2015/09/01 by Paolo Facchi, Giancarlo Garnero, Giuseppe Marmo +1 · 11 citations
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Geometric phase #Hamiltonian (control theory) #Hamiltonian mechanics #Particle in a box #Phase (matter) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum particle #Renormalization #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1016/j.aop.2016.05.007
published in Annals of Physics 372, 201-214 (Elsevier BV) · 16 pages, 5 figures
arxiv created 2015/09/01 · openalex publication_date 2016/05/17 · arxiv updated 2016/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.