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Junctions and potentials -- scattering and bound states

In quantum mechanics, it is well known that a potential scatters any impinging particle. If the potential is attractive, it may trap the particle within a bound state. These processes are the outcome of competition between kinetic and potential energies. The same processes can occur in the absence of a potential, where all energy is kinetic. This happens in singular spaces composed of smooth spaces that intersect one another. We demonstrate this physics within a tight binding setup -- describing intersecting wires, sheets and 3D spaces. 

Our results bring out a quantitative equivalence between junctions and potentials. Each junction can be assigned an equivalent potential that produces the same scattering amplitude. The junction even produces the same bound state as the potential.

This leads to counter-intuitive results. The more the number of channels that meet at a junction, (a) the more it reflects an incoming particle and (b) the more tight is the bound state around it. 

I will discuss connections to random walks, Anderson localization, network transmission, etc. 

Host: Arun Paramekanti
Event series  Toronto Quantum Matter Seminars