Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2

The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the Gaussian symplectic ensemble is demonstrated. A duality between the underlying generating functions of the orthogonal and symplectic symmetry classes is semiclassically established

Semiclassical approach to discrete symmetries in quantum chaos

We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to irreducible representations of the corresponding symmetry group. We show that for (spinless) time reversal invariant systems the statistics inside these subspectra depend on the type of irreducible representation. For real representations the spectral statistics agree with those of the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory (RMT), whereas complex representations correspond to the Gaussian Unitary Ensemble (GUE). For systems without time reversal invariance all subspectra show GUE statistics. There are no correlations between non-degenerate subspectra. Our techniques generalize recent developments in the semiclassical approach to quantum chaos allowing one to obtain full agreement with the two-point correlation function predicted by RMT, including oscillatory contributions.Comment: 26 pages, 8 Figure

Russia’s Legal Transitions: Marxist Theory, Neoclassical Economics and the Rule of Law

We review the role of economic theory in shaping the process of legal change in Russia during the two transitions it experienced during the course of the twentieth century: the transition to a socialist economy organised along the lines of state ownership of the means of production in the 1920s, and the transition to a market economy which occurred after the fall of the Soviet Union in the 1990s. Despite differences in methodology and in policy implications, Marxist theory, dominant in the 1920s, and neoclassical economics, dominant in the 1990s, offered a similarly reductive account of law as subservient to wider economic forces. In both cases, the subordinate place accorded to law undermined the transition process. Although path dependence and history are frequently invoked to explain the limited development of the rule of law in Russia during the 1990s, policy choices driven by a deterministic conception of law and economics also played a role.This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s40803-015-0012-

Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces

In this article we consider solvable hypersurfaces of the form with induced metrics in the symmetric space , where H a suitable unit length vector in the subgroup A of the Iwasawa decomposition . Since M is rank 2, A is 2-dimensional and we can parametrize these hypersurfaces via an angle determining the direction of H. We show that one of the hypersurfaces (corresponding to ) is minimally embedded and isometric to the non-symmetric 7-dimensional Damek-Ricci space. We also provide an explicit formula for the Ricci curvatures of these hypersurfaces and show that all hypersurfaces for admit planes of both negative and positive sectional curvature. Moreover, the symmetric space M admits a minimal foliation with all leaves isometric to the non-symmetric 7-dimensional Damek-Ricci space