On the Topological Origin of Entanglement in Ising Spin Glasses

The origin of thermal and quantum entanglement in a class of three-dimensional spin models, at low momenta, is traced to purely topological reasons. The establishment of the result is facilitated by the gauge principle which, when used in conjunction with the duality mapping of the spin models, enables us to recast them as lattice Chern-Simons gauge theories. The thermal and quantum entanglement measures are expressed in terms of the expectation values of Wilson lines, loops, and their generalisations. For continuous spins, these are known to yield the topological invariants of knots and links. For Ising-like models, they are expressible in terms of the topological invariants of three-manifolds obtained from finite group cohomology -- the so-called Dijkgraaf-Witten invariants.Comment: RevTex4, 6 page

Coherent States of SU(l,1)SU(l,1) groups

This work can be considered as a continuation of our previous one (J.Phys., 26 (1993) 313), in which an explicit form of coherent states (CS) for all SU(N) groups was constructed by means of representations on polynomials. Here we extend that approach to any SU(l,1) group and construct explicitly corresponding CS. The CS are parametrized by dots of a coset space, which is, in that particular case, the open complex ball $CD^{l}$. This space together with the projective space $CP^{l}$, which parametrizes CS of the SU(l+1) group, exhausts all complex spaces of constant curvature. Thus, both sets of CS provide a possibility for an explicit analysis of the quantization problem on all the spaces of constant curvature.Comment: 22 pages, to be published in "Journal of Physics A

Supersymmetric null-surfaces

Single trace operators with the large R-charge in supersymmetric Yang-Mills theory correspond to the null-surfaces in $AdS_5\times S^5$. We argue that the moduli space of the null-surfaces is the space of contours in the super-Grassmanian parametrizing the complex $(2|2)$-dimensional subspaces of the complex $(4|4)$-dimensional space. The odd coordinates on this super-Grassmanian correspond to the fermionic degrees of freedom of the superstring.Comment: v4: added a reference to the earlier work; corrected the formula for the stabilizer of the BMN vacuum; added the discussion of the complex structure of the odd coordinates in Section 3.

Ordering in discotic liquid crystals

Phase transitions in discotic liquid crystals are analysed in the Landau theory. Possible types of order in such systems are studied.On analyse sur la base de la théorie de Landau les transitions de phases dans des cristaux liquides discotiques. On étudie les types d'ordre possibles dans ces systèmes

Rapid computation of optimal control for vehicles

This paper describes a rapid computational method of optimal control for vehicles and the software realizing it. The optimal control problem is solved with the dynamic programming technique. A traditional engineering simulator is used to predict the vehicle's performance and economy. An objective function is suggested that permits high-speed computation. Results show the dependence of optimal fuel consumption on average speed for various vehicle masses in a number of situations: acceleration from rest to cruising speed, driving between stop signs and driving on hilly terrain. Findings include that one can travel up to 20 to 80% (depending on the situation) faster than the most economical average speed without increasing fuel consumption more than an equal amount.