The Microwave Background Bispectrum, Paper I: Basic Formalism

In this paper, we discuss the potential importance of measuring the CMB anisotropy bispectrum. We develop a formalism for computing the bispectrum and for measuring it from microwave background maps. As an example, we compute the bispectrum resulting from the 2nd order Rees-Sciama effect, and find that is undetectable with current and upcoming missions.Comment: 18 Pages, 3 Postscript Figures; Minor changes in response to referee's repor

Lambda Models From Chern-Simons Theories

In this paper we refine and extend the results of arXiv:1701.04138, where a connection between the $AdS_{5}\times S^{5}$ superstring lambda model on $S^{1}=\partial D$ and a double Chern-Simons (CS) theory on $D$ based on the Lie superalgebra $\mathfrak{psu}(2,2|4)$ was suggested, after introduction of the spectral parameter $z$. The relation between both theories mimics the well-known CS/WZW symplectic reduction equivalence but is non-chiral in nature. All the statements are now valid in the strong sense, i.e. valid on the whole phase space, making the connection between both theories precise. By constructing a $z$-dependent gauge field in the 2+1 Hamiltonian CS theory it is shown that: i) by performing a symplectic reduction of the CS theory the Maillet algebra satisfied by the extended Lax connection of the lambda model emerges as a boundary current algebra and ii) the Poisson algebra of the supertraces of $z$-dependent Wilson loops in the CS theory obey some sort of spectral parameter generalization of the Goldman bracket. The latter algebra is interpreted as the precursor of the (ambiguous) lambda model monodromy matrix Poisson algebra prior to the symplectic reduction. As a consequence, the problematic non-ultralocality of lambda models is avoided (for any value of the deformation parameter $\lambda \subset [0,1]$), showing how the lambda model classical integrable structure can be understood as a byproduct of the symplectic reduction process of the $z$-dependent CS theory.Comment: Published version+Erratum (of typos), 57 page

Integrability vs Supersymmetry: Poisson Structures of The Pohlmeyer Reduction

We construct recursively an infinite number of Poisson structures for the supersymmetric integrable hierarchy governing the Pohlmeyer reduction of superstring sigma models on the target spaces AdS_{n}\times S^n, n=2,3,5. These Poisson structures are all non-local and not relativistic except one, which is the canonical Poisson structure of the semi-symmetric space sine-Gordon model (SSSSG). We verify that the superposition of the first three Poisson structures corresponds to the canonical Poisson structure of the reduced sigma model. Using the recursion relations we construct commuting charges on the reduced sigma model out of those of the SSSSG model and in the process we explain the integrable origin of the Zukhovsky map and the twisted inner product used in the sigma model side. Then, we compute the complete Poisson superalgebra for the conserved Drinfeld-Sokolov supercharges associated to an exotic kind of extended non-local rigid 2d supersymmetry recently introduced in the SSSSG context. The superalgebra has a kink central charge which turns out to be a generalization to the SSSSG models of the well-known central extensions of the N=1 sine-Gordon and N=2 complex sine-Gordon model Poisson superalgebras computed from 2d superspace. The computation is done in two different ways concluding the proof of the existence of 2d supersymmetry in the reduced sigma model phase space under the boost invariant SSSSG Poisson structure.Comment: 33 pages, Published versio

The EPR Paradox Implies A Minimum Achievable Temperature

We carefully examine the thermodynamic consequences of the repeated partial projection model for coupling a quantum system to an arbitrary series of environments under feedback control. This paper provides observational definitions of heat and work that can be realized in current laboratory setups. In contrast to other definitions, it uses only properties of the environment and the measurement outcomes, avoiding references to the `measurement' of the central system's state in any basis. These definitions are consistent with the usual laws of thermodynamics at all temperatures, while never requiring complete projective measurement of the entire system. It is shown that the back-action of measurement must be counted as work rather than heat to satisfy the second law. Comparisons are made to stochastic Schr\"{o}dinger unravelling and transition-probability based methods, many of which appear as particular limits of the present model. These limits show that our total entropy production is a lower bound on traditional definitions of heat that trace out the measurement device. Examining the master equation approximation to the process at finite measurement rates, we show that most interactions with the environment make the system unable to reach absolute zero. We give an explicit formula for the minimum temperature achievable in repeatedly measured quantum systems. The phenomenon of minimum temperature offers a novel explanation of recent experiments aimed at testing fluctuation theorems in the quantum realm and places a fundamental purity limit on quantum computers.Comment: 15 pages, 5 figures (submitted

Secured Credit and Bankruptcy: A Call for the Federalization of Personal Property Security Law

In recent years, the need for systems monitoring the current in ation pressure in pneumatic tires has grown dramatically. One way to monitor the in ation pressure is to use the fact that the tire reacts like a spring when excited from road roughness. The resonance frequency of the tire can be estimated with standard signal processing procedures. Three different approaches for vibration analysis are studied using a simulation model similar to the tire model. The first approach uses the raw wheel speed which is highly over-sampled. In the second approach a pre-filter is used to remove the disturbances and the third approach uses down sampling to isolate the vibration frequency. Especially bias in the estimation is studied