Geometry And Topology

Topology in Ordered Phases: Proceedings of the 1st by Satoshi Tanda, Toyoki Matsuyama, Migaku Oda, Yasuhiro Asano,

By Satoshi Tanda, Toyoki Matsuyama, Migaku Oda, Yasuhiro Asano, Kousuke Yakubo

The idea that of topology has turn into usual in quite a few medical fields. the subsequent degree is to collect the information gathered in those fields. This quantity comprises articles on experiments and theories in reference to topology, together with wide-ranging fields akin to fabrics technology, superconductivity, cost density waves, superfluidity, optics, and box thought. The approximately 60 peer-reviewed papers comprise contributions through famous authors Michael V Berry and Roman W Jackiw. The e-book serves as a great reference for either researchers and graduate scholars.

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Additional info for Topology in Ordered Phases: Proceedings of the 1st International Symposium on Top 2005 Sapporo, Japan 7 - 10 March 2005

Example text

Ipi(x) and Ax are the order parameter of the i-th chain and the ^-component of the vector potential, respectively. The number of the chains is assumed to be even (= 2K) for simplicity, v is a parameter of the interchain Josephson coupling. The vector potential is taken to be a constant Ax = /L, where is the magnetic flux enclosed by the ring. We assume that the magnetic flux on the strip is negligible. a and (3 are constants, where a — a0(t — 1) with t begin T/Tc (Tc is the SC transition temperature in the bulk).

16) and differentiating with respect to e, the extremal condition yields 0 = de f = f tr{»)(VVt-VrV't-VWt)}di. (18) Thus we obtain the Euler-Lagrange equation —(i/yt - vv* + vnv^) = o. (19) The extremal condition with respect to fi(i) reproduces the horizontal equation V^V = 0. (13) and (19). Equation (19) is integrated to yield VV1 - VV^ + V W f = const = X e u{N). (13) yields V^V = 0. (21) from the left we obtain n = V^XV. (22) We can show Q, = 0 by a straightforward calculation. Hence, Q(t) is actually a constant matrix.

To satisfy these two contradicting conditions we need to make the loop in the control parameter manifold as short as possible while keeping the specified holonomy. Thus, we are naturally led to the isoholonomic problem. We would like to emphasize that a quantum computer is actually not a digital computer but an analog computer in its nature. Hence, the geometric and topological approaches are useful for building and optimizing quantum computers. This paper is based on collaboration with D. Hayashi and M.

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