arXiv subjects

Markus Mueller

Publications and source records attributed to Markus Mueller.

At least 37 records · Page 2Linked to original sources

arXiv2012

Mean field theory of superglasses

We study the interplay of superfluidity and glassy ordering of hard core bosons with random, frustrating interactions. This is motivated by bosonic systems such as amorphous supersolid, disordered superconductors with preformed pairs, and helium in porous media. We analyze the fully connected mean field version of this problem, which exhibits three low-temperature phases, separated by two continuous phase transitions: an insulating, glassy phase with an amorphous frozen density pattern, a nonglassy superfluid phase, and an intermediate phase, in which both types of order coexist. We elucidate the nature of the phase transitions, highlighting in particular the role of glassy correlations across the superfluid-insulator transition. The latter suppress superfluidity down to T=0, due to the depletion of the low-energy density of states, unlike in the standard BCS scenario. Further, we investigate the properties of the coexistence (superglass) phase. We find anticorrelations between the local order parameters and a nonmonotonous superfluid order parameter as a function of T. The latter arises due to the weakening of the glassy correlation gap with increasing temperature. Implications of the mean field phenomenology for finite dimensional bosonic glasses with frustrating Coulomb interactions are discussed.

cond-mat.dis-nn↗

arXiv2011

Equilibrium avalanches in spin glasses

We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at zero temperature upon small changes in the magnetic field. For the infinite-range Sherrington-Kirkpatrick model we present a detailed derivation of the density rho(Delta M) of the magnetization jumps Delta M. It is obtained by introducing a multi-component generalization of the Parisi-Duplantier equation, which allows us to compute all cumulants of the magnetization. We find that rho(Delta M) ~ (Delta M)^(-tau) with an avalanche exponent tau=1 for the SK model, originating from the marginal stability (criticality) of the model. It holds for jumps of size 1 << Delta M < N^(1/2) being provoked by changes of the external field by delta H = O(N^[-1/2]) where N is the total number of spins. Our general formula also suggests that the density of overlap q between initial and final state in an avalanche is rho(q) ~ 1/(1-q). These results show interesting similarities with numerical simulations for the out-of-equilibrium dynamics of the SK model. For finite-range models, using droplet arguments, we obtain the prediction tau= (d_f + theta)/d_m, where d_f,d_m and theta are the fractal dimension, magnetization exponent and energy exponent of a droplet, respectively. This formula is expected to apply to other glassy disordered systems, such as the random-field model and pinned interfaces. We make suggestions for further numerical investigations, as well as experimental studies of the Barkhausen noise in spin glasses.

cond-mat.dis-nn↗

arXiv2011

Effective complexity of stationary process realizations

The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, that is probability distributions on finite binary strings. In our previous paper we propose a definition of effective complexity in precise terms of algorithmic information theory. Here we investigate the effective complexity of binary strings generated by stationary, in general not computable, processes. We show that under not too strong conditions long typical process realizations are effectively simple. Our results become most transparent in the context of coarse effective complexity which is a modification of the original notion of effective complexity that uses less parameters in its definition. A similar modification of the related concept of sophistication has been suggested by Antunes and Fortnow.

cs.IT↗

arXiv2011

Collision-dominated spin transport in graphene and Fermi liquids

In a clean Fermi liquid, due to spin up/spin down symmetry, the dc spin current driven by a magnetic field gradient is finite even in the absence of impurities. Hence, the spin conductivity sigma_s assumes a well-defined collision-dominated value in the disorder-free limit, providing a direct measure for the inverse strength of electron-electron interactions. In neutral graphene, with Fermi energy at the Dirac point, the Coulomb interactions remain unusually strong, such that the inelastic scattering rate comes close to a conjectured upper bound 1/τ_{inel} <= k_B T/\hbar, similarly as in strongly coupled quantum critical systems. The strong scattering is reflected by a minimum of the spin conductivity at the Dirac point, where it reaches sigma_s = (0.121/alpha^2) * (mu_B^2/\hbar) at weak Coulomb coupling alpha. Up to the replacement of quantum units, e^2/\hbar -> mu_s^2/\hbar, this result equals the collision-dominated electrical conductivity obtained previously. This accidental symmetry is, however, broken to higher orders in the interaction strength. For gated graphene, and 2d metals in general, we show that the transport time is parametrically smaller than the collision time. We exploit this to compute the collision-limited sigma_s analytically as sigma_s= (1/C) * (mu/T)^2 * (mu_B^2/\hbar) with C=4 pi^2 alpha^2 [2/3 ln(1/(2α))-1] for weak Coulomb coupling alpha.

