Quantized chaotic dynamics and non-commutative KS entropy

We study the quantization of two examples of classically chaotic dynamics, the Anosov dynamics of "cat maps" on a two dimensional torus, and the dynamics of baker's maps. Each of these dynamics is implemented as a discrete group of automorphisms of a von Neumann algebra of functions on a quantized torus. We compute the non- commutative generalization of the Kolmogorov-Sinai entropy, namely the Connes-Stormer entropy, of the generator of this group, and find that its value is equal to the classical value. This can be interpreted as a sign of persistence of chaotic behavior in a dynamical system under quantization.Comment: a number of misprints corrected, new references and a new section added. 21 pages, plain Te

Supersymmetry and Fredholm modules over quantized spaces

The purpose of this paper is to apply the framework of non- commutative differential geometry to quantum deformations of a class of Kahler manifolds. For the examples of the Cartan domains of type I and flat space, we construct Fredholm modules over the quantized manifolds using the supercharges which arise in the quantization of supersymmetric generalizations of the manifolds. We compute the explicit formula for the Chern character on generators of the Toeplitz C^* -algebra.Comment: 24

Matrix Cartan superdomains, super Toeplitz operators, and quantization

We present a general theory of non-perturbative quantization of a class of hermitian symmetric supermanifolds. The quantization scheme is based on the notion of a super Toeplitz operator on a suitable Z_2 -graded Hilbert space of superholomorphic functions. The quantized supermanifold arises as the C^* -algebra generated by all such operators. We prove that our quantization framework reproduces the invariant super Poisson structure on the classical supermanifold as Planck's constant tends to zero.Comment: 52

Delivering a low-cost, reliable drip irrigation filtration system for micro-irrigation in developing countries

The cylindrical filters presently used in drip irrigation systems frequently clog, increasing pressure loss and lowering the flow rate through the filters. This work investigates alternative filtration strategies that increase the reliability of, and are compatible with, existing systems. To test different filtration strategies, a drip irrigation test setup was built to measure the pressure loss across different filters as particles accumulated. These experiments found that pleated cartridge filters, with high effective surface area, incurred the lowest pressure losses. More significantly, it was observed during these tests that the filtered out particles settled to the bottom of the filter housing when flow through the filter ceased. This inspired the redesign of the filter housing such that the housing extended far below the filter, providing a catch basin away from the filter for the particles to settle. Fixing the filter independently of the bottom casing significantly improves the overall performance of the filtration system and can be inexpensively manufactured via blow molding. This paper experimentally demonstrates that the cartridge filter inside the redesigned housing can filter out over 2 kg of sand while maintaining less than a .03 bar pressure drop across the filter at a flow rate of 25 l/s.MIT Tata Center for Technology and DesignMassachusetts Institute of Technology. Department of Mechanical EngineeringInternational Development Enterprise

Design and Testing of a Low-Cost and Low-Maintenance Drip Irrigation Filtration System for Micro-Irrigation in Developing Countries

The cylindrical filters presently used in <1000 m2 drip irrigation systems are frequently clogged, increasing pressure loss and lowering the flow rate through the filters. This work investigates the mechanisms for this clogging and proposes an alternative filtration design that would enable both more reliable and lower maintenance filtering. This proposed system is compatible with existing drip irrigation systems and could be made inexpensively with plastic bottle manufacturing equipment. To compare the proposed design to off-the-shelf options, a drip irrigation test setup was built to measure the pressure loss across different filters as particles accumulated. These experiments confirmed that pleated cartridge filters, with high effective surface area, incurred lower pressure losses than cylindrical filters. These tests revealed that the greatest reason for clogged performance was that filtered particles (not the cartridge filter itself) eventually restricted the flow of water through the system. This inspired the redesign of the filter housing such that the housing extended far below the filter, providing a catch basin away from the filter for the particles to settle. Fixing the filter independently of the bottom casing significantly improved the overall performance of the filtration system, reduced the maintenance requirement necessary from the user, and would enable inexpensive manufacturing via blow molding. This paper experimentally demonstrates that the cartridge filter inside the redesigned housing can filter out over 2 kg of sand while maintaining less than a .03 bar pressure drop across the filter at a flow rate of 25 l/s.Massachusetts Institute of Technology. Tata Center for Technology and DesignMassachusetts Institute of Technology. Department of Mechanical Engineerin

Statistical distinguishability between unitary operations

The problem of distinguishing two unitary transformations, or quantum gates, is analyzed and a function reflecting their statistical distinguishability is found. Given two unitary operations, $U_1$ and $U_2$, it is proved that there always exists a finite number $N$ such that $U_1^{\otimes N}$ and $U_2^{\otimes N}$ are perfectly distinguishable, although they were not in the single-copy case. This result can be extended to any finite set of unitary transformations. Finally, a fidelity for one-qubit gates, which satisfies many useful properties from the point of view of quantum information theory, is presented.Comment: 6 pages, REVTEX. The perfect distinguishability result is extended to any finite set of gate

Metric adjusted skew information: Convexity and restricted forms of superadditivity

We give a truly elementary proof of the convexity of metric adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric adjusted skew informations. Recently, Luo and Zhang introduced the notion of semi-quantum states on a bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew informations for such states. We extend this result to general metric adjusted skew informations. We finally show that a recently introduced extension to parameter values $1<p\le 2$ of the WYD-information is a special case of (unbounded) metric adjusted skew information.Comment: An error in the literature is pointed ou