Entropy Production of Doubly Stochastic Quantum Channels

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly-stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.Comment: 24 page

Casimir energy density in closed hyperbolic universes

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with compact spatial sections of negative spatial curvature.Comment: 10 pages. Contribution to the "Fifth Alexander Friedmann International Seminar on Gravitation and Cosmology," Joao Pessoa, Brazil, 2002. Revised version, with altered Abstract and one new referenc

Relative Entropy Convergence for Depolarizing Channels

We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the log-Sobolev-1 constant. Our main result is the computation of this constant. As an application we use the log-Sobolev-1 constant of the depolarizing channels to improve the concavity inequality of the von-Neumann entropy. This result is compared to similar bounds obtained recently by Kim et al. and we show a version of Pinsker's inequality, which is optimal and tight if we fix the second argument of the relative entropy. Finally, we consider the log-Sobolev-1 constant of tensor-powers of the completely depolarizing channel and use a quantum version of Shearer's inequality to prove a uniform lower bound.Comment: 21 pages, 3 figure

The Nature of Active Galactic Nuclei with Velocity Offset Emission Lines

We obtained Keck/OSIRIS near-IR adaptive optics-assisted integral-field spectroscopy to probe the morphology and kinematics of the ionized gas in four velocity-offset active galactic nuclei (AGNs) from the Sloan Digital Sky Survey. These objects possess optical emission lines that are offset in velocity from systemic as measured from stellar absorption features. At a resolution of ~0.18", OSIRIS allows us to distinguish which velocity offset emission lines are produced by the motion of an AGN in a dual supermassive black hole system, and which are produced by outflows or other kinematic structures. In three galaxies, J1018+2941, J1055+1520 and J1346+5228, the spectral offset of the emission lines is caused by AGN-driven outflows. In the remaining galaxy, J1117+6140, a counterrotating nuclear disk is observed that contains the peak of Pa$\alpha$ emission 0.2" from the center of the galaxy. The most plausible explanation for the origin of this spatially and kinematically offset peak is that it is a region of enhanced Pa$\alpha$ emission located at the intersection zone between the nuclear disk and the bar of the galaxy. In all four objects, the peak of ionized gas emission is not spatially coincident with the center of the galaxy as traced by the peak of the near-IR continuum emission. The peaks of ionized gas emission are spatially offset from the galaxy centers by 0.1"-0.4" (0.1-0.7 kpc). We find that the velocity offset originates at the location of this peak of emission, and the value of the offset can be directly measured in the velocity maps. The emission-line ratios of these four velocity-offset AGNs can be reproduced only with a mixture of shocks and AGN photoionization. Shocks provide a natural explanation for the origin of the spatially and spectrally offset peaks of ionized gas emission in these galaxies.Comment: 14 pages, 12 figures, accepted for publication in Ap

Is the gamma risk of options insurable?

In this article we analyze the risk associated with hedging written call options. We introduce a way to isolate the gamma risk from other risk types and present its loss distribution, which has heavy tails. Moving to an insurance point of view, we define a loss ratio that we find to be well behaved with a slightly negative correlation to traditional lines of insurance business, offering diversification opportunities. The tails of the loss distribution are shown to be much fatter than those of the underlying stock returns. We also show that badly estimated volatility, in the Black-Scholes model, leads to considerably biased values for the replicating portfolio. Operational risk is defined as caused by imperfect delta hedging and is found to be limited in today's markets where the autocorrelation of stock returns is small.Option; Insurance; Risk

Adsorption studies of DNA origami on silicon dioxide

Self-assembled DNA nanostructures promise low-cost ways to create nanoscale shapes. DNA nanostructures can also be used to position particles with nanometer precision. Yet, reliable and low-cost ways of integrating the structures with MEMS technology still have to be developed and innovations are of great interest to the field. We have examined in detail the adherence of DNA origami tiles on silicon oxide surfaces of wafers in dependence on pH-value and magnesium ion concentration. The results of this work will help to pursue new strategies of positioning DNA nanostruc-tures on SiO2. Precise control over the strength of structure-surface adhesion is a prerequisite of relia-ble processes

Testing quantum gravity with interactive information sensing

We suggest a test of a central prediction of perturbatively quantized general relativity: the coherent communication of quantum information between massive objects through gravity. To do this, we introduce the concept of interactive quantum information sensing, a protocol tailored to the verification of dynamical entanglement generation between a pair of systems. Concretely, we propose to monitor the periodic wavefunction collapse and revival in an atomic interferometer which is gravitationally coupled to a mechanical oscillator. We prove a theorem which shows that, under the assumption of time-translation invariance, this collapse and revival is possible if and only if the gravitational interaction forms an entangling channel. Remarkably, as this approach improves at moderate temperatures and relies primarily upon atomic coherence, our numerical estimates indicate feasibility with current devices.Comment: 24 pages + appendices, 6 figure

Chiral 1D Floquet topological insulators beyond rotating wave approximation

We study one-dimensional (1D) Floquet topological insulators with chiral symmetry going beyond the standard rotating wave approximation. The occurrence of many anticrossings between Floquet replicas leads to a dramatic extension of phase diagram regions with stable topological edge states (TESs). We present an explicit construction of all TESs in terms of a truncated Floquet Hamiltonian in frequency space, prove the bulk-boundary correspondence, and analyze the stability of the TESs in terms of their localization lengths. We propose experimental tests of our predictions in curved bilayer graphene.Comment: 4+9 page

Quasiparticles governing the zero-temperature dynamics of the 1D spin-1/2 Heisenberg antiferromagnet in a magnetic field

The T=0 dynamical properties of the one-dimensional (1D) $s=1/2$ Heisenberg antiferromagnet in a uniform magnetic field are studied via Bethe ansatz for cyclic chains of $N$ sites. The ground state at magnetization $0<M_z<N/2$, which can be interpreted as a state with $2M_z$ spinons or as a state of $M_z$ magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the {\em psinons} and {\em antipsinons}. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for (i) the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, (ii) the calculation of spectral boundaries and densities of states for each continuum, (iii) the calculation of transition rates between the ground state and the dynamically dominant collective excitations, (iv) the prediction of lineshapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including KCuF$_3$, Cu(C$_4$H$_4$N$_2)(NO_3)_2$, and CuGeO$_3$.Comment: 13 pages, 12 figure

Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model

The fidelity metric has recently been proposed as a useful and elegant approach to identify and characterize both quantum and classical phase transitions. We study this metric on the manifold of thermal states for the Lipkin-Meshkov-Glick (LMG) model. For the isotropic LMG model, we find that the metric reduces to a Fisher-Rao metric, reflecting an underlying classical probability distribution. Furthermore, this metric can be expressed in terms of derivatives of the free energy, indicating a relation to Ruppeiner geometry. This allows us to obtain exact expressions for the (suitably rescaled) metric in the thermodynamic limit. The phase transition of the isotropic LMG model is signalled by a degeneracy of this (improper) metric in the paramagnetic phase. Due to the integrability of the isotropic LMG model, ground state level crossings occur, leading to an ill-defined fidelity metric at zero temperature.Comment: 18 pages, 3 figure