26 citations · 65 across the 5 of their papers we have counts for
5 papers
Integrability in 1D Quantum Chaos
Yu. Dabaghian, R. V. Jensen, R. Blümel
Explicit, exact periodic orbit expansions for individual eigenvalues exist for a subclass of quantum networks called regular quantum graphs. We prove that all linear chain graphs h…
Spectra of regular quantum graphs
Yu. Dabaghian, R. V. Jensen, R. Blümel
We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable…
Exact, convergent periodic-orbit expansions of individual energy eigenvalues of regular quantum graphs
R. Blümel, Y. Dabaghian, R. V. Jensen
We present exact, explicit, convergent periodic-orbit expansions for individual energy levels of regular quantum graphs. One simple application is the energy levels of a particle i…
One-dimensional quantum chaos: Explicitly solvable cases
Yu. Dabaghian, R. V. Jensen, R. Blümel
We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the c…
Exact trace formulae for a class of one-dimensional ray-splitting systems
Y. Dabaghian, R. V. Jensen, R. Blümel
Based on quantum graph theory we establish that the ray-splitting trace formula proposed by Couchman {\it et al.} (Phys. Rev. A {\bf 46}, 6193 (1992)) is exact for a class of one-d…