1301.2326 (Jarrod R. McClean et al.)

Feynman's clock, a new variational principle, and quantum time-orbitals    [PDF]

Jarrod R. McClean, John A. Parkhill, Alán Aspuru-Guzik

We introduce a new discrete-time variational principle inspired by the quantum clock originally proposed by Feynman, and use it to write down quantum evolution as a ground state eigenvalue problem. This allows one to apply ground state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. We draw an explicit connection between previously known time-dependent variational principles and the new time embedded variational principle presented. Sample calculations are presented applying the idea to the electronic degrees of freedom in a Hydrogen molecule and the spin degrees of freedom of a model inorganic compound. We employ the configuration-interaction approximation on a basis in which time is a variable. Finally, we take advantage of the unique perspective of the new variational principle to examine the error of basis approximations in quantum dynamics.

View original: http://arxiv.org/abs/1301.2326