The Heat Kernel Expansion for the Electromagnetic Field in a Cavity

We derive the first six coefficients of the heat kernel expansion for the electromagnetic field in a cavity by relating it to the expansion for the Laplace operator acting on forms. As an application we verify that the electromagnetic Casimir energy is finite. Communicated by Vincent Rivasseau submitted 17/02/03, accepted: 04/07/03     

Improving the modulation efficiency of high-power distributed Bragg reflector tapered diode lasers

Different measures to improve the modulation efficiency of a distributed Bragg reflector tapered diode laser emitting at 1060 nm were investigated. Due to the 6-mm long cavity, the device reached an output power of 10 W with a nearly diffraction-limited beam quality. The input currents to the ridge-waveguide (RW) and tapered gain-region sections can be independently controlled. This allows a low-current modulation of the optical output power in the Watt range. Under optimized quasi-static conditions the power could be modulated between 0.2 and 3.1 W (4.8 W) by a variation of the RW current between 0 and 50 mA (350 mA). Due to the integrated 6th order surface Bragg grating the emission wavelength remains within the spectral range of 80 pm.     

Synchronization in asymmetrically coupled networks with node balance

We study global stability of synchronization in asymmetrically connected networks of limit-cycle or chaotic oscillators. We extend the connection graph stability method to directed graphs with node balance, the property that all nodes in the network have equal input and output weight sums. We obtain the same upper bound for synchronization in asymmetrically connected networks as in the network with a symmetrized matrix, provided that the condition of node balance is satisfied. In terms of graphs, the symmetrization operation amounts to replacing each directed edge by an undirected edge of half the coupling strength. It should be stressed that without node balance this property in general does not hold.     

Persistent clusters in lattices of coupled nonidentical chaotic systems

Two-dimensional (2D) lattices of diffusively coupled chaotic oscillators are studied. In previous work, it was shown that various cluster synchronization regimes exist when the oscillators are identical. Here, analytical and numerical studies allow us to conclude that these cluster synchronization regimes persist when the chaotic oscillators have slightly different parameters. In the analytical approach, the stability of almost-perfect synchronization regimes is proved via the Lyapunov function method for a wide class of systems, and the synchronization error is estimated. Examples include a 2D lattice of nonidentical Lorenz systems with scalar diffusive coupling. In the numerical study, it is shown that in lattices of Lorenz and Rossler systems the cluster synchronization regimes are stable and robust against up to 10%-15% parameter mismatch and against small noise.     

Stereo vision in spatial-light-modulator-based microscopy

We propose a technique for realizing stereoscopic microscopy. We employ a spatial-light-modulator-based microscope to record two images under different angles in one shot. We additionally investigate the possibilities of dynamic aberration correction. It is found that aberration correction is unavoidable because of the employed commercial liquid crystal on a silicon modulator. Also, imaging of phase objects and highly reflective specimens is experimentally investigated. For some of the specimens, an inversion of the recorded intensity is observed, which leads to problems when viewing the stereo pairs. We explain the origin of this effect and show that a reasonable visualization of microscopic three-dimensional objects can be achieved by simple image inversion.     

Multistability of twisted states in non-locally coupled Kuramoto-type models

A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sign which has a profound influence on its behavior. Without the limitation of the generality, the frequency of the free-running oscillators can be set to zero. The resulting system is of gradient type, and therefore, all its solutions converge to an equilibrium point. All so-called q-twisted states, where the phase difference between neighboring oscillators on the ring is 2πq/N, are equilibrium points, where q is an integer. Their stability in the limit N → ∞ is discussed along the line of Wiley et al. [Chaos 16, 015103 (2006)] In addition, we prove that when a twisted state is asymptotically stable for the infinite system, it is also asymptotically stable for sufficiently large N. Note that for smaller N, the same q-twisted states may become unstable and other q-twisted states may become stable. Finally, the existence of additional equilibrium states, called here multi-twisted states, is shown by numerical simulation. The phase difference between neighboring oscillators is approximately 2πq/N in one sector of the ring, -2πq/N in another sector, and it has intermediate values between the two sectors. Our numerical investigation suggests that the number of different stable multi-twisted states grows exponentially as N → ∞. It is possible to interpret the equilibrium points of the coupled phase oscillator network as trajectories of a discrete-time translational dynamical system where the space-variable (position on the ring) plays the role of time. The q-twisted states are then fixed points, and the multi-twisted states are periodic solutions of period N that are close to a heteroclinic cycle. Due to the apparently exponentially fast growing number of such stable periodic solutions, the system shows spatial chaos as N → ∞.     

Smoothness and analyticity of perturbation expansions in qed

We consider the ground state of an atom in the framework of non-relativistic qed. We assume that the ultraviolet cutoff is of the order of the Rydberg energy and that the atomic Hamiltonian has a non-degenerate ground state. We show that the ground state energy and the ground state are k-times continuously differentiable functions of the fine structure constant and respectively the square root of the fine structure constant on some nonempty interval [0,ck).     

Existence of the D0−D4 Bound State: a Detailed Proof

We consider the supersymmetric quantum mechanical system which is obtained by dimensionally reducing d = 6, N = 1 supersymmetric gauge theory with gauge group U(1) and a single charged hypermultiplet. Using the deformation method and ideas introduced by Porrati and Rozenberg [1], we present a detailed proof of the existence of a normalizable ground state for this system.submitted 12/08/04, accepted 22/08/04