseudogap to be universal due to a fixed point in Parisi's flow equations. The latter is given a physical interpretation in terms of a dynamical self-similarity of the system in the long time limit, shedding new light on the concept of effective temperature. From the low temperature solution we infer properties of the hierarchical energy landscape, which we use to make predictions about the master function governing the aging in relaxation experiments.

cond-mat.dis-nn↗