cond-mat.str-el↗

arXiv2011

How to Add a Noninteger Number of Terms: From Axioms to New Identities

Starting from a small number of well-motivated axioms, we derive a unique definition of sums with a noninteger number of addends. These "fractional sums" have properties that generalize well-known classical sum identities in a natural way. We illustrate how fractional sums can be used to derive infinite sum and special functions identities; the corresponding proofs turn out to be particularly simple and intuitive.

math.CA↗

arXiv2010

Concentration of measure for quantum states with a fixed expectation value

Given some observable H of a finite-dimensional quantum system, we investigate the typical properties of random quantum state vectors that have a fixed expectation value with respect to H. Under some some conditions on the spectrum, we prove that this manifold of quantum states shows a concentration of measure phenomenon: any continuous function on this set is almost everywhere close to its mean. We also give a method to estimate the corresponding expectation values analytically, and we prove a formula for the typical reduced density matrix in the case that H is a sum of local observables. We discuss the implications of our results as new proof tools in quantum information theory and to study phenomena in quantum statistical mechanics. As a by-product, we derive a method to sample the resulting distribution numerically, which generalizes the well-known Gaussian method to draw random states from the sphere.

quant-ph↗

arXiv2010

Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice

The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain the density of zeros for the infinite system size by using the cavity method. The phase boundaries thus derived from the location of the zeros are consistent with the results of direct analytical calculations. This is the first example in which the spin glass transition is related to the distribution of zeros directly in the thermodynamical limit. We clarify how the spin glass transition is characterized by the zeros of the partition function. It is also shown that in the spin glass phase a continuous distribution of singularities touches the axes of real field and temperature.

cond-mat.dis-nn↗

arXiv2010

Efficient quantum repeater based on deterministic Rydberg gates

We propose an efficient quantum repeater architecture with mesoscopic atomic ensembles, where the Rydberg blockade is employed for deterministic local entanglement generation, entanglement swapping and entanglement purification. Compared with conventional atomic-ensemble-based quantum repeater, the entanglement distribution rate is improved by up to two orders of magnitude with the help of the deterministic Rydberg gate. This new quantum repeater scheme is robust and fast, and thus opens up a new way for practical long-distance quantum communication.

quant-ph↗

arXiv2010

All reversible dynamics in maximally non-local theories are trivial

A remarkable feature of quantum theory is non-locality (i.e. the presence of correlations which violate Bell inequalities). However, quantum correlations are not maximally non-local, and it is natural to ask whether there are compelling reasons for rejecting theories in which stronger violations are possible. To shed light on this question, we consider post-quantum theories in which maximally non-local states (non-local boxes) occur. It has previously been conjectured that the set of dynamical transformations possible in such theories is severely limited. We settle the question affirmatively in the case of reversible dynamics, by completely characterizing all such transformations allowed in this setting. We find that the dynamical group is trivial, in the sense that it is generated solely by local operations and permutations of systems. In particular, no correlations can ever be created; non-local boxes cannot be prepared from product states (in other words, no analogues of entangling unitary operations exist), and classical computers can efficiently simulate all such processes.

quant-ph↗

arXiv2009

Graphene: Relativistic transport in a nearly perfect quantum liquid

Electrons and holes in clean, charge-neutral graphene behave like a strongly coupled relativistic liquid. The thermo-electric transport properties of the interacting Dirac quasiparticles are rather special, being constrained by an emergent Lorentz covariance at hydrodynamic frequency scales. At small carrier density and high temperatures, graphene exhibits signatures of a quantum critical system with an inelastic scattering rate set only by temperature, a conductivity with a nearly universal value, solely due to electron-hole friction, and a very low viscosity. In this regime one finds pronounced deviations from standard Fermi liquid behavior. These results, obtained by Boltzmann transport theory at weak electron-electron coupling, are fully consistent with the predictions of relativistic hydrodynamics. Interestingly, very analogous behavior is found in certain strongly coupled relativistic liquids, which can be analyzed exactly via the AdS-CFT correspondence, and which had helped identifying and establishing the peculiar properties of graphene.

