Physical Sciences and Mathematics Commons^™

Geometrical Phases And Symmetries In Dissipative Systems, Adam S. Landsberg

WM Keck Science Faculty Papers

A geometrical phase is constructed for dissipative dynamical systems possessing continuous symmetries. It emerges as the natural analog of the holonomy associated with the adiabatic variation of parameters in quantum-mechanical and classical Hamiltonian systems. In continuous media, the physical manifestation of this phase is a spatial shift of a wave pattern, typically a translation or rotation. An illustration associated with pattern formation in fluids is provided.