Classical optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result allows one to write a factor of N2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion. It is shown how to write arbitrary 2D patterns by using this method.

Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera state.

We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and chemistry problems) for which all known classical algorithms require exponential time. Applications of the algorithm to specific problems are considered, and we find that classically intractable and interesting problems from atomic physics may be solved with between 50 and 100 quantum bits.

We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case. In order to accommodate fermions using a first quantized Hamiltonian, an efficient quantum algorithm for anti-symmetrization is given. Finally, a simulation of the Hubbard model is discussed in detail.Comment: Submitted 11/7/96 to Phys. Rev. Lett. 10 pages, 0 figure

A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist. This state of broken symmetry, which usually coexists with a stable spatially symmetric state, has intrigued the nonlinear dynamics community since its discovery in the early 2000s. Recent experiments have led to increasing interest in the origin and dynamics of these states. Here we review the history of research on chimera states and highlight major advances in understanding their behaviour.

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Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized sub-populations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf and homoclinic bifurcations of chimeras. [2]. When brain waves are recorded, the awake side of the brain shows desynchronized electrical activity, corresponding to millions of neurons oscillating out of phase, whereas the sleeping side is highly synchronized.From a physicist's perspective, unihemispheric sleep suggests the following (admittedly, extremely idealized) problem: What's the simplest system of two oscillator populations, loosely analogous to the two hemispheres, such that one synchronizes while the other does not?Our work in this direction was motivated by a series of recent findings in nonlinear dynamics [3,4,5,6,7,8]. In 2002, Kuramoto and Battogtokh reported that arrays of nonlocally coupled oscillators could spontaneously split into synchronized and desynchronized subpopulations [3]. The existence of such "chimera states" came as a surprise, given that the oscillators were identical and symmetrically coupled. On a one-dimensional ring [3,4] the chimera took the form of synchronized domain next to a desynchronized one. In two dimensions, it appeared as a strange new kind of spiral wave [5], with phase-locked oscillators in its arms coexisting with phaserandomized oscillators in its core-a circumstance made possible only by the nonlocality of the coupling. These phenomena were unprecedented in studies of pattern formation [9] and synchronization [10] in physics, chemistry, and biology, and remain poorly understood.Previous mathematical studies of chimera states have assumed that they are statistically stationary [3,4,5,6,7]. What has been lacking is an analysis of their dynamics, stability, and bifurcations.In this Letter we obtain the first such results by considering the simplest model that supports chimera states: a pair of oscillator populations in which each oscillator is coupled equally to all the others in its group, and less strongly to those in the other group. For this model we solve for the stationary chimeras and delineate where they exist in parameter space. An unexpected finding is that chimeras need not be stationary. They can breathe. Then the phase coherence in the desynchronized population waxes and wanes, while the phase difference between the two populations begins to wobble.The governing equations for the model arewhere σ = 1, 2 and N σ is the number of oscillators in population σ. The oscillators are assumed identical, so the frequency ω and phase lag α are the same for all of them. The strength of the coupling from oscillators in σ ′ onto those in σ...

Soon after the crowd streamed on to London's Millennium Bridge on the day it opened, the bridge started to sway from side to side: many pedestrians fell spontaneously into step with the bridge's vibrations, inadvertently amplifying them. Here we model this unexpected and now notorious phenomenon--which was not due to the bridge's innovative design as was first thought--by adapting ideas originally developed to describe the collective synchronization of biological oscillators such as neurons and fireflies. Our approach should help engineers to estimate the damping needed to stabilize other exceptionally crowded footbridges against synchronous lateral excitation by pedestrians.