The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RGâ€¦ (More)

We make a brief review of (optical) Holonomic Quantum Computer (or Computation) proposed by Zanardi and Rasetti (quantâ€“ph 9904011) and Pachos and Chountasis (quantâ€“ph 9912093), and give aâ€¦ (More)

In the first half we show an interesting relation between coherent states and the Bell states in the case of spin 1/2, which was suggested by Fivel. In the latter half we treat generalized coherentâ€¦ (More)

We give a possible generalization to the example in the paper of Zanardi and Rasetti (quantâ€“ph 9904011). For this generalized one explicit forms of adiabatic connection, curvature and etc. are given.â€¦ (More)

We have constructed the coherent state of U(N, 1) , which is an extension of the Barut-Girardello (BG) coherent state of SU(1, 1), in our previous paper. However there is a restriction that theâ€¦ (More)

Geometrical aspects of quantum computing are reviewed elementarily for nonexperts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half we show howâ€¦ (More)

In this letter we make a brief review of some basic properties (the matrix elements, the trace, the Glauber formula) of coherent operators and study the corresponding ones for generalized coherentâ€¦ (More)

We treat in this paper non-linear sigma models such as CP -model, QP -model and etc, in 1 + 2 dimensions. For submodels of such ones we definitely construct an infinite number of nontrivial conservedâ€¦ (More)

U(N) coherent states over Grassmann manifold, GN,n â‰ƒ U(N)/(U(n) Ã— U(N âˆ’ n)), are formulated to be able to argue the WKB-exactness, so called the localization of Duistermaat-Heckman, in the pathâ€¦ (More)

In this paper we consider a model of quantum computation based on n atoms of laserâ€“cooled and trapped linearly in a cavity and realize it as the n atoms Tavisâ€“ Cummings Hamiltonian interacting with nâ€¦ (More)