last updated 2010 May 20
RESEARCH PROGRAM
1: TOPOLOGICAL QUANTUM CONDENSATES :The topics is to deal with the vortex in superfluid He4 as well as the vortex in anisotropic superfluid He3-A. The original idea stems from my paper on Hamiltonian dymamics of quantum vortex (PRL'92). Some interesting results are statistical partition function for quantum vortex gas in terms of Riemann zeta function (paper 1) and the vortex dynamics for the condensates accomodating the texture structure; (paper 2). The same idea can be applied to the non-singular vortex appearing in superfluid He3-A, ( paper 4)
2: LIGHT POLARIZATION THEORY: This topics is my latest one. Dr.Kakigi and I have developed a new theory of polarized light by starting from the first principe based on the Maxwell equation. The outline is to reduce the M-equation to the Schroedinger equation and by using the density matrix the evolutionary equation of the Stokes parameter is obtained in concise form. Amazing is that the resultant equation can be written in terms of the Larmour equation of spin in external magnetic field. ( paper 4).
For last several years professor Robert Botet (LPS, Orsay, France) has newly joined this project and we have publishsed seveal papers; maily the polarization evolution in birefringent media.
An interesting application of the the light polarization effect is applied to the anisotropica bose condensate ( paper 5)
3: GEOMETRIC PHASES AND ITS RELATED: This topics has been my long term plan since 1985. The geometric phase now becomes a "lingua franca"(after Wilczek and Shapere). I have long been interested in the quantized transport phenomena steming from this specific phase. Following the paper on the quantized Hall conductance that had been published a decade ago, I recently got a general formula for the adiabatic transport coefficient; but it does not give a quatization of tranport in general.
4: MODULI THEORY: The concept of moduli describes the whole structure of a set of mathematical or physically defined objects, which can be paramtetized by appropriate parameters. The space of this parameters forms a moduli space. A typical example is the moduli space of Riemann surfaces. An interesting question is that: if one is given a "function" (more suitably, section of vector bundle) on the moduli space, what becomes of the infinitesimal change of the point of the moduli space ? In order to carry out this, the idea of quantum adiabatic theorem may play a powerful tool (paper 6)
5: ZETA FUNCTION AND PATH INTEGRAL: This work is my latest topics. (see ref.7)
PUBLICATIONS
1. H.Ono and H.K. cond-mat/9411004
2. H.K. and H.Yabu, J.Phys.A29(1996)p6505,ibid, A31(1998)L61-L65
3.Phys.Rev.B. 59(1999)pp11175-11178.
4. H.K. and S.Kakigi, Phys.Rev. Lett. 60(1998). pp1888-1891.
5.Memoirs of Institute of Science and Engineering Ritsumeikan university, no58, 1999.
6: reported in Path integral symposium at Antwerpen, May 2002. unpublished