Phase extraction in disordered isospectral shapes

Quantum phase extraction in isospectral electronic nanostructures.

Quantum phase is not directly observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability densities. We harness the mathematical discovery of drum-like manifolds bearing different shapes but identical resonances, and construct quantum isospectral...

Isospectral shapes with Neumann and alternating boundary conditions.

The isospectrality of a well-known pair of shapes constructed from two arrangements of seven congruent right isosceles triangles with the Neumann boundary condition is verified numerically to high precision. Equally strong numerical evidence for isospectrality is presented for the eigenvalues of this standard pair in new boundary configurations with alternating Dirichlet and Neumann boundary co...

Transition from simple to complex behavior of single molecule line shapes in disordered condensed phase

Isospectral Graphs and Isospectral Surfaces

In memory of Hubert Pesce In this paper, we investigate the following question: to what extent is there a converse to the Theorem of Sunada Su] in the context of graphs? Our experience in dealing with the question, \Can one hear the shape of a drum?" is that the many facets of this question turn out to be surprisingly delicate. The present instance is no exception. We will rst present a partial...

Disordered Systems in Phase Space

As a function of the disorder strength in a mesoscopic system, the electron dynamics crosses over from the ballistic through the diffusive towards the localized regime. The ballistic and the localized situation correspond to integrable or regular behavior while diffusive conductors correspond to chaotic behavior. The chaotic or regular character of single wave functions can be inferred from pha...