Quantum scattering theory on graphs with tails

Abstract

We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved as well as some other of its properties such as its transformation under time reversal. A spectral decomposition of the identity for the Hamiltonian of the graph is derived using its eigenvectors. We derive formulas for the S-matrix of a graph under certain operation such as cutting a tail, attaching a tail or connecting two tails to form an edge.

12 pages

References in corpus (6)

• Universal computation by quantum walk
• Quantum walks with infinite hitting times
• Quantum speedup of classical mixing processes
• Hitting time for the continuous quantum walk
• Almost uniform sampling via quantum walks
• Modifying quantum walks: A scattering theory approach

Cited by in corpus (10)

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• Levinson's theorem for graphs II
• Levinson's theorem for graphs
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• Single-qubit unitary gates by graph scattering
• Two-Particle Scattering on Non-Translation Invariant Line Lattices
• Momentum switches
• Time delay matrix at the spectrum edge and the minimal chaotic cavities
• Two-particle scattering on general graphs