A min symposium on complex eigenvalue problems of Liouville operators

9:00-10:20 Tomio Petrosky (Texas at Austin) Complex Eigenvalue Problem of Liouville Operator and it Application to Biological Problems
- Abstract: The energy transport in an 1D protein chain under a thermal noise is analyzed in terms of the complex spectral representation of the Liouville - von Neumann operator. Contrary to simple intuition, thermal noise ensures an effective propagation of the energy through a stable sound mode in quantum hydrodynamic modes.
10:40-12:00 Satoshi Tanaka (Osaka prefacture Univ.) Band structure in the spectrum of the collision operator of one-dimensional protein molecule
- The spectrum of the collision operator describing the relaxation of the momentum distribution in one-dimensional protein molecule is investigated. We found that the eigenvalue of the collision operator, which corresponds to the imaginary part of the eigenvalue of the Liouville operator, shows a band structure. The relaxation dynamics of the system with the band structure will be discussed.

9:00-10:30 Naomichi Hatano (IIS, Univ. of Tokyo) Quantum Resonance and Electronic Conduction in Mesoscopic Systems
- Abstract: We define a resonant state as an eigenstate of the Schr\"{o}dinger equation. We then discuss physical significance of the resonant eigenstate. We show that the resonant eigenstate does observe the particle number conservation. We also argue that the Fano resonance, which is often found in the electric conductance of mesoscopic systems as an asymmetric peak, can be explained as interference effect among resonant states and bound states.
10:50-12:20 Buang Ann Tay (Univ.of Putra Malaysia) Biorthonormal Eigenbasis of a Markovian Master Equation for the Quantum Brownian Motion
- The solution to a quantum Markovian master equation of a harmonic oscillator weakly coupled to a thermal reservoir is investigated as a non-hermitian eigenvalue problem in space coordinates. We apply the solution to simple quantum systems.
13:30-15:00 Kazuki Kanki (Osaka Prefacture Univ.) Eigenfunction expansion in an extended functional space for classical and quantum Brownian particles
- The norm of a momentum distribution function for a Brownian particle diverges in the case the distribution is characterized by a temperature higher than twice the environmental temperature. For this case the eigenfunction expansion of a distribution function can be understood as defining a linear functional over a class of test functions.

9:00-10:30 Valeri Barsegov (Univ. of Massachusetts) Computer simulations of proteins: all-atom and coarse-grained models
- Abstract: In my talk I will describe current state-of-the-art computer simulations of biomolecules (proteins): force-fields, potential functions, approximations, timescales. The two main approaches utilize the all-atomic description of a protein, or coarse-grained models of various sorts. The scope of applicability of these descriptions will be discussed by using particular examples. In addition, I will also discuss a recent newly emerging direction in computer simulations, which employs high performance graphics cards. I will briefly discuss the underlying architecture, and will give a few examples.
10:50-12:20 Hisao Hayakawa (YITP, Kyoto University) Liouville equation for granular gases
- Granular particles are characterized by inelastic collisions. Eventually, we have to analyze complex eigenvalue problems to analyze such systems. In my talk, I will survey what the Liouville equation for granular gases is, and the change from classical hard spherical atoms. I will also comment on the application of this formulation to actual phenomena of granular particles.