Quantum channels with polytopic images and image additivity
2014
Abstract: We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of the minimal output entropy can be violated in this class. We then provide a complete characterization of quantum channels T that are universally image additive in the sense that for any quantum channel S, the image of T \otimes S is the convex hull of the tensor product of the images of T and S. These channels turn out to form a strict subset of entanglement breaking channels with polytopic images and a strict superset of classical-quantum channels. |
The exponent in the orthogonality catastrophe for Fermi gases
2014
Abstract: We quantify the asymptotic vanishing of the ground-state overlap of two non-interacting Fermi gases in d-dimensional Euclidean space in the thermodynamic limit. Given two one-particle Schrödinger operators in finite-volume which differ by a compactly supported bounded potential, we prove a power-law upper bound on the ground-state overlap of the corresponding non-interacting N-particle systems. We interpret the decay exponent γ in terms of scattering theory and find γ = π^{-2}{\lVert\arcsin\lvert T_E/2\rvert}\rVert_{\mathrmHS}^2, where T_E is the transition matrix at the Fermi energy E. This exponent reduces to the one predicted by Anderson [Phys. Rev. 164, 352--359 (1967)] for the exact asymptotics in the special case of a point-like perturbation. We therefore expect the upper bound to coincide with the exact asymptotics of the overlap. |
Ergodicity and dynamical localization for Delone-Anderson operators
2014
Abstract: We study the ergodic properties of Delone-Anderson operators, using the framework of randomly coloured Delone sets and Delone dynamical systems. In particular, we show the existence of the integrated density of states and, under some assumptions on the geometric complexity of the underlying Delone sets, we obtain information on the almost-sure spectrum of the family of random operators. We then exploit these results to study the Lifshitz-tail behaviour of the integrated density of states of a Delone-Anderson operator at the bottom of the spectrum. This is used as an input for the multi scale analysis to prove dynamical localization. We also estimate the size of the spectral region where dynamical localization occurs. |
Construction of spin models displaying quantum criticality from quantum field theory
Nuclear Physics B
, Volume 886,, page: 63-74
2014
Abstract: We provide a method for constructing finite temperature states of one-dimensional spin chains displaying quantum criticality. These models are constructed using correlators of products of quantum fields and have an analytical purification. Their properties can be investigated by Monte-Carlo simulations, which enable us to study the low-temperature phase diagram and to show that it displays a region of quantum criticality. The mixed states obtained are shown to be close to the thermal state of a simple nearest neighbour Hamiltonian. |
The effect of spin-orbit interactions on the 0.7-anomaly in quantum point contacts
2014
Abstract: We study how the conductance of a quantum point contact is affected by spin-orbit interactions, for systems at zero temperature both with and without electron-electron interactions. In the presence of spin-orbit coupling, tuning the strength and direction of an external magnetic field can change the dispersion relation and hence the local density of states in the point contact region. This modifies the effect of electron-electron interactions, implying striking changes in the shape of the 0.7-anomaly and introducing additional distinctive features in the first conductance step. |
Equilibrium Fermi-liquid coefficients for the fully screened N-channel Kondo model
Phys. Rev. B
, Volume 89,, page: 195131
2014
Abstract: We analytically and numerically compute three equilibrium Fermi-liquid coefficients of the fully screened N-channel Kondo model, namely c_B, c_T and c_\varepsilon, characterizing the magnetic field and temperature dependence of the resisitivity, and the curvature of the equilibrium Kondo resonance, respectively. We present a compact, unified derivation of the N-dependence of these coefficients, combining elements from various previous treatments of this model. We numerically compute these coefficients using the numerical renormalization group, with non-Abelian symmetries implemented explicitly, finding agreement with Fermi-liquid predictions on the order of 5% or better. |
Low dimensionality of the surface conductivity of diamond
Phys. Rev. B
, Volume 89, page: 115426
2014
