Generalized Coherent States and Spin S≥1S\geq 1 Systems

Generalized Coherent States (GCS) are constructed (and discussed) in order to study quasiclassical behaviour of quantum spin models of the Heisenberg type. Several such models are taken to their semiclassical limits, whose form depends on the spin value as well as the Hamiltonian symmetry. In the continuum approximation, SU(2)/U(1) GCS when applied give rise to the well-known Landau-Lifshitz classical phenomenology. For arbitrary spin values one obtains a lattice of coupled nonlinear oscillators. Corresponding classical continuum models are described as well.Comment: 18 pages, LaTeX. Submitted to J. of Phys. A: Math. and Ge

Mean-Reverting Stochastic Processes, Evaluation of Forward Prices and Interest Rates

We consider mean-reverting stochastic processes and build self-consistent models for forward price dynamics and some applications in power industries. These models are built using the ideas and equations of stochastic differential geometry in order to close the system of equations for the forward prices and their volatility. Some analytical solutions are presented in the one factor case and for specific regular forward price/interest rates volatility. Those models will also play a role of initial conditions for a stochastic process describing forward price and interest rates volatility. Subsequently, the curved manifold of the internal space i.e. a discrete version of the bond term space (the space of bond maturing) is constructed. The dynamics of the point of this internal space that correspond to a portfolio of different bonds is studied. The analysis of the discount bond forward rate dynamics, for which we employed the Stratonovich approach, permitted us to calculate analytically the regular and the stochastic volatilities. We compare our results with those known from the literature.: Stochastic Differential Geometry, Mean-Reverting Stochastic Processes and Term Structure of Specific (Some) Economic/Finance Instruments

Quantifying Flexibility Real Options Calculus

We expose a real options theory as a tool for quantifying the value of the operating flexibility of real assets. Additionally, we have pointed out that this theory is an appropriated methodology for determining optimal operating policies, and provide an example of successful application of our approach to power industries, specifically to valuate the power plant of electricity. In particular by increasing the volatility of prices will eventually lead to higher assets values.real options, Black-Scholes Approach, Wiener processes, stochastic processes, Quantifying Flexibility, volatility

A BPS Skyrme model and baryons at large Nc

Within the class of field theories with the field contents of the Skyrme model, one submodel can be found which consists of the square of the baryon current and a potential term only. For this submodel, a Bogomolny bound exists and the static soliton solutions saturate this bound. Further, already on the classical level, this BPS Skyrme model reproduces some features of the liquid drop model of nuclei. Here, we investigate the model in more detail and, besides, we perform the rigid rotor quantization of the simplest Skyrmion (the nucleon). In addition, we discuss indications that the viability of the model as a low energy effective field theory for QCD is further improved in the limit of a large number of colors N_c.Comment: latex, 23 pages, 1 figure, a numerical error in section 3.2 corrected; matches published versio

Integrable subsystem of Yang--Mills dilaton theory

With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton. Here integrability means the existence of infinitely many symmetries and infinitely many conserved currents. Further, we construct infinitely many static solutions of this integrable subsystem. These solutions can be identified with certain limiting solutions of the full system, which have been found previously in the context of numerical investigations of the Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the integrable subsystem and show that our static solutions are, in fact, Bogomolny solutions. This explains the linear growth of their energies with the topological charge, which has been observed previously. Finally, we discuss some generalisations.Comment: 25 pages, LaTex. Version 3: appendix added where the equivalence of the field equations for the full model and the submodel is demonstrated; references and some comments adde

Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schr\"odinger equations

Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients are obtained by using Hirota's bilinearization method. Generally, for the mixed N-CNLS equations the bright and dark solitons can be split up in $(N-1)$ ways. By analysing the collision dynamics of these coupled bright and dark solitons systematically we point out that for $N>2$, if the bright solitons appear in at least two components, non-trivial effects like onset of intensity redistribution, amplitude dependent phase-shift and change in relative separation distance take place in the bright solitons during collision. However their counterparts, the dark solitons, undergo elastic collision but experience the same amplitude dependent phase-shift as that of bright solitons. Thus in the mixed CNLS system there co-exist shape changing collision of bright solitons and elastic collision of dark solitons with amplitude dependent phase-shift, thereby influencing each other mutually in an intricate way.Comment: Accepted for publication in Physical Review

Quantifying Flexibility Real Options Calculus

We expose a real options theory as a tool for quantifying the value of the operating flexibility of real assets. Additionally, we have pointed out that this theory is an appropriated methodology for determining optimal operating policies, and provide an example of successful application of our approach to power industries, specifically to valuate the power plant of electricity. In particular by increasing the volatility of prices will eventually lead to higher assets values

Mean-Reverting Stochastic Processes, Evaluation of Forward Prices and Interest Rates

We consider mean-reverting stochastic processes and build self-consistent models for forward price dynamics and some applications in power industries. These models are built using the ideas and equations of stochastic differential geometry in order to close the system of equations for the forward prices and their volatility. Some analytical solutions are presented in the one factor case and for specific regular forward price/interest rates volatility. Those models will also play a role of initial conditions for a stochastic process describing forward price and interest rates volatility. Subsequently, the curved manifold of the internal space i.e. a discrete version of the bond term space (the space of bond maturing) is constructed. The dynamics of the point of this internal space that correspond to a portfolio of different bonds is studied. The analysis of the discount bond forward rate dynamics, for which we employed the Stratonovich approach, permitted us to calculate analytically the regular and the stochastic volatilities. We compare our results with those known from the literature