In our laboratory we theoretically study
various problems emerging from nonlinear
and nonequilibrium phenomena in **condensed matter physics**. Any kind of subject may be investigated
if one wishes. Our works are featured in
terms of keywords in nonlinear science such
as **chaos**, **solitons**, **fractals** and **pattern formations**. In particular, we explore how such **nonlinear and nonequilibrium phenomena** show up in actual experimental situations.
We believe that this kind of approach leads
to exciting issues.

Examples of our study are as follows:

- Quantum transport and quantum chaos in mesoscopic systems
- Pattern formation and chaos in nonequilibrium ferromagnets and Bose-Einstein condensations
- Dynamical response and impurity effects of solitons in organic conductors
- Quantum dissipative dynamics of small junctions made by using superconductors

Staffs are Prof. Katsuhiro Nakamura, Associate Prof. Akira Terai, and Lecturer Ayumu Sugita. The member in our laboratory can be found here. Our Laboratory was established in 1992 with new staffs, and current staffs are not graduates of Osaka City University. Also, fairly large number of doctor-course and master-course students come from other universities. We think that this high mobility of our laboratory leads to the active atmosphere and guarantees to contribute to pioneering works.

**1. Quantum Chaos and Mesoscopic Physics**

In the systems showing chaos classically, the stable torus in phase space is broken, and the action (adiabatic invariant), which should be quantized, disappears. Then, various interesting problems appears if we apply quantum mechanics to the systems showing classical chaos. This constitutes the subject of "quantum chaos." Especially, quantum dynamics in the system showing chaos classically, presents only a quasi-periodic behavior and shows no chaotic behavior (absence of classical-quantal correspondence in classically-chaotic systems). This is a riddle. On the other hand, using mesoscopic or nanoscale electronic devices, we can capture "quantum chaos," namely quantum manifestations of classical chaos. For a long time people have studied stadium and Sinai billiards as typical examples of dynamical system showing chaos and ergodicity. Such billiards whose size are of nanoscale is now being made at the interface of semiconductor heterojunctions, and experiments on ballistic quantum transport in these quantum dots are in progress. We can now observe quantum chaos through the diamagnetic susceptibility and the electric conductivity of electron gas in quantum dots. Thus, in our laboratory, we are largely involved in quantum chaos and quantum transport in mesoscopic systems.

**2. Nonlinear and Nonequilibrium States in
Condensed Matters**

We are also trying to understand mechanisms underlying the morphological nonequilibrium phase transitions. For instance, we study pattern formations in magnetic thin films in the presence of time-periodic magnetic field by using the fundamental equation (Landau-Lifshitz equation). Compared with turbulence in fluid dynamics, the time scale of the nonequilibrium phenomena is extremely short in microscopic condensed matters physics and we can observe interesting patterns on short time scale. We shall develop amplitude and phase equations for nonlinear and nonequilibrium magnets and understand morphological transitions related to domain walls and domain structures. Since such a study has a quite general and universal feature, we also want to analyze dynamics of vortices or textures in various Bose-Einstein condensations, too.

**3. 1-D Electric Conductor and Soliton Excitation**

We theoretically study a phonon configuration, an infrared absorption, Raman scattering and a soliton propagation of trans-form polyacethylene, which is typical 1-D electric conductor. Experiments show that man can theoretically predict the peak of infrared absorption by soliton which is a concept of a non-linear excitation. Also, we study, configurations and motions of soliton under the insulator-metal transition or electric field, a stability when soliton pair and polaron pair collide, configurations and motions of the non-linear excitation in the spin density wave state, and so on. And we develop the high-order factoring method of the exponent operator in the numerical calculation of the spin density wave.

**4. Quantum Transport in a Proximity Effect
System of a Superconductor**

On the surface of a superconductor-normalconductor junction, Andreev reflection, scattering from an electron to a hole(or from a hole to an electron), occurs. We can think an electric conduction in a proximity effect system, including Josephson current occurs by this reflection. In the superconductor-normalconductor multi-mesoscopic system, a offdiagonal phase coherence occurs between an electron and a hole by Andreev reflection, so an electron wave coherence effect different from one in the normal mesoscopic system appears in an electric conduction. It is one of the aim of this research that we clear this abnormal behavier. Also, we expect that interactions between electrons strongly influence it in the small size system, because an electron-hole pair is related to Andreev reflection. However, this problem has not been examined yet. Another aim of this research is clearing the influence of an interaction for an Andreev reflection process.