Abstract: Undoped diamond, a remarkable bulk electrical insulator, exhibits a high surface conductivity in air when the surface is hydrogen terminated. Although theoretical models have claimed that a two-dimensional hole gas is established as a result of surface energy-band bending, no definitive experimental demonstration has been reported so far. Here, we prove the two-dimensional character of the surface conductivity by low-temperature characterization of diamond in-plane gated field-effect transistors that enable the lateral confinement of the transistor's drain-source channel to nanometer dimensions. In these devices, we observe Coulomb blockade effects of multiple quantum islands varying in size with the gate voltage. The charging energy and thus the size of these zero-dimensional islands exhibit a gate-voltage dependence which is the direct result of the two-dimensional character of the conductive channel formed at hydrogen-terminated diamond surfaces. |
Far-from-equilibrium spin transport in Heisenberg quantum magnets
2014
Abstract: We study experimentally the far-from-equilibrium dynamics in ferromagnetic Heisenberg quantum magnets realized with ultracold atoms in an optical lattice. After controlled imprinting of a spin spiral pattern with adjustable wave vector, we measure the decay of the initial spin correlations through single-site resolved detection. On the experimentally accessible timescale of several exchange times we find a profound dependence of the decay rate on the wave vector. In one-dimensional systems we observe diffusion-like spin transport with a dimensionless diffusion coefficient of 0.22(1). We show how this behavior emerges from the microscopic properties of the closed quantum system. In contrast to the one-dimensional case, our transport measurements for two-dimensional Heisenberg systems indicate anomalous super-diffusion. |
Semicircle law for a matrix ensemble with dependent entries
2014
Abstract: We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss-type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the eigenvalue distribution measure. In case of Curie-Weiss distributions this criterion applies above the critical temperature (i.e. β<1). We also investigate the largest eigenvalue of certain ensembles of Curie-Weiss type and find a transition in its behavior at the critical temperature. |
Determination of effective mechanical properties of a double-layer beam by means of a nano-electromechanical transducer
2014
Abstract: We investigate the mechanical properties of a doubly-clamped, double-layer nanobeam embedded into an electromechanical system. The nanobeam consists of a highly pre-stressed silicon nitride and a superconducting niobium layer. By measuring the mechanical displacement spectral density both in the linear and the nonlinear Duffing regime, we determine the pre-stress and the effective Young's modulus of the nanobeam. An analytical double-layer model quantitatively corroborates the measured values. This suggests that this model can be used to design mechanical multilayer systems for electro- and optomechanical devices, including materials controllable by external parameters such as piezoelectric, magnetrostrictive, or in more general multiferroic materials. |
Sinkhorn normal form for unitary matrices
2014
Abstract: Sinkhorn proved that every entry-wise positive matrix can be made doubly stochastic by multiplying with two diagonal matrices. In this note we prove a recently conjectured analogue for unitary matrices: every unitary can be decomposed into two diagonal unitaries and one whose row- and column sums are equal to one. The proof is non-constructive and based on a reformulation in terms of symplectic topology. As a corollary, we obtain a decomposition of unitary matrices into an interlaced product of unitary diagonal matrices and discrete Fourier transformations. This provides a new decomposition of linear optics arrays into phase shifters and canonical multiports described by Fourier transformations. |
An invitation to trees of finite cone type: random and deterministic operators
2014
Abstract: Trees of finite cone type have appeared in various contexts. In particular, they come up as simplified models of regular tessellations of the hyperbolic plane. The spectral theory of the associated Laplacians can thus be seen as induced by geometry. Here we give an introduction focusing on background and then turn to recent results for (random) perturbations of trees of finite cone type and their spectral theory. |
Physicists create quantum system, which is robust to mixing by periodic forces
A new method to characterize the valley index of transition metal dichalcogenides
A team of physicists from MPQ, Caltech, and ICFO proposes the combination of nano-photonics with...
The surface of topological insulators conducts electricity exceptionally well....
Scientists from the MPQ, LMU, and the FUB analyse how fast order can appear in a quantum-mechanical...