Quantifying the Effect of Non-Larmor Motion of Electrons on the Pressure Tensor

In space plasma, various effects of magnetic reconnection and turbulence cause the electron motion to significantly deviate from their Larmor orbits. Collectively these orbits affect the electron velocity distribution function and lead to the appearance of the "non-gyrotropic" elements in the pressure tensor. Quantification of this effect has important applications in space and laboratory plasma, one of which is tracing the electron diffusion region (EDR) of magnetic reconnection in space observations. Three different measures of agyrotropy of pressure tensor have previously been proposed, namely, $A\varnothing_e$, $D_{ng}$ and $Q$. The multitude of contradictory measures has caused confusion within the community. We revisit the problem by considering the basic properties an agyrotropy measure should have. We show that $A\varnothing_e$, $D_{ng}$ and $Q$ are all defined based on the sum of the principle minors (i.e. the rotation invariant $I_2$) of the pressure tensor. We discuss in detail the problems of $I_2$-based measures and explain why they may produce ambiguous and biased results. We introduce a new measure $AG$ constructed based on the determinant of the pressure tensor (i.e. the rotation invariant $I_3$) which does not suffer from the problems of $I_2$-based measures. We compare $AG$ with other measures in 2 and 3-dimension particle-in-cell magnetic reconnection simulations, and show that $AG$ can effectively trace the EDR of reconnection in both Harris and force-free current sheets. On the other hand, $A\varnothing_e$ does not show prominent peaks in the EDR and part of the separatrix in the force-free reconnection simulations, demonstrating that $A\varnothing_e$ does not measure all the non-gyrotropic effects in this case, and is not suitable for studying magnetic reconnection in more general situations other than Harris sheet reconnection.Comment: accepted by Phys. of Plasm

Control of cellular automata

We study the problem of master-slave synchronization and control of totalistic cellular automata (CA) by putting a fraction of sites of the slave equal to those of the master and finding the distance between both as a function of this fraction. We present three control strategies that exploit local information about the CA, mainly, the number of nonzero Boolean derivatives. When no local information is used, we speak of synchronization. We find the critical properties of control and discuss the best control strategy compared with synchronization

On the Angular Dependence of the Radiative Gluon Spectrum

The induced momentum spectrum of soft gluons radiated from a high energy quark produced in and propagating through a QCD medium is reexamined in the BDMPS formalism. A mistake in our published work (Physical Review C60 (1999) 064902) is corrected. The correct dependence of the fractional induced loss $R(\theta_{{\rm cone}})$ as a universal function of the variable $\theta^2_{{\rm cone}} L^3 \hat q$ where $L$ is the size of the medium and $\hat q$ the transport coefficient is presented. We add the proof that the radiated gluon momentum spectrum derived in our formalism is equivalent with the one derived in the Zakharov-Wiedemann approach.Comment: LaTex, 5 pages, 1 figur

Casimir Forces between Compact Objects: I. The Scalar Case

We have developed an exact, general method to compute Casimir interactions between a finite number of compact objects of arbitrary shape and separation. Here, we present details of the method for a scalar field to illustrate our approach in its most simple form; the generalization to electromagnetic fields is outlined in Ref. [1]. The interaction between the objects is attributed to quantum fluctuations of source distributions on their surfaces, which we decompose in terms of multipoles. A functional integral over the effective action of multipoles gives the resulting interaction. Each object's shape and boundary conditions enter the effective action only through its scattering matrix. Their relative positions enter through universal translation matrices that depend only on field type and spatial dimension. The distinction of our method from the pairwise summation of two-body potentials is elucidated in terms of the scattering processes between three objects. To illustrate the power of the technique, we consider Robin boundary conditions $\phi -\lambda \partial_n \phi=0$, which interpolate between Dirichlet and Neumann cases as $\lambda$ is varied. We obtain the interaction between two such spheres analytically in a large separation expansion, and numerically for all separations. The cases of unequal radii and unequal $\lambda$ are studied. We find sign changes in the force as a function of separation in certain ranges of $\lambda$ and see deviations from the proximity force approximation even at short separations, most notably for Neumann boundary conditions.Comment: 27 pages, 9 figure

Perturbative and non-perturbative studies with the delta function potential

We show that the delta function potential can be exploited along with perturbation theory to yield the result of certain infinite series. The idea is that any exactly soluble potential if coupled with a delta function potential remains exactly soluble. We use the strength of the delta function as an expansion parameter and express the second-order energy shift as an infinite sum in perturbation theory. The analytical solution is used to determine the second-order energy shift and hence the sum of an infinite series. By an appropriate choice of the unperturbed system, we can show the importance of the continuum in the energy shift of bound states.Comment: 19 pages, 2 table

Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets

Starting from a microscopic tight-binding model and using second order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet. The Rashba interaction parameter is first order in the atomic carbon spin-orbit coupling strength $\xi$ and first order in the external electric field $E$ perpendicular to the graphene plane, whereas the intrinsic spin-orbit interaction which survives at E=0 is second order in $\xi$. The spin-orbit terms in the low-energy effective Hamiltonian have the form proposed recently by Kane and Mele. \textit{Ab initio} electronic structure calculations were performed as a partial check on the validity of the tight-binding model.Comment: 5 pages, 2 figures; typos corrected, references update

Neural Network Model for Apparent Deterministic Chaos in Spontaneously Bursting Hippocampal Slices

A neural network model that exhibits stochastic population bursting is studied by simulation. First return maps of inter-burst intervals exhibit recurrent unstable periodic orbit (UPO)-like trajectories similar to those found in experiments on hippocampal slices. Applications of various control methods and surrogate analysis for UPO-detection also yield results similar to those of experiments. Our results question the interpretation of the experimental data as evidence for deterministic chaos and suggest caution in the use of UPO-based methods for detecting determinism in time-series data.Comment: 4 pages, 5 .eps figures (included), requires psfrag.sty (included

Local entanglement generation in the adiabatic regime

We study entanglement generation in a pair of qubits interacting with an initially correlated system. Using time independent perturbation theory and the adiabatic theorem, we show conditions under which the qubits become entangled as the joint system evolves into the ground state of the interacting theory. We then apply these results to the case of qubits interacting with a scalar quantum field. We study three different variations of this setup; a quantum field subject to Dirichlet boundary conditions, a quantum field interacting with a classical potential and a quantum field that starts in a thermal state.Comment: 9 pages, 6 figures. v2: reference [14] adde

The general-covariant and gauge-invariant theory of quantum particles in classical backgrounds

A new approach to the concept of particles and their production in quantum field theory is developed. A local operator describing the current of particle density is constructed for scalar and spinor fields in arbitrary gravitational and electromagnetic backgrounds. This enables one to describe particles in a local, general-covariant and gauge-invariant way. However, the current depends on the choice of a 2-point function. There is a choice that leads to the local non-conservation of the current in a gravitational or an electromagnetic background, which describes local particle production consistent with the usual global description based on the Bogoliubov transformation. The most natural choice based on the Green function calculated using the Schwinger-DeWitt method leads to the local conservation of the current, provided that interactions with quantum fields are absent. Interactions with quantum fields lead to the local non-conservation of the current which describes local particle production consistent with the usual global description based on the interaction picture.Comment: 34 pages, revised, to appear in Int. J. Mod. Phys.

Noise resistance of adiabatic quantum computation using random matrix theory

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure