On the structure of the body of states with positive partial transpose

We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random boundary state to be separable, provided the random states are generated uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An analogous property holds for the set of positive-partial-transpose states for an arbitrary bipartite system.Comment: 10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma

Transport and conservation laws

We study the lowest order conservation laws in one-dimensional (1D) integrable quantum many-body models (IQM) as the Heisenberg spin 1/2 chain, the Hubbard and t-J model. We show that the energy current is closely related to the first conservation law in these models and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero frequency component of the conductivity) and so ideal conductivity at finite temperatures.Comment: 6 pages, Late

Jacobi structures revisited

Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie algebroids in the sense of Iglesias and Marrero and can be viewed also as odd Jacobi brackets on the supermanifolds associated with the vector bundles. Jacobi bialgebroids are defined in the same manner. A lifting procedure of elements of this Grassmann algebra to multivector fields on the total space of the vector bundle which preserves the corresponding brackets is developed. This gives the possibility of associating canonically a Lie algebroid with any local Lie algebra in the sense of Kirillov.Comment: 20 page

Interplane magnetic coupling effects in the multilattice compound Y_2Ba_4Cu_7O_{15}

We investigate the interplane magnetic coupling of the multilattice compound Y_2Ba_4Cu_7O_{15} by means of a bilayer Hubbard model with inequivalent planes. We evaluate the spin response, effective interaction and the intra- and interplane spin-spin relaxation times within the fluctuation exchange approximation. We show that strong in-plane antiferromagnetic fluctuations are responsible for a magnetic coupling between the planes, which in turns leads to a tendency of the fluctuation in the two planes to equalize. This equalization effect grows whit increasing in-plane antiferromagnetic fluctuations, i. e., with decreasing temperature and decreasing doping, while it is completely absent when the in-layer correlation length becomes of the order of one lattice spacing. Our results provide a good qualitative description of NMR and NQR experiments in Y_2Ba_4Cu_7O_{15}.Comment: Final version, to appear. in Phys. Rev. B (Rapid Communications), sched. Jan. 9

Differential Geometry of Quantum States, Observables and Evolution

The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the relevant geometrical structures and their associated algebraic properties are highlighted, and the Qubit example is thoroughly discussed.Comment: 20 pages, comments are welcome

Effects of Electronic Correlations on the Thermoelectric Power of the Cuprates

We show that important anomalous features of the normal-state thermoelectric power S of high-Tc materials can be understood as being caused by doping dependent short-range antiferromagnetic correlations. The theory is based on the fluctuation-exchange approximation applied to Hubbard model in the framework of the Kubo formalism. Firstly, the characteristic maximum of S as function of temperature can be explained by the anomalous momentum dependence of the single-particle scattering rate. Secondly, we discuss the role of the actual Fermi surface shape for the occurrence of a sign change of S as a function of temperature and doping.Comment: 4 pages, with eps figure

A Tale of Two Set Theories

We describe the relationship between two versions of Tarski-Grothendieck set theory: the first-order set theory of Mizar and the higher-order set theory of Egal. We show how certain higher-order terms and propositions in Egal have equivalent first-order presentations. We then prove Tarski's Axiom A (an axiom in Mizar) in Egal and construct a Grothendieck Universe operator (a primitive with axioms in Egal) in Mizar

New symmetries of the chiral Potts model

In this paper a hithertho unknown symmetry of the three-state chiral Potts model is found consisting of two coupled Temperley-Lieb algebras. From these we can construct new superintegrable models. One realisation is in terms of a staggered isotropic XY spin chain. Further we investigate the importance of the algebra for the existence of mutually commuting charges. This leads us to a natural generalisation of the boost-operator, which generates the charges.Comment: 19 pages, improved notation, made the text easier to read, corrected some typo

Possible high TcT_c superconductivity mediated by antiferromagnetic spin fluctuations in systems with Fermi surface pockets

We propose that if there are two small pocket-like Fermi surfaces, and the spin susceptibility is pronounced around a wave vector {\bf Q} that bridges the two pockets, the spin-singlet superconductivity mediated by spin fluctuations may have a high transition temperature. Using the fluctuation exchange approximation, this idea is confirmed for the Hubbard on a lattice with alternating hopping integrals, for which $T_c$ is estimated to be almost an order of magnitude larger than those for systems with a large connected Fermi surface.Comment: 5 pages, uses RevTe

The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature

Motivated by recent investigations of transport properties of strongly correlated 1d models and thermal conductivity measurements of quasi 1d magnetic systems we present results for the integrable spin-1/2 $XXZ$ chain. The thermal conductivity $\kappa(\omega)$ of this model has $\Re\kappa(\omega)=\tilde\kappa \delta(\omega)$, i.e. it is infinite for zero frequency $\omega$. The weight $\tilde\kappa$ of the delta peak is calculated exactly by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy are presented. The low and high temperature limits are studied analytically.Comment: 12 page