Power-Law Relaxation and Cumulative Information

We associate the cumulative information of a system relaxing towards equilibrium with a divergent integral when a power-law relaxation holds. We discuss and illustrate numerically how this implies that a system that relaxes to equilibrium through a power-law has a cumulative information content that progressively diverges from that of its equilibrium realization to which it is relaxing. Our findings shed light on some aspects of weak ergodicity breaking and suggest that power-laws imply a form of complexity that does not require dissipation or built-in disorder.     

Giant magnetic anisotropy in tetragonal FeCo alloys

In order to further increase the recording density in hard disk drives, new media materials are required. Two essential parameters of future recording media are a large uniaxial magnetic anisotropy energy (MAE) K(u) and a large saturation magnetization M(s). Based on first-principles theory, we predict that very specific structural distortions of FeCo alloys possess these desired properties. The discovered alloy has a saturation magnetization that is about 50% larger than that of FePt--a compound that has received considerable attention lately-with a uniaxial MAE that can easily be tailored reaching a maximum value that is 50% larger than that of FePt.     

On the standard form of the Bloch equation

The requirement is often made in non-equilibrium statistical mechanics that a transport equation should be derived as that which governs the subdynamics relative to a (small) part of a (large) conservative dynamical system close to equilibrium. We show that such a requirement on the Markovian relaxation of a 1/2-spin imposes that this process be described by a Bloch equation of a very specific form, which we call standard. We show that this reduced dynamics is quasi-free if, and only if, the relaxation time is maximally anisotropic.Research supported in part by NSF grant MCS 76-07286     

Simultaneity on the Rotating Disk

The disk that rotates in an inertial frame in special relativity has long been analysed by assuming a Lorentz contraction of its peripheral elements in that frame, which has produced widely varying views in the literature. We show that this assumption is unnecessary for a disk that corresponds to the simplest form of rotation in special relativity. After constructing such a disk and showing that observers at rest on it do not constitute a true rotating frame, we choose a “master” observer and calculate a set of disk coordinates and spacetime metric pertinent to that observer. We use this formalism to resolve the “circular twin paradox”, then calculate the speed of light sent around the periphery as measured by the master observer, to show that this speed is a function of sent-direction and disk angle traversed. This result is consistent with the Sagnac Effect, but constitutes a finer analysis of that effect, which is normally expressed using an average speed for a full trip of the periphery. We also use the formalism to give a resolution of “Selleri’s paradox”.     

Black holes in the Brans-Dicke

It is shown that a stationary space containing a black hole is a solution of the Brans-Dicke field equations if and only if it is a solution of the Einstein field equations. This implies that when the star collapses to form a black hole, it loses that fraction (about 7%) of its measured gravitational mass that arises from the scalar interaction. This mass loss is in addition to that caused by emission of scalar or tensor gravitational radiation. Another consequence is that there will not be any scalar gravitational radiation emitted when two black holes collide.     

On the Foundations of Superstring Theory

Superstring theory is an extension of conventional quantum field theory that allows for stringlike and branelike material objects besides pointlike particles. The basic foundations on which the theory is built are amazingly shaky, and, equally amazingly, it seems to be this lack of solid foundations to which the theory owes its strength. We emphasize that such a situation is legitimate only in the development phases of a new doctrine. Eventually, a more solidly founded structure must be sought. Although it is advertised as a “candidate theory of quantum gravity”, we claim that string theory may not be exactly that. Rather, just like quantum field theory itself, it is a general mathematical framework for a class of theories. Its major flaw could be that it still embraces a Copenhagen view on the relation between quantum mechanics and reality, while any “theory of everything”, that is, a theory for the entire cosmos, should do better than that.     

Quantum structure emerging from the transformation design of the Dirac equation

It is shown that a quantum structure can be created by a set of chosen constraint conditions that emerge from the transformation design of the Dirac equation in general relativity. As an explanation, the constraints that cause novel bound states with the quantization rule of a 2D Coulomb system are presented. The discussion in this paper provides a systematic way to look for constraints that generate a required quantization rule.     

Optimization of robustness and connectivity in complex networks

Scale-free networks rely on a relatively small number of highly connected nodes to achieve a high degree of interconnectivity and robustness to random failure, but suffer from a high sensitivity to directed attack. In this paper we describe a parameterized family of networks and analyze their connectivity and sensitivity, identifying a network that has an interconnectedness closer to that of a scale-free network, a robustness to attack closer to that of an exponential network, and a resistance to failure better than that of either of those networks.     

Oscillating cracks in glassy films on silicon substrates

Cracks that propagate with near-perfect sinusoidal form are reported in amorphous silicon-rich silica films deposited onto (001) silicon substrates by plasma-enhanced chemical vapour deposition and subjected to thermal annealing. The cracks are shown to result from high tensile stresses that develop in the film during thermal annealing at temperatures in the range up to 700°C, a process shown to be correlated with the loss of hydrogen from the films. Two distinct modes of crack propagation are reported: straight cracks that propagate along directions parallel to [100] cube-edge directions in the substrate, and oscillating cracks that propagate with sinusoidal form parallel to [110] diagonal directions. Sections through the cracks show that the oscillating cracks have a complex three-dimensional structure that extends through the glassy film and into the underlying silicon substrate. This involves a correlated oscillation between the crystallographic orientation of the crack in the surface plane and that of the crack extension into the substrate. Whereas a complete theoretical treatment of this behaviour would be extremely complicated, a simple theory is developed to demonstrate that an oscillating crack has a minimum energy per unit length for a particular wavelength and amplitude that depends upon the physical parameters of both film and substrate. The energy at this minimum is shown to be lower than that of a straight crack for certain parameter ranges so that the oscillating geometry is preferred.     

