Thermodynamics and conformal properties of XXZ chains with alternating spins

The quantum periodic XXZ chain with alternating spins is studied. The properties of the related R-matrix and Hamiltonians are discussed. A compact expression for the ground state energy is obtained. The corresponding conformal anomaly is found via the finite-size computations and also by means of the Bethe ansatz method. In the presence of an external magnetic field, the magnetic susceptibility is derived. The results are also generalized to the case of a chain containing several different spins.Comment: 28 pages, LaTeX2

Loop Quantum Gravity a la Aharonov-Bohm

The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin-network graphs. In this paper I investigate the possibility of obtaining this state space from the quantization of a topological field theory with many degrees of freedom. The starting point is a 3-manifold with a network of defect-lines. A locally-flat connection on this manifold can have non-trivial holonomy around non-contractible loops. This is in fact the mathematical origin of the Aharonov-Bohm effect. I quantize this theory using standard field theoretical methods. The functional integral defining the scalar product is shown to reduce to a finite dimensional integral over moduli space. A non-trivial measure given by the Faddeev-Popov determinant is derived. I argue that the scalar product obtained coincides with the one used in Loop Quantum Gravity. I provide an explicit derivation in the case of a single defect-line, corresponding to a single loop in Loop Quantum Gravity. Moreover, I discuss the relation with spin-networks as used in the context of spin foam models.Comment: 19 pages, 1 figure; v2: corrected typos, section 4 expanded

Stability boundary analysis of magnetohydrodynamic circulator for the intermediate heat transfer system of prototype gen IV sodium fast reactor

One of the most important parts in the development of generation IV nuclear reactors is safety. In the research on generation IV sodium???cooled fast reactors, magnetohydrodynamic (MHD) circulators have received attention for the stable transport of coolants. In this study, the stability of an MHD circulator was evaluated using a mathematical approach to obtain the critical value of the developed pressure. The critical developed pressure equation is a function of the flow rate and dimensionless parameters, which were derived from the theoretical model of the MHD circulator with a dimensionless scaled velocity, flow rate, and pressure. The stability conditions expressed using the critical value of the developed pressure and dimensionless parameters were investigated according to the changes in the main design variables of the MHD circulator. The relationships between the dimensionless parameters, stability, and main design variables constituting the stability boundary of the MHD circulator were analysed. The stability of the MHD circulator is considered safe when the stability criterion ?? is lower than 1. The geometrical variables such as the duct thickness or width of the flow gap and electrical variables such as the frequency were the main parameters affecting the flow stability in the MHD circulator