Thermodynamics of micellization of oppositely charged polymers

The complexation of oppositely charged colloidal objects is considered in this paper as a thermodynamic micellization process where each kind of object needs the others to micellize. This requirement gives rise to quantitatively different behaviors than the so-called mixed-micellization where each specie can micellize separately. A simple model of the grand potential for micelles is proposed to corroborate the predictions of this general approach.Comment: 7 pages, 2 figures. Accepted for publication in Europhysics Letter

Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems

We introduce a one-parameter generalized oscillator algebra A(k) (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter k. We define an (Hamiltonian) operator associated with A(k) and examine the degeneracies of its spectrum. For the finite (when k < 0) and the infinite (when k > 0 or = 0) representations of A(k), we construct the associated phase operators and build temporally stable phase states as eigenstates of the phase operators. To overcome the difficulties related to the phase operator in the infinite-dimensional case and to avoid the degeneracy problem for the finite-dimensional case, we introduce a truncation procedure which generalizes the one used by Pegg and Barnett for the harmonic oscillator. This yields a truncated generalized oscillator algebra A(k,s), where s denotes the truncation order. We construct two types of temporally stable states for A(k,s) (as eigenstates of a phase operator and as eigenstates of a polynomial in the generators of A(k,s)). Two applications are considered in this article. The first concerns physical realizations of A(k) and A(k,s) in the context of one-dimensional quantum systems with finite (Morse system) or infinite (Poeschl-Teller system) discrete spectra. The second deals with mutually unbiased bases used in quantum information.Comment: Accepted for publication in Journal of Physics A: Mathematical and Theoretical as a pape

Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect

We clearly show that the symplectic structures deformations lead, upon quantization, to quantum theories of non commutative fields. Two variants of deformations are considered. The quantization is performed and the modes expansions of the quantum fields are derived. The Hamiltonians are given and the degeneracies lifting induced by the deformation is also discussed. As illustration, we consider the noncommutative chiral boson fields in the context of fractional quantum Hall effect. A generalized fractional filling factor is derived and shown to reproduce the Jain Hall states. We also show that the coupling of left and right edge excitations of a quantum Hall sample, gives rise a noncommutative chiral boson theory. The coupling or the non-commutativity induces a shift of the chiral components velocities. A non linear dispersion relation is obtained corroborating some recent analytical and numerical analysis.Comment: 23 pages, Accepted for publication in IJMP