Moving Walls and Geometric Phases
arXiv:1509.00381 · doi:10.1016/j.aop.2016.05.007
Abstract
We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.
16 pages, 5 figures
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- On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain
- Boundary conditions for the quantum Hall effect
- Quantum magnetic billiards: boundary conditions and gauge transformations