cond-mat.str-el↗

arXiv2009

Purely electronic transport and localization in the Bose glass

We discuss transport and localization properties on the insulating side of the disorder dominated superconductor-insulator transition, described in terms of the dirty boson model. Analyzing the spectral properties of the interacting bosons in the absence of phonons, we argue that the Bose glass phase admits three distinct regimes. For strongest disorder the boson system is a fully localized, perfect insulator at any temperature. At smaller disorder, only the low temperature phase exhibits perfect insulation while delocalization takes place above a finite temperature. We argue that a third phase must intervene between these perfect insulators and the superconductor. This conducting Bose glass phase is characterized by a mobility edge in the many body spectrum, located at finite energy above the ground state. In this insulating regime purely electronically activated transport occurs, with a conductivity following an Arrhenius law at asymptotically low temperatures, while a tendency to superactivation is predicted at higher T. These predictions are in good agreement with recent transport experiments in highly disordered films of superconducting materials.

cond-mat.supr-con↗

arXiv2009

Temperature dependence of the conductivity of ballistic graphene

We investigate the temperature dependence of the conductivity in ballistic graphene using Landauer transport theory. We obtain results which are qualitatively in agreement with many features recently observed in transport measurements on high mobility suspended graphene. The conductivity σat high temperature T and low density n grows linearly with T, while at high n we find σ~ |n|^1/2 with negative corrections at small T due to the T-dependence of the chemical potential. At moderate densities the conductivity is a non-monotonic function of T and n, exhibiting a minimum at T=0.693 \hbar v |n|^1/2 where v is the Fermi velocity. We discuss two kinds of Fabry-Perot oscillations in short nanoribbons and their stability at finite temperatures.

cond-mat.mes-hall↗

arXiv2009

Graphene - a nearly perfect fluid

Hydrodynamics and collision dominated transport are crucial to understand the slow dynamics of many correlated quantum liquids. The ratio η/s of the shear viscosity ηto the entropy density s is uniquely suited to determine how strongly the excitations in a quantum fluid interact. We determine η/s in clean undoped graphene using a quantum kinetic theory. As a result of the quantum criticality of this system the ratio is smaller than in many other correlated quantum liquids and, interestingly, comes close to a lower bound conjectured in the context of the quark gluon plasma. We discuss possible consequences of the low viscosity, including pre-turbulent current flow.

cond-mat.mes-hall↗

arXiv2009

On the Quantum Kolmogorov Complexity of Classical Strings

We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the corresponding string. It follows that quantum complexity is an extension of classical complexity to the domain of quantum states. This is true even if we allow a small probabilistic error in the quantum computer's output. We outline a mathematical proof of this statement, based on an inequality for outputs of quantum operations and a classical program for the simulation of a universal quantum computer.

quant-ph↗

arXiv2009

Convex Trace Functions on Quantum Channels and the Additivity Conjecture

We study a natural generalization of the additivity problem in quantum information theory: given a pair of quantum channels, then what is the set of convex trace functions that attain their maximum on unentangled inputs, if they are applied to the corresponding output state? We prove several results on the structure of the set of those convex functions that are "additive" in this more general sense. In particular, we show that all operator convex functions are additive for the Werner-Holevo channel in 3x3 dimensions, which contains the well-known additivity results for this channel as special cases.

quant-ph↗

arXiv2009

Does Probability become Fuzzy in Small Regions of Spacetime?

In a recent paper, Buniy et al. have argued that a possible discretization of spacetime leads to an unavoidable discretization of the state space of quantum mechanics. In this paper, we show that this conclusion is not limited to quantum theory: in any classical, quantum, or more general probabilistic theory, states (i.e. probabilities or corresponding amplitudes) become discrete or fuzzy for observers, as long as time evolution is reversible and entropy is locally bounded. Specifically, we show that the Bekenstein bound suggests that probabilities in small closed regions of space carry an uncertainty inversely proportional to the the square root of the system's effective radius and energy.

hep-th↗

arXiv2009

Stationary Algorithmic Probability

Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural approach to eliminate this machine-dependence. Our method is to assign algorithmic probabilities to the different computers themselves, based on the idea that "unnatural" computers should be hard to emulate. Therefore, we study the Markov process of universal computers randomly emulating each other. The corresponding stationary distribution, if it existed, would give a natural and machine-independent probability measure on the computers, and also on the binary strings. Unfortunately, we show that no stationary distribution exists on the set of all computers; thus, this method cannot eliminate machine-dependence. Moreover, we show that the reason for failure has a clear and interesting physical interpretation, suggesting that every other conceivable attempt to get rid of those additive constants must fail in principle, too. However, we show that restricting to some subclass of computers might help to get rid of some amount of machine-dependence in some situations, and the resulting stationary computer and string probabilities have beautiful properties.

cs.IT↗

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↗