A generalized Pancharatnam geometric phase formula for three level systems

We describe a generalisation of the well known Pancharatnam geometric phase formula for two level systems, to evolution of a three-level system along a geodesic triangle in state space. This is achieved by using a recently developed generalisation of the Poincare sphere method, to represent pure states of a three-level quantum system in a convenient geometrical manner. The construction depends on the properties of the group SU(3)\/ and its generators in the defining representation, and uses geometrical objects and operations in an eight dimensional real Euclidean space. Implications for an n-level system are also discussed.Comment: 12 pages, Revtex, one figure, epsf used for figure insertio

Characterisations of Classical and Non-classical states of Quantised Radiation

A new operator based condition for distinguishing classical from non-classical states of quantised radiation is developed. It exploits the fact that the normal ordering rule of correspondence to go from classical to quantum dynamical variables does not in general maintain positivity. It is shown that the approach naturally leads to distinguishing several layers of increasing nonclassicality, with more layers as the number of modes increases. A generalisation of the notion of subpoissonian statistics for two-mode radiation fields is achieved by analysing completely all correlations and fluctuations in quadratic combinations of mode annihilation and creation operators conserving the total photon number. This generalisation is nontrivial and intrinsically two-mode as it goes beyond all possible single mode projections of the two-mode field. The nonclassicality of pair coherent states, squeezed vacuum and squeezed thermal states is analysed and contrasted with one another, comparing the generalised subpoissonian statistics with extant signatures of nonclassical behaviour.Comment: 16 pages, Revtex, One postscript Figure compressed and uuencoded Replaced, minor changes in eq 4.30 and 4.32. no effect on the result

Too Complex to Work: A Critical Assessment of the Bail-In Tool Under the European Bank Recovery and Resolution Regime

This paper analyses the bail-in tool under the BRRD and predicts that it will not reach its policy objective. To make this argument, this paper first describes the policy rationale that calls for mandatory PSI. From this analysis the key features for an effective bail-in tool can be derived. These insights serve as the background to make the case that the European resolution framework is likely ineffective in establishing adequate market discipline through risk-reflecting prices for bank capital. The main reason for this lies in the avoidable embeddedness of the BRRD’s bail-in tool in the much broader resolution process which entails ample discretion of the authorities also in forcing private sector involvement. Finally, this paper synthesized the prior analysis by putting forward an alternative regulatory approach that seeks to disentangle private sector involvement as a precondition for effective bank-resolution as much as possible form the resolution process as such