Squeezed coherent states and the one-dimensional Morse quantum system

The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of harmonic oscillator using ladder operators. Properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule.Comment: 15 pages, 10 figures. $\bullet$Revised section 4, results unchanged. Correction of formulas 35 and 37. Results unchanged because all variables are real numbers. arXiv admin note: substantial text overlap with arXiv:1010.327

Simple Applications of q-Bosons

A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which is a generalisation of the Heisenberg-Weyl algebra obtained by introducing a deformation parameter $q$. Further, we present a new algebraic realization of the $q$-bosons, for the case of $q$ being a root of unity, which corresponds to a periodic structure described by a finite-dimensional representation. We show that this structure represents the symmetry of a linear lattice with periodic boundary conditions.Comment: LATEX2e, 10 pages, v2: few misprints corrected, added Journal-re

Dynamic model of gene regulation for the lac operon

Gene regulatory network is a collection of DNA which interact with each other and with other matter in the cell. The lac operon is an example of a relatively simple genetic network and is one of the best-studied structures in the Escherichia coli bacteria. In this work we consider a deterministic model of the lac operon with a noise term, representing the stochastic nature of the regulation. The model is written in terms of a system of simultaneous first order differential equations with delays. We investigate an analytical and numerical solution and analyse the range of values for the parameters corresponding to a stable solution

Surface effects in preparation of cell-size liposomes

AbstractEffects of surface type and area were shown to be important in the yield of cell-size liposomes, but not in determining their size. The liposomes were prepared by dissolving lipids in a chloroform-methanol solution and then evaporating the solvent under nitrogen in the presence of glass beads. After evaporation of the solvent, which was rapid due to the increased surface area, the dried lipids were then swollen in water at high temperatures (higher than the phase transition of the lipids), which led to formation of giant liposomes. The number of liposomes prepared in the presence of pyrex glass beads, which increase more than 100-times the surface area of lipid-glass contact, is more than 5-times larger than in the control experiments without glass beads. The yield of liposomes in the presence of another type of glass bead was almost the same as in the control experiments. These effects may be due to long- and short-range intermolecular interactions in the glass/water/lipid system

Global Stability and Periodicity in a Glucose-Insulin Regulation Model with a Single Delay

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be globally asymptotically stable. They are given in terms of the global attractivity of the fixed point in a limiting interval map. The existence of slowly oscillating periodic solutions is shown in the case when the equilibrium is unstable. The mathematical results are supported by extensive numerical simulations. It is shown that typical behaviour in the system is the convergence to either a stable periodic solution or to the unique stable equilibrium. The coexistence of several periodic solutions together with the stable equilibrium is demonstrated as a possibility.Comment: Accepted to Communications in Nonlinear Science and Numerical Simulatio

Generalized Heisenberg Algebras and Fibonacci Series

We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two previous levels. This happens, for example, for systems having the energy spectrum given by Fibonacci sequence. Moreover, the algebraic structure depends on two functions f(x) and g(x). When these two functions are linear we classify, analysing the stability of the fixed points of the functions, the possible representations for this algebra.Comment: 24 pages, 2 figures, subfigure.st