Erratum: Kinematic Approach to the Mixed State Geometric Phase in Nonunitary Evolution [Phys. Rev. Lett.93, 080405 (2004)]

Geometric magnetism in open quantum systems

“…Note the prominent difference that Kubo's formula (41) gives an expression (linear in R) for the difference between the nonequilibrium expectation of O at time τ , and its equilibrium expectation at time 0, whereas the present formula (14) gives an expression (linear inṘ) for the difference between the nonequilibrium expectation of O at time τ , and its equilibrium expectation at the same time τ . Thus in Kubo's theory the small parameter is the strength of the driving whereas in our theory the small parameter is the speed.…”

“…(14,16) are geometric, i.e., they depend on time only through the time dependent parameters R τ . Following Berry and Robbins [7] we assume for simplicity a parameter space of dimension N = 3 and rewrite Eq.…”

“…Thus, the study of geometric phases in realistic open quantum systems has become of paramount importance. This problem has been typically addressed from a dynamics point of view, that is, one researches proper definitions of phases with respect to non-unitary dynamics [11][12][13][14][15][16][17][18][19][20][21] (which are the relevant ones for open systems), instead of the unitary dynamics originally considered by Berry.…”

Geometric phase outside a Schwarzschild black hole and the Hawking effect

“…However, due to the inevitable interactions between the qubits and the environment, a pure state will be driven to a mixed one. Therefore, the study of geometric phase of systems under nonunitary evolutions becomes important, and some work has been done to generalize the geometric phase to open quantum systems [16][17][18][19][20], and the effects of different kinds of decoherence sources on the geometric phase have been analyzed [21][22][23][24][25]. By studying the geometric phase of an open system, we can draw some information about the nonunitary evolution of the system and the characteristics of the environment the system coupled to.…”

Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states

“…The generalization to nonunitary evolution has also been addressed in Refs. [13,14,15] and experimental test of the phase concept in Ref. [11] has been carried out using nuclear magnetic * Electronic address: eriks@kvac.uu.se † Electronic address: sfilipp@ati.ac.at ‡ Electronic address: phyohch@nus.edu.sg resonance [16].…”