Abstract
There is a natural connection and parallel transport on the Hilbert tensor product ℋ⊗ℋ (or, equivalently, the space of Hilbert-Schmidt operators), the elements of which represent density matrices in ℋ up to unitary operators. We postulate a time evolution equation, which leads to this connection after extracting a proper ‘dynamical’ unitary phase. As an example, we compute the holonomy of a loop of temperature states for the spin in a rotating magnetic field.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
DeclacrétazG., GrantE. R., WhettenR. L., WöskL. and ZwanzigerJ. W.,Phys. Rev. Lett. 56, 2598 (1986); Tomita, A. and Chiao, R. Y.,Phys. Lett. 57, 937 (1986); Tycko, R.,Phys. Rev. Lett. 58, 2281 (1987); Bitter, T. and Dubbers, D.,Phys. Rev. Lett. 59, 251 (1987); Bhandari, R. and Samuel, J.,Phys. Rev. Lett. 60, 1211 (1988); Chiao, R. Y., Antaramian, A., Ganga, K. M., Jiao, H. and Wilkonson, S. R.,Phys. Rev. Lett. 60, 1214 (1988); Suter, D., Mueller, K. T. and Pines, A.,Phys. Rev. Lett. 60, 1218 (1988); Simon, R., Kimble, H. J. and Sudarshan, E. G. C.,Phys. Rev. Lett. 61, 19 (1988); Richardson, D. J., Kilvington, A. I., Green, K. and Lamoreaux, S. K.,Phys. Rev. Lett. 61, 2030 (1988).
BerryM. V.,Proc. Roy. Soc. London, Ser. A 392, 45 (1984).
SimonB.,Phys. Rev. Lett. 51, 2167 (1983).
WilczekF. and ZeeA.,Phys. Rev. Lett. 52, 2111 (1984).
ThirringW.,A Course in Mathematical Physics, Vol. 3, Quantum Mechanics of Atoms and Molecules, Springer, New York, 1981.
Dabrowski, L. and Jadczyk, A., Quantum statistical holonomy, SISSA preprint 155/88.
UhlmannA.,Rep. Math. Phys. 24, 229 (1986).
AnandanJ.,Phys. Lett. A 133, 171 (1988).
Dabrowski, L., SISSA preprint 156/88/FM.
Author information
Authors and Affiliations
Additional information
Supported by ‘Fonds zur Förderung der wissenschaftlichen Forschung in Österreich’, Project No. P5588.