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Quantum Graphology
Tsampikos Kottos
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This oper…
Quantum decay of an open chaotic system: a semiclassical approach
Mathias Puhlmann, Holger Schanz, Tsampikos Kottos +1
We study the quantum probability to survive in an open chaotic system in the framework of the van Vleck-Gutzwiller propagator and present the first such calculation that accounts f…
Scars on quantum networks ignore the Lyapunov exponent
Holger Schanz, Tsampikos Kottos
We show that enhanced wavefunction localization due to the presence of short unstable orbits and strong scarring can rely on completely different mechanisms. Specifically we find t…
Statistical properties of resonance widths for open Quantum Graphs
Tsampikos Kottos, Holger Schanz
We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related…
Quantum Graphs: A simple model for Chaotic Scattering
Tsampikos Kottos, Uzy Smilansky
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an…
Quantum Graphs: A model for Quantum Chaos
Tsampikos Kottos, Holger Schanz
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operat…
Parametric dependent Hamiltonians, wavefunctions, random-matrix-theory, and quantal-classical correspondence
Doron Cohen, Tsampikos Kottos
We study a classically chaotic system which is described by a Hamiltonian where are the canonical coordinates of a particle in a 2D well, and is a parameter.…