We discuss a class of phantom ($p < - \varrho$) cosmological models. Except
for phantom we admit various forms of standard types of matter and discuss the
problem of singularities for these cosmologies. The singularities are different
from those of standard matter cosmology since they appear for infinite values
of the scale factor. We also find an interesting relation between the phantom
models and standard matter models which is like the duality symmetry of string
cosmology.Comment: 10 pages, Revtex4, 10 figures, an improved version. references adde
It is shown that in the Rabi model, for an integer value of the spectral
parameter $x$, in addition to the finite number of the classical Judd states
there exist infinitely many possible eigenstates. These eigenstates exist if
the parameters of the problem are zeros of a certain transcendental function;
in other words, there are infinitely many possible choices of parameters for
which integer $x$ belongs to the spectrum. Morover, it is shown that the
classical Judd eigenstates appear as degenerate cases of the confluent Heun
function.Comment: 7 pages, 4 figure
We formulate a universal method for solving an arbitrary quantum system which, in the Bargmann representation, is described by a system of linear equations with one independent variable, such as one-and multi-photon Rabi models, or N level systems interacting with a single mode of the electromagnetic field and their various generalizations. We explain three types of conditions that determine the spectrum and show their usage for two deformations of the Rabi model. We prove that the spectra of both models are just zeros of transcendental functions, which in one case are given explicitly in terms of confluent Heun functions.
We analyse the double pendulum system numerically, using a modified mid point integrator. Poincaré sections and bifurcation diagrams are constructed for certain, characteristic values of energy. The largest Lyapunov characteristic exponents are also calculated. All three methods confirm the passing of the system from the regular low energy limit into chaos as energy is increased.
In this paper we study the flat (k = 0) cosmological FRW model with holonomy corrections of Loop Quantum Gravity. The considered universe contains a massless scalar field and the cosmological constant Λ. We find analytical solutions for this model in different configurations and investigate its dynamical behaviour in the whole phase space. We show the explicit influence of Λ on the qualitative and quantitative character of solutions. Even in the case of positive Λ the oscillating solutions without the initial and final singularity appear as a generic case for some quantisation schemes. * Electronic address: jakubm@poczta.onet.pl † Electronic address:
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