Group of  Nonlinear Dynamics & Complex Systems

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Research Fields —Microscopic chaos and macroscopic transport

Electron conduction and thermal conduction are two fundamental energy transport phenomena in the nature. The research of electron conduction lead to the invention of transistor and changed our daily life now. However, unlike electron conduction, heat conduction has been neglected for a while.

The research of heat conduction in low dimensional systems is very important both from fundamental point view and from application point of view. One the one hand, heat conduction is a vivid example of the so-called irreversible paradox in statistical mechanics. Namely, the motion of atoms and molecules is reversible at any instant microscopically, however, heat conduction is an irreversible phenomenon, i.e., no one has ever observed the heat flows from a cold object to a hotter one. The research on heat conduction will improve our understanding of all other irreversible phenomena including life processes. On the other hand, the understanding of heat flow has potentially very important practical applications, e.g. in the development of new materials with controlled heat conducting properties. It may also shed lights in explaining the controlled energy transport in living organisms on a cellular level. A great potential application might be the design of new thermal devices such as thermal rectifiers and thermal transistors etc.

The group has made several contributions in this field. They have clarified several long standing misunderstanding points in heat conduction. For example, recently they have disproved the lore that the microscopic chaos plays an important role in the onset of transport process and hence in the origin of irreversible behavior. In addition, they have proposed several microscopic mechanisms for a normal heat conduction such as the phonon - on-site potential scattering mechanism, phonon-disorder scattering mechanism etc.  

(a) Time evolution of the displacement of the 1D Fermi-Pasta-Ulam model  of  64 particles. (b) Same as (a) but after wavelet transform. (c) Subtraction of (b) from (a). (d) Time evolution of local heat flux. Horizontal axis is time, vertical axis is the  lattice site. The color changes from yellow to red corresponding to the change of amplitude of the displacement (a-c) and heat flux (d). A Recurrent of large amplitude of displacement in (a-b) demonstrates the solitary wave (long-wave length mode) propagating along the lattice. (c) demonstrates the short wave excitations move left and right carrying away the energy. This is also seen in  the time evolution of local heat flux (d).

Electronic transport in mesoscopic systems or nanoscale structures has received extensive theoretical and experimental attention. In mesoscopic systems the sample size is smaller than the phase coherent length, and electrons retain their phase when travelling through the sample. In the ballistic limit, i.e., when the dimensions of the sample are smaller than the mean free path, electrons can traverse the system without any scattering. In contrast to macroscopic systems, the conductance of mesoscopic systems is sample-specific, since electron wavefunctions are strongly dependent on the form of the boundary of the sample and the configuration of scatterers located within the sample.

Related publications:

Z-Y Zeng, B Li, and F Claro, Eur Phys J. B 32, 401 (2003)

Incommensurate and quasiperiodic structures appear in many physical systems such as quasicrystals, two-dimensional electron systems, magnetic superlattices, charge-density waves, organic conductors, and various atomic monolayers adsorbed on crystalline substrates. All of these phenomena can be described by a theoretical model Frenkel Kontorova model. We have calculated numerically the energy spectra and quantum diffusion of an electron in the 1D incommensurate Frenkel-Kontorova model. We found that the spectral and dynamical properties of an electron display quite different behaviors in the invariant circle regime and in the Cantorus regime. In the former case, it is similar to that of the Harper model, whereas in the latter case, it is similar to that of the Fibonacci model.   Related publications: P Q Tong, B Li, and B Hu, Phys. Rev. Lett. 88, 046804 (2002).