Optimal control of dissipation by nano-mechanical systems via manipulations of the potential energy


A widely used mathematical model of nano-mechanical system is the Langevin-Kramers equation describing a dynamics governed by a kinetic plus potential Hamiltonian, linear friction and in contact to a thermal environment. In realistic experimental settings it is possible to steer finite time transitions of a nano-mechanical system between target states by manipulating an external potential field. In the talk I discuss the optimal potential energy control problem associated to transitions occurring at minimal dissipation.