138 research outputs found
Generalized Coherent States and Spin 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 ways. By analysing the collision
dynamics of these coupled bright and dark solitons systematically we point out
that for , 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
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