Efficient collinear fourth-harmonic generation by two-channel multistep cascading in a single two-dimensional nonlinear photonic crystal

We investigate efficient fourth-harmonic generation in a single two-dimensional (2D) quadratically nonlinear photonic crystal. We propose a novel parametric process that starts with phase-matched generation of a pair of symmetric second-harmonic waves, which then interact to produce a fourth-harmonic wave that is collinear to the fundamental. We show that this process is more efficient than conventional fourth-harmonic-generation schemes by a factor that reaches 4 at low intensities and discuss how to design and optimize the nonlinear 2D photonic crystals that are implemented in LiNbO(3) and LiTaO(3) .     

EPR studies of a two-nitrogen-atom centre in natural,plastically-deformed diamond

The hyperfine structure of an EPR system in a natural, brown diamond implies that the system is due to a centre containing two nitrogen atoms on almost equivalent sites. X-ray topographic evidence shows that the sample has been plastically deformed and it is suggested that a possible model for the defect is that of an ionized, substitutional N pair with a dislocation nearby.     

Single and paired point defects in a 2D Wigner crystal

Using the path-integral Monte Carlo method, we calculate the energy to form single and pair vacancies and interstitials in a two-dimensional Wigner crystal of electrons. We confirm that the lowest energy point defects of a 2D electron Wigner crystal are interstitials, with a creation energy roughly 2/3 that of a vacancy. The formation energy of the defects goes to zero at melting, suggesting that point defects may be the melting mechanism and that the melting could be a continuous transition. In addition, we find that the interaction between defects is strongly attractive, so that most defects will exist as bound pairs.     

Enhanced cooling of a V-type three-level atom in an optical cavity

We have studied theoretically and numerically the enhanced cooling of a V-type three-level atom in a high-finesse optical cavity and shown that the cooling rate can be increased by one order of magnitude over that of a two-level atom, and the momentum amplitude tends to a stationary state much smaller than that of a two-level atom. We have further shown that the cooling rate can be significantly improved by using feedback and a time-dependent pump.     

A Domain of Spacetime Intervals in General Relativity

We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emerges from something discrete.     

Semi-Classical Quantum Fields Theories and Frobenius Manifolds

We show that a semi-classical quantum field theory comes with a versal family with the property that the corresponding partition function generates all path integrals., satisfies a system of second order differential equations determined by algebras of classical observables. This versal family gives rise to a notion of special coordinates that is analogous to that in string theories. We also show that for a large class of semi-classical theories, their moduli space has the structure of a Frobenius super-manifold. This work was supported by KOSEF Interdisciplinary Research Grant No. R01-2006-000-10638-0.     

Rapid measurement of quantum systems using feedback control

We introduce a feedback control algorithm that increases the speed at which a measurement extracts information about a d-dimensional system by a factor that scales as d(2). Generalizing this algorithm, we apply it to a register of n qubits and show an improvement of O(n). We derive analytical bounds on the benefit provided by the feedback and perform simulations that confirm that this speedup is achieved.     

A No-Go Theorem for Compatibility Between Involutions of First Order Differentials on a Lattice and Continuum Limit

We prove that the following three properties cannot match each other on a lattice, that differentials of coordinate functions are algebraically dependent on their involutive conjugates, that the involution on a lattice is an antihomomorphism, and that differential calculus has a natural continuum limit.     

Zero-temperature phases of many-atom Bose systems

We show that a many-atom Bose system at zero temperature has, in general, a liquid phase in addition to its well-known gaseous phase. A universal phase diagram is presented that is applicable to all Bose systems with a -C6/r6 type of interaction at large interparticle separations. We show that the predicted phase structure has implications on the stability of a gaseous Bose-Einstein condensate (BEC) even at dilute densities that are routinely achieved under existing experimental conditions. We also predict that should have a gaseous BEC phase below a critical density of 5.58 x 10(15) 1/cm3.     

Tangency properties of a pentagonal tiling generated by a piecewise isometry

Piecewise isometries (PWIs) are known to have dynamical properties that generate interesting geometric planar packings. We analyze a particular PWI introduced by Goetz that generates a packing by periodically coded cells, each of which is a pentagon. Our main result is that the tangency graph associated with this packing is a forest (i.e., has no nontrivial cycles). We show, however, that this is not a general property of PWIs by giving an example that has an infinite number of cycles in the tangency graph of its periodically coded cells.     

Determination of the possibility of controlling the optical properties of dielectric photonic-crystal fibers with semiconductor inclusions

We have shown that the characteristics of propagation of optical radiation in a photonic-crystal fiber that contains semiconductor elements can be controlled by external radiation that acts on the structure. We have studied a photonic-crystal fiber that is formed by air holes in a dielectric that contains a semiconductor (GaAs) tube in the central region (core region) filled inside with the same dielectric. We have shown that the power of the radiation that is necessary to control the transmission characteristics at a wavelength λ = 1550 nm is determined by the construction of the device and can be fairly small (10⁹ W/m²).