Gen Kimura

The Bloch vector for N-level systems

We determine the set of the Bloch vectors for N-level systems, generalizing the familiar Bloch ball in 2-level systems. An origin of the structural difference from the Bloch ball in 2-level systems is clarified.

The Bloch Vector for N-Level Systems

We explicitly determine the Bloch-vector space for arbitrary N -level systems, which generalizes a familiar Bloch ball in 2-level systems.

Kraus representation in the presence of initial correlations

We examine the validity of the Kraus representation in the presence of initial correlations and show that it is assured only when a joint dynamics is locally unitary.

Restriction on relaxation times derived from the lindblad-type master equations for two-level systems

We discuss a restriction on relaxation times derived from the Lindblad-type master equations for two-level systems and show that none of the inverse relaxation times can be greater than the sum of the others. The relation is experimentally proved or disproved and can be considered to be a measure for or against the applicability of the Lindblad-type master equations, and therefore, of the so-called completely positive condition.

On the assumption of initial factorization in the master equation for weakly coupled systems I: General framework

We analyze the dynamics of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. In the weak-coupling (van Hove) limit, the dynamics can be properly described in terms of a master equation, but a consistent application of Nakajima–Zwanzig’s projection method requires that the reference (not necessarily equilibrium) state of the reservoir be endowed with the mixing property.

Stochastic limit approximation for rapidly decaying systems

The stochastic limit approximation method for ``rapid decay is presented, where the damping rate gamma is comparable to the system frequency Omega, i.e., gamma sim Omega, whereas the usual stochastic limit approximation is applied only to the weak damping situation gamma > hbarOmega and the master equations obtained are of the Lindblad form even for the Caldeira-Leggett model. The validity of the method is confirmed by comparing the master equation derived through this method with the exact one.

On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models

We analyze some solvable models of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. We apply Nakajima–Zwanzig’s projection method by choosing a reference state of the reservoir endowed with the mixing property. In van Hove’s limit, the dynamics is described in terms of a master equation. We observe that Markovianity becomes a valid approximation for timescales that depend both on the form factors of the interaction and on the observables of the reservoir that can be measured.

Bifurcation phenomenon in spin relaxation

Spin relaxation in a strong-coupling regime (with respect to the spin system) is investigated in detail based on the spin-boson model in a stochastic limit. We find a bifurcation phenomenon in temperature dependence of relaxation constants, which is never observed in the weak-coupling regime. We also discuss inequalities among the relaxation constants in our model and show the well-known relation 2gamma(T)>or=gamma(L), for example, for a wider parameter region than before.

A Note on Positive Maps and Classification of States

The relation between positive maps on Mn and subsets of self-adjoint elements from Mn ⊗ Mn is investigated. It has been shown that there exists the isomorphism between the set of all positive normalized maps on Mn and the subset of separable states on Mn ⊗ Mn.