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Title:
Time dependent quantum graphs and the geometric phase
Speaker:
Abstract:
Consider a metric graph whose edge lengths are functions of time. While this systemis relatively simple to describe (at least naively), it turns out that presenting it as awell posed boundary value problem holds several diculties. For instance, the changein time of the domain which supports the eigenfunctions gives rise to non-unitary timeevolution. This problem has been discussed by Duca and Joly in [1] in the context ofthe Schrödinger equation on moving domains.We attempt to solve this problem by suggesting an alternative description of thesystem. We show that the original problem can be translated into the time independentproblem of a harmonic oscillator on a non-homogeneous quantum graph, along with amagnetic potential.One can then derive an expression for the geometric phase (dened in [2]) accu-mulated by the wave function as the edge lengths complete a cycle in the parameterspace.The talk is based on a work in progress with Uzy Smilansky.
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