We present a general formulation to suppress pure dephasing by multipulse control. The formula is free from a specific form of interaction and is expressed in terms of the correlation function of arbitrary system-reservoir interaction. We first apply the formula to a phenomenological twolevel model where the correlation function of the interaction decays exponentially. In this case, we analytically show that the pure dephasing time is effectively lengthened by the multipulse control. Secondly, we apply the formula to the spin-boson model where a spin nonlinearly interacts with a boson reservoir. We find the multipulse control works well when the pulse interval is sufficiently shorter than the correlation time of system-reservoir interaction. Moreover, in this case, the pure dephasing can also be suppressed by adjusting the pulse interval to the period of dynamical motion of reservoir.

We explore the behavior in time of the energy exchange between a system of interest and its environment, together with its relationship to the non-Markovianity of the system dynamics. In order to evaluate the energy exchange we rely on the full counting statistics formalism, which we use to evaluate the first moment of its probability distribution. We focus in particular on the energy backflow from environment to system, to which we associate a suitable condition and quantifier, which enables us to draw a connection with a recently introduced notion of non-Markovianity based on information backflow. This quantifier is then studied in detail in the case of the spin-boson model, described within a second order time-convolutionless approximation, observing that non-Markovianity allows for the observation of energy backflow. This analysis allows us to identify the parameters region in which energy backflow is higher.Comment: 11 pages, 5 figures; published versio

The method of projection operators, which plays an important role in the field of nonequilibrium statistical mechanics, has been established with the use of the Liouville-von Neumann equation for a density matrix to eliminate irrelevant information from a whole system. We formulate a unified and general projection operator method for dynamical variables. The main features of our formalism parallel those for the Liouville-von Neumann equation. (1) Two types of basic equations, time-convolution and time-convolutionless decompositions, are systematically obtained without specifying a projection operator. (2) Expansion formulas for both decompositions are also obtained. (3) Problems incorporating a time-dependent Liouville operator can be flexibly treated. We apply the formulas to problems in random frequency modulation and low field resonance. In conclusion, our formalism yields a more direct and easier means of determining the average time evolution of an operator than the one for the Liouville-von Neumann equation.