Qubit Decoherence and Non-Markovian Dynamics at Low Temperatures via an Effective Spin-Boson Model

Quantum Brownian oscillator model (QBM), in the Fock-space representation, can be viewed as a multi-level spin-boson model. At sufficiently low temperature, the oscillator degrees of freedom are dynamically reduced to the lowest two levels and the system behaves effectively as a two-level (E2L) spin-boson model (SBM) in this limit. We discuss the physical mechanism of level reduction and analyze the behavior of E2L-SBM from the QBM solutions. The availability of close solutions for the QBM enables us to study the non-Markovian features of decoherence and leakage in a SBM in the non-perturbative regime (e.g. without invoking the Born approximation) in better details than before. Our result captures very well the characteristic non-Markovian short time low temperature behavior common in many models.Comment: 19 pages, 8 figure

Team incentives in relational employment contracts

The paper analyzes conditions for implementing incentive schemes based on, respectively joint, relative and independent performance, in a relational contract between a principal and a team of two agents. A main result is that the optimal incentive regime depends on the productivity of the agents, or more precisely on the returns from high effort. This occurs because agents’ productivities affect the principal’s temptation to renege on the relational contract. The analysis suggests that we will see a higher frequency of relative performance evaluation (RPE) - and schemes that lie close to independent performance evaluation - as we move from low-productive to high-productive environments. In particular, it is shown that if effort-productivity is sufficiently high, the optimal scheme for the principal is (for a range of discount factors) a collusion-proof RPE scheme, even if there is no common shock that affects the agents’ output