An extension of the Kac ring model

We introduce a unitary dynamics for quantum spins which is an extension of a model introduced by Mark Kac to clarify the phenomenon of relaxation to equilibrium. When the number of spins gets very large, the magnetization satisfies an autonomous equation as function of time with exponentially fast relaxation to the equilibrium magnetization as determined by the microcanonical ensemble. This is proven as a law of large numbers with respect to a class of initial data. The corresponding Gibbs-von Neumann entropy is also computed and its monotonicity in time discussed.Comment: 15 pages, v2 -> v3: minor typographic correctio

Statistical uncertainty in quantum optical photodetection measurements

We present a complete statistical analysis of quantum optical measurement schemes based on photodetection. Statistical distributions of quantum observables determined from a finite number of experimental runs are characterized with the help of the generating function, which we derive using the exact statistical description of raw experimental outcomes. We use the developed formalism to point out that the statistical uncertainty results in substantial limitations of the determined information on the quantum state: though a family of observables characterizing the quantum state can be safely evaluated from experimental data, its further use to obtain the expectation value of some operators generates exploding statistical errors. These issues are discussed using the example of phase-insensitive measurements of a single light mode. We study reconstruction of the photon number distribution from photon counting and random phase homodyne detection. We show that utilization of the reconstructed distribution to evaluate a simple well-behaved observable, namely the parity operator, encounters difficulties due to accumulation of statistical errors. As the parity operator yields the Wigner function at the phase space origin, this example also demonstrates that transformation between various experimentally determined representations of the quantum state is a quite delicate matter.Comment: 18 pages REVTeX, 7 figures included using epsf. Few minor corrections made, clarified conclusion

Engineering Quantum States, Nonlinear Measurements, and Anomalous Diffusion by Imaging

We show that well-separated quantum superposition states, measurements of strongly nonlinear observables, and quantum dynamics driven by anomalous diffusion can all be achieved for single atoms or molecules by imaging spontaneous photons that they emit via resonance florescence. To generate anomalous diffusion we introduce continuous measurements driven by L\'evy processes, and prove a number of results regarding their properties. In particular we present strong evidence that the only stable L\'evy density that can realize a strictly continuous measurement is the Gaussian.Comment: revtex4-1, 17 pages, 7 eps figure

Magnetic structures of RbCuCl_3 in a transverse field

A recent high-field magnetization experiment found a phase transition of unknown character in the layered, frustrated antiferromagnet RbCuCl_3, in a transverse field (in the layers). Motivated by these results, we have examined the magnetic structures predicted by a model of RbCuCl_3, using the classical approximation. At small fields, we obtain the structure already known to be optimal, an incommensurate (IC) spiral with wave vector q in the layers. At higher fields, we find a staircase of long-period commensurate (C) phases (separated initially by the low-field IC phase), then two narrow IC phases, then a fourth IC phase (also with intermediate C phases), and finally the ferromagnetically aligned phase at the saturation field H_S. The three-sublattice C states familiar from the theory of the triangular antiferromagnet are never optimal. The C phases and the two intermediate IC phases were previously unknown in this context. The magnetization is discontinuous at a field \approx 0.4H_S, in qualitative agreement with experiment, though we find much fine structure not reported.Comment: 9 pages, 8 figure

Inclusion Polymerization and Doping in Zeolite Channels. Polyaniline

Aniline has been polymerized in the three-dimensional channel system of zeolite Y. The monomer was diffused into zeolites with different levels of acidity from hexane solution. Subsequent admission of peroxydisulfate or iodate from aqueous solution yielded the intrazeolite polymers, as demonstrated by FT-IR, electronic absorption data and recovery of the included polymer. With S2O82-, the intrazeolite products are a function of the proton content of the zeolite. Polymer is only formed when a sufficient supply of protons is present in the zeolite host. When neutral iodate solution is used, no polymer is formed in NaY and acid zeolites, but at low pH aniline polymerizes in all zeolites. The open pore system of the zeolite host can be accessed by base such that the intrazeolite protonated polymer is transformed into the corresponding neutral polymer. The polymer chains encapsulated in zeolite hosts represent a new class of low- dimensional electronic materials

The Spoor Law: An Anachronism or Constitutional Misfit?

The spoor law is a rule of African customary law that determines liability for stock theft. It provides that, if the tracks of lost or stolen livestock can be traced to a homestead or its immediate surrounds, the head of that establishment will be held liable. If the direction of the spoor do not point to a specific homestead, all those in the vicinity become jointly liable. As a convenient deterrent to the theft of livestock, the spoor law was incorporated into the laws of the Cape Province, Natal and the Transkeian Territories at the end of the nineteenth century, making it the only rule of customary law to be applicable without regard to race prior to the new Constitution. This article questions whether the spoor law still is, and should be, part of South African law. It has never been formally repealed, and still survives in the 1983 Transkei Penal Code. Although the law has not been mentioned in a reported case for many years, it might play a valuable role in crime control, since stock theft remains a serious and pervasive crime in South Africa. The article argues, however, that it will probably not survive constitutional review, because it has the effect of imposing a reverse onus of proof