A class of cubic Rauzy Fractals

In this paper, we study arithmetical and topological properties for a class of Rauzy fractals ${\mathcal R}_a$ given by the polynomial $x^3- ax^2+x-1$ where $a \geq 2$ is an integer. In particular, we prove the number of neighbors of ${\mathcal R}_a$ in the periodic tiling is equal to $8$. We also give explicitly an automaton that generates the boundary of ${\mathcal R}_a$. As a consequence, we prove that ${\mathcal R}_2$ is homeomorphic to a topological disk

Noise properties of two single electron transistors coupled by a nanomechanical resonator

We analyze the noise properties of two single electron transistors (SETs) coupled via a shared voltage gate consisting of a nanomechanical resonator. Working in the regime where the resonator can be treated as a classical system, we find that the SETs act on the resonator like two independent heat baths. The coupling to the resonator generates positive correlations in the currents flowing through each of the SETs as well as between the two currents. In the regime where the dynamics of the resonator is dominated by the back-action of the SETs, these positive correlations can lead to parametrically large enhancements of the low frequency current noise. These noise properties can be understood in terms of the effects on the SET currents of fluctuations in the state of a resonator in thermal equilibrium which persist for times of order the resonator damping time.Comment: Accepted for publication in Phys. Rev.

Generalization of Dirac Non-Linear Electrodynamics, and Spinning Charged Particles

In this note we generalized the Dirac non-linear electrodynamics, by introducing two potentials (namely, the vector potential A and the pseudo-vector potential gamma^5 B of the electromagnetic theory with charges and magnetic monopoles) and by imposing the pseudoscalar part of the product omega.omega* to be zero, with omega = A + gamma^5 B. We show that the field equations of such a theory possess a soliton-like solution which can represent a priori a "charged particle", since it is endowed with a Coulomb field plus the field of a magnetic dipole. The rest energy of the soliton is finite, and the angular momentum stored in its electromagnetic field can be identified --for suitable choices of the parameters-- with the spin of the charged particle. Thus this approach seems to yield a classical model for the charged (spinning) particle, which does not meet the problems met by earlier attempts in the same direction.Comment: standard LaTeX file; 16 pages; it is a corrected version of a paper appeared in Found. Phys. (issue in honour of A.O.Barut) 23 (1993) 46

Bifurcations from families of periodic solutions in piecewise differential systems

Consider a differential system of the form $$x'=F_0(t,x)+\sum_{i=1}^k \varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon),$$ where $F_i:\mathbb{S}^1 \times D \to \mathbb{R}^m$ and $R:\mathbb{S}^1 \times D \times (-\varepsilon_0,\varepsilon_0) \to \mathbb{R}^m$ are piecewise $C^{k+1}$ functions and $T$-periodic in the variable $t$. Assuming that the unperturbed system $x'=F_0(t,x)$ has a $d$-dimensional submanifold of periodic solutions with $d<m$, we use the Lyapunov-Schmidt reduction and the averaging theory to study the existence of isolated $T$-periodic solutions of the above differential system

Dynamical instabilities of a resonator driven by a superconducting single-electron transistor

We investigate the dynamical instabilities of a resonator coupled to a superconducting single-electron transistor (SSET) tuned to the Josephson quasiparticle (JQP) resonance. Starting from the quantum master equation of the system, we use a standard semiclassical approximation to derive a closed set of mean field equations which describe the average dynamics of the resonator and SSET charge. Using amplitude and phase coordinates for the resonator and assuming that the amplitude changes much more slowly than the phase, we explore the instabilities which arise in the resonator dynamics as a function of coupling to the SSET, detuning from the JQP resonance and the resonator frequency. We find that the locations (in parameter space) and sizes of the limit cycle states predicted by the mean field equations agree well with numerical solutions of the