Combinatorial Optimization by Iterative Partial Transcription

A procedure is presented which considerably improves the performance of local search based heuristic algorithms for combinatorial optimization problems. It increases the average `gain' of the individual local searches by merging pairs of solutions: certain parts of either solution are transcribed by the related parts of the respective other solution, corresponding to flipping clusters of a spin glass. This iterative partial transcription acts as a local search in the subspace spanned by the differing components of both solutions. Embedding it in the simple multi-start-local-search algorithm and in the thermal-cycling method, we demonstrate its effectiveness for several instances of the traveling salesman problem. The obtained results indicate that, for this task, such approaches are far superior to simulated annealing.Comment: RevTex-file: 18 pages, 3 Postscript figures. Accepted for publication in Phys. Rev.

Comments on ``A note on first-order formalism and odd-derivative actions'' by S. Deser

We argue that the obstacles to having a first-order formalism for odd-derivative actions presented in a pedagogical note by Deser are based on examples which are not first-order forms of the original actions. The general derivation of an equivalent first-order form of the original second-order action is illustrated using the example of topologically massive electrodynamics (TME). The correct first-order formulations of the TME model keep intact the gauge invariance presented in its second-order form demonstrating that the gauge invariance is not lost in the Ostrogradsky process.Comment: 6 pages, references are adde

General relativistic corrections to the Sagnac effect

The difference in travel time of corotating and counter-rotating light waves in the field of a central massive and spinning body is studied. The corrections to the special relativistic formula are worked out in a Kerr field. Estimation of numeric values for the Earth and satellites in orbit around it show that a direct measurement is in the order of concrete possibilities.Comment: REVTex, accepted for publication on Phys. Rev.

Quantum Phase and Quantum Phase Operators: Some Physics and Some History

After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions of the field: Are there (unique) quantum phase operators and are there quantum systems which can determine their nature? I conclude with a critique of recent proposals which have shed new light on the problem.Comment: 19 pages, 2 Figs. taken from published articles, LaTeX, to be published in Physica Scripta, Los Alamos preprint LA-UR-92-352

On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page