Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain

Using recently proposed measures for non-Markovianity [H.-P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)], we study the dynamics of a qubit coupled to a spin environment via an energy-exchange mechanism. We show the existence of a point, in the parameter space of the system, where the qubit dynamics is effectively Markovian and that such a point separates two regions with completely different dynamical behaviors. Indeed, our study demonstrates that the qubit evolution can in principle be tuned from a perfectly forgetful one to a deep non-Markovian regime where the qubit is strongly affected by the dynamical backaction of the environmental spins. By means of a theoretical quantum process tomography analysis, we provide a complete and intuitive characterization of the qubit channel.

The Implications of Bach's Introduction of New Fugal Techniques and Procedures in the Well-Tempered Clavier Book Two

Among the fugues of the WTC II, there are some fugal techniques and procedures that were not explored in the first book. Here, the ‘fugal techniques’ include parallel entries (as used in the fugues in D-sharp minor, G minor and B-flat minor) and double counterpoint at the tenth or twelfth as well as fifteenth (as used in the fugues in G minor and B major). The ‘fugal procedures’, on the other hand, refer to meticulously planned multi-exposition architecture (as seen in the fugues in F-sharp minor exploiting two subsidiary subjects, and B-flat minor exploiting inversion and stretto) and a form in which the appearance of the subsidiary subject is gradually predicted in the fugal discourse (viz. C-sharp minor, G-sharp minor and B major). All these new ideas helped Bach to write more dramatic, more profound fugues for WTC II. The paper will consider how Bach came to acquire the new techniques and to use them in such ways, and what motivated him to adopt these new compositional approaches. Do they offer any clues for our better understanding of why Bach compiled the WTC II?

Book Review: Critical Perspectives on Human Rights and Disability Law

Book Review