I develop a novel method based on sources and absorbers to examine quantum scattering in finite, nanoscale systems. I first show that Cauchy (mixed) boundary conditions (BCs) are needed to put scattering into an action integral formulation. These complex BCs for scattering are reduced to simpler Dirichlet BCs by introducing totally absorbing “stealth regions,” whose material properties are optimized to give decaying solutions in these enclosed regions, so that the scattering amplitudes vanish at finite boundaries. With the physical domain now surrounded by stealth regions, we then allow for an “antenna” to provide incident waves in the active scattering region. The method retains all the physical aspects of the usual theory while providing new insights into scattering effects, and gives accurate predictions for “near-field” solutions. The action integral is discretized and evaluated to derive the local wave function everywhere. In two-dimensional quantum waveguides, we obtain the scattered wave functions for geometrically complex scattering centers, for multiple-scattering effects that go beyond the traditional perturbative estimates, and also for the far field region. The modal decomposition of reflected and transmitted waves allows us to obtain transmission coefficients for both propagating and evanescent modes.
- Fano resonances associated with interference between bound states and propagating states are shown to have their analogs with the evanescent modes also, and this is seen to be an unusual, universal effect.
- The effect of waveguide tapering for the first time, and the effect of curvature on transmission coefficients. (A patent application has been for initiated for a nano-rectifier device.
- The conductance given by the Landauer-Buttiker formalism, the Seebeck coefficient, and the thermopower are determined in waveguides. We show that the quantum dots or attractive impurity potentials embedded in the interior of a waveguide are good candidates for enhancing thermoelectric energy conversion since they yield large a Seebeck coefficient (thermopower) and the power factor.
The new formalism of sources and absorbers for scattering theory is leading to a re-examination of the textbook results and provides answers to very complex questions in new scattering phenomena.
Undergraduate & graduate students are especially invited to attend – details of the theory will be made manageable.
Refreshments will be served in Olin Hall 118 at 3:30 P.M.