PT-symmetric deformations of integrable models

We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero-Moser-Sutherland type and non-linear integrable field equations of Korteweg-de-Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero-Moser-Sutherland models we provide three alternative deformations: A complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real valued field equations of non linear integrable systems and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of KdV-type are studied with regard to different kinds of PT-symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.Comment: 21 pages, 3 figure

Fredholm's Minors of Arbitrary Order: Their Representations as a Determinant of Resolvents and in Terms of Free Fermions and an Explicit Formula for Their Functional Derivative

We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the $n$th and $n-1$th minors, whose solution is a representation of the $n$th minor as an $n\times n$ determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit formula for the functional derivative of a Fredholm minor of order $n$ with respect to the kernel. Our formula is a linear combination of the $n$th and the $n\pm 1$th minors.Comment: 17 pages, Latex, no figures connection to supplementary compound matrices mentioned, references added, typos correcte

Correlated tunneling into a superconductor in a multiprobe hybrid structure

We consider tunneling in a hybrid system consisting of a superconductor with two or more probe electrodes which can be either normal metals or polarized ferromagnets. In particular we study transport at subgap voltages and temperatures. Besides Andreev pair tunneling at each contact, in multi-probe structures subgap transport involves additional channels, which are due to coherent propagation of two particles (electrons or holes), each originating from a different probe electrode. The relevant processes are electron cotunneling through the superconductor and conversion of two electrons stemming from different probes in a Cooper pair. These processes are non-local and decay when the distance between the pair of involved contacts is larger than the superconducting coherence length. The conductance matrix of a the three terminal hybrid structure is calculated. The multi-probe processes enhance the conductance of each contact. If the contacts are magnetically polarized the contribution of the various conduction channels may be separately detected.Comment: 7 pages, 1 figure, accepted in Europhysics Letters, minor changes, 3 references adde

Long Range Forces from Pseudoscalar Exchange

Using dispersion theoretic techniques, we consider coherent long range forces arising from double pseudoscalar exchange among fermions. We find that Yukawa type coupling leads to $1/r^3$ spin independent attractive potentials whereas derivative coupling renders $1/r^5$ spin independent repulsive potentials.Comment: 27 pages, REVTeX, 3 figures included using epsfi

Long Range Forces from Two Neutrino Exchange Revisited

The exchange of two massless neutrinos gives rise to a long range force which couples to weakly charged matter. As has been noted previously in the literature, the potential for this force is \VN \propto G_{F}^2 / r^5 with monopole-monople, spin-spin and more complicated interactions. Unfortunately, this is far too small to be observed in present day experiments. We calculate \VN explicitly in the electroweak theory, and show that under very general assumptions forces arising from the exchange of two massless fermions can at best yield $1 / r^5$ potentials.Comment: 5 pages + 1 figure (not included), UFIFT-HEP-92-28/HUTP-92-A04

Effects of Bose-Einstein Condensation on forces among bodies sitting in a boson heat bath

We explore the consequences of Bose-Einstein condensation on two-scalar-exchange mediated forces among bodies that sit in a boson gas. We find that below the condensation temperature the range of the forces becomes infinite while it is finite at temperatures above condensation.Comment: 10 pages, 2 figure

Effective Non-Hermitian Hamiltonians for Studying Resonance Statistics in Open Disordered Systems

We briefly discuss construction of energy-dependent effective non-hermitian hamiltonians for studying resonances in open disordered systemsComment: Latex, 20 pages, 1 fig. Expanded version of a talk at the Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics IX, June 21-24 2010, Zhejiang University, Hangzhou, China. Accepted for publication in the Internationa Journal of Theoretical Physics (Springer Verlag

Suspicionless Canine Sniffs: Does the Fourth Amendment Prohibit Public Schools from Using Dogs to Search Students without Individualized Suspicion?

Drugs plague our nation’s schools. Since traditional methods of fighting the problem are proving ineffective, some schools are trying new approaches. One such approach is using specially trained dogs to indiscriminately sniff students for the presence of illegal drugs. Using dogs to sniff students is controversial and has sparked a constitutional debate. The Supreme Court has not expressly ruled on whether suspicionless canine sniffs violate a public school student’s Fourth Amendment protection against unreasonable searches. In fact, the Court has acted in a manner that actually increases uncertainty around the issue. This uncertainty makes employing suspicionless canine sniffs difficult for public schools. My article helps public school officials make sense of the legal uncertainty in this area. First, the article provides background on how the Fourth Amendment governs public school officials. Second, it discusses how the Supreme Court’s actions have helped fuel uncertainty about whether suspicionless canine searches in schools violate the Fourth Amendment. Finally, the article provides five steps that public schools should take in deciding if a suspicionless canine sniff program is appropriate for their schools and, if so, how to best implement such a program

Spaceborne power systems preference analyses. Volume 2: Decision analysis

Sixteen alternative spaceborne nuclear power system concepts were ranked using multiattribute decision analysis. The purpose of the ranking was to identify promising concepts for further technology development and the issues associated with such development. Four groups were interviewed to obtain preference. The four groups were: safety, systems definition and design, technology assessment, and mission analysis. The highest ranked systems were the heat-pipe thermoelectric systems, heat-pipe Stirling, in-core thermionic, and liquid-metal thermoelectric systems. The next group contained the liquid-metal Stirling, heat-pipe Alkali Metal Thermoelectric Converter (AMTEC), heat-pipe Brayton, liquid-metal out-of-core thermionic, and heat-pipe Rankine systems. The least preferred systems were the liquid-metal AMTEC, heat-pipe thermophotovoltaic, liquid-metal Brayton and Rankine, and gas-cooled Brayton. The three nonheat-pipe technologies selected matched the top three nonheat-pipe systems ranked by this study