The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

Supersymmetric large extra dimensions and the cosmological constant: an update

This article critically reviews the proposal for addressing the cosmological constant problem within the framework of supersymmetric large extra dimensions (SLED), as recently proposed in hep-th/0304256. After a brief restatement of the cosmological constant problem, a short summary of the proposed mechanism is given. The emphasis is on the perspective of the low-energy effective theory in order to see how it addresses the problem of why low-energy particles like the electron do not contribute too large a vacuum energy. This is followed by a discussion of the main objections, which are grouped into the following five topics: (1) Weinberg’s No-Go Theorem. (2) Are hidden tunings of the theory required, and are these stable under renormalization? (3) Why should the mechanism apply only now and not rule out possible earlier epochs of inflationary dynamics? (4) How big are quantum effects, and which are the most dangerous? and (5) Even if successful, can the mechanism be consistent with cosmological or current observational constraints? It is argued that there are plausible reasons why the mechanism can thread the potential objections, but that a definitive proof that it does depends on addressing well-defined technical points. These points include identifying what fixes the size of the extra dimensions, checking how topological obstructions renormalize and performing specific calculations of quantum corrections. More detailed studies of these issues, which are well within reach of our present understanding of extra-dimensional theories, are currently underway. As such, the jury remains out concerning the proposal, although the prospects for acquittal still seem good. (An abridged version of this article appears in the proceedings of SUSY 2003.)     

Branes,Quantum Nambu Brackets and the Hydrogen Atom

The Nambu-bracket quantization of the hydrogen atom is worked out as an illustration of the general method. The dynamics of topological open branes is controlled classically by Nambu brackets. Such branes then may be quantized through the consistent quantization of the underlying Nambu brackets: properly defined, the quantum Nambu-brackets comprise an associative structure, although the naive derivation property is mooted through operator entwinement. For superintegrable systems, such as the hydrogen atom, the results coincide with those furnished by Hamiltonian quantization - but the method is not limited to Hamiltonian systems.     

Quadratic Integrals of Motion for the Systems of Identical Particles

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in Hamilton-Jacobi equation is clarified.     

直径不超过4的树的割宽

§ 1　IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th…     

Doppler cooling a single Ca+ ion with a violet extended-cavity diode laser

We present a scheme for employing a violet extended-cavity diode laser in experiments with single, trapped ions. For this the grating-stabilised laser is spatially and spectrally filtered and referenced to a Fabry–Pérot cavity. We measure an upper limit to the line width by observing a 305-kHz FWHM beat note with the second harmonic of a titanium sapphire laser. The laser is subsequently used to optically cool a single ⁴⁰Ca⁺ ion close to the Doppler limit. PACS 03.67.Lx; 32.80.Pj; 42.55.Px     

Wave function mapping of self-assembled quantum dots by capacitance spectroscopy

We use frequency-dependent capacitance–voltage spectroscopy to study the dynamic charging of self-assembled InAs quantum dots. With increasing frequency, the AC charging becomes suppressed, beginning with the low-energy states. By applying an in-plane magnetic field, we generate an additional magnetic confinement that alters the tunneling barrier and hence the charging dynamics. In traveling through the potential barrier, the electrons acquire an additional momentum k₀, proportional to the magnetic field B. As the tunneling is enhanced, when k₀ matches the maximum of the electronic wave function Ψ (in momentum representation), we are able to map out the shape of Ψ by varying B.