Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Time-independent or memoryless master equations, in particular, can be cast in the well-known Lindblad form. Any time-local master equation, Markovian or non-Markovian, may in fact also be written in a Lindblad-like form. A diagonalisation procedure results in a unique, and in this sense canonical, representation of the equation, which may be used to fully characterize the non-Markovianity of the time evolution. Recently, several different measures of non-Markovianity have been presented which reflect, to varying degrees, the appearance of negative decoherence rates in the Lindblad-like form of the master equation. We therefore propose using the negative decoherence rates themselves, as they appear in the canonical form of the master equation, to completely characterize non-Markovianity. The advantages of this are especially apparent when more than one decoherence channel is present. We show that a measure proposed by Rivas et al. is a surprisingly simple function of the canonical decoherence rates, and give an example of a master equation that is non-Markovian for all times t > 0, but to which nearly all proposed measures are blind. We also give necessary and sufficient conditions for trace distance and volume measures to witness non-Markovianity, in terms of the Bloch damping matrix.

No abstract

For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure is reviewed for constructing the corresponding linear map from the initial state to the state at time t, including its Kraus-type representations. Formally, this is equivalent to solving the master equation. For an N-dimensional Hilbert space it requires (i) solving a first order N^2 x N^2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalising a related N^2 x N^2 matrix (to obtain a Kraus-type representation). Conversely, for a given time-dependent linear map, a necessary and sufficient condition is given for the existence of a corresponding master equation, where the (not necessarily unique) form of this equation is explicitly determined. It is shown that a `best possible' master equation may always be defined, for approximating the evolution in the case that no exact master equation exists. Examples involving qubits are given.Comment: 16 pages, no figures. Appeared in special issue for conference QEP-16, Manchester 4-7 Sep 200

We consider two recently proposed measures of non-Markovianity applied to a particular quantum process describing the dynamics of a driven qubit in a structured reservoir. The motivation of this study is twofold: on one hand, we study the differences and analogies of the non-Markovianity measures and on the other hand, we investigate the effect of the driving force on the dissipative dynamics of the qubit. In particular we ask if the drive introduces new channels for energy and/or information transfer between the system and the environment, or amplifies existing ones. We show under which conditions the presence of the drive slows down the inevitable loss of quantum properties of the qubit.

The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature T. However, non-negligible interactions between system and environment can give rise to an altered state. Here, we derive general expressions for this mean force Gibbs state, valid for any system that interacts with a bosonic reservoir. First, we derive the state in the weak coupling limit and find that, in general, it maintains coherences with respect to the bare system Hamiltonian. Second, we develop a new expansion method suited to investigate the ultrastrong coupling regime. This allows us to derive the explicit form for the mean force Gibbs state, and we find that it becomes diagonal in the basis set by the systemreservoir interaction instead of the system Hamiltonian. Several examples are discussed including a single qubit, a three-level V-system, and two coupled qubits all interacting with bosonic reservoirs. The results shed light on the presence of coherences in the strong coupling regime, and provide key tools for nanoscale thermodynamics investigations.

No abstract

No abstract

We present a Markovian quantum theory of friction. Our approach is based on the idea that collisions between a Brownian particle and single molecules of the surrounding medium constitute, as far as the particle is concerned, instantaneous simultaneous measurements of its position and momentum