A generating functional approach to the Hubbard model

The method of generating functional is generalized to the case of strongly correlated systems, and applied to the Hubbard model. For the electronic Green's function constructed for Hubbard operators, an equation using variational derivatives with respect to the fluctuating fields has been derived and its multiplicative form has been determined. Corrections for the electronic self-energy are calculated up to the second order with respect to the parameter W/U (W width of the band), and a mean field type approximation was formulated, including both charge and spin static fluctuations. The equations for the Bose-like Green's functions have been derived, describing the collective modes: the magnons and doublons. The properties of the poles of the doublon Green's functions depend on electronic filling. The investigation of the special case n=1 demonstrates that the doublon Green's function has a soft mode at the wave vector Q=(pi,pi,...), indicating possible instability of the uniform paramagnetic phase relatively to the two sublattices charge ordering. However this instability should compete with an instability to antiferromagnetic ordering.Comment: 31 pages, 7 figures, to be published in Eur. Phys. J.

Enumeration of chord diagrams on many intervals and their non-orientable analogs

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the former case, we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter, we instead record the number of boundary cycles of each fixed length. Second order, non-linear, algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes. Moreover, these generating functions provide multi-parameter families of solutions to the KP hierarchy. For each model, there is furthermore a non-orientable analog, and each such model likewise has its own associated differential equation. The enumerative problems we solve are interpreted in terms of certain polygon gluings. As specific applications, we discuss models of several interacting RNA molecules. We also study a matrix integral which computes numbers of chord diagrams in both orientable and non-orientable cases in the model with bivalent vertices, and the large-N limit is computed using techniques of free probability.Comment: 23 pages, 7 figures; revised and extended versio

Prediction of physical-chemical and fire hazard characteristics by carbon chain rules. 2. Carboxylic acids

Investigation of the dependence of physico-chemical and fire hazard properties from the chemical structure of carboxylic acids is carried out. Forecasting of the boiling temperature, the flash point, the temperature and the concentration flammability limits, the heats of combustion and vaporization is performed by the carbon chain rules (CCR). The following empirical equations for the calculation of physico-chemical and fire hazard indices from the conventional carbon chain and from the number of carbon atoms are proposed for the convenience of practical application of the CCR. A comparative analysis of the proposed methods for the flash point calculating and the already known methods of GOST 12.1.044-89, Mendeleev and ACD/Lab 2014 is carried out. It is shown, basically, that the new methods give more accurate calculation results than the comparison design procedures. © Siberian Federal University. All rights reserve

On Possible Measurement of Gravitational Interaction Parameters on Board a Satellite

The recently suggested SEE (Satellite Energy Exchange) method of measuring the gravitational constant $G$, possible equivalence principle violation (measured by the E\"{o}tv\"{o}s parameter $\eta$) and the hypothetic 5th force parameters $\alpha$ and $\lambda$ on board a drag-free Earth's satellite is discussed and further developed. Various particle trajectories near a heavy ball are numerically simulated. Some basic sources of error are analysed. The $G$ measurement procedure is modelled by noise insertion to a ``true'' trajectory. It is concluded that the present knowledge of $G, \alpha$ (for $\lambda \geq 1$ m) and $\eta$ can be improved by at least two orders of magnitude.Comment: (only two misprints on title page) 7 page

Plasma Catalytic Reforming of Natural Gas

In this paper, recent results of plasma processing of natural gas are described. The use of a plasma reformer for the generation of hydrogen rich gas from natural gas has been investigated. In an accompanying paper, progress in plasma reforming of diesel fuel is described. The reformate composition has been investigated as a function of the initial mixture of air and methane. High methane conversion, near 100%, was obtained at relatively low values of plasmatron power. Soon-to-be-implements improvements in the overall reformer, including multiple heat exchanger for efficient thermal management and multiple water shift reactors, are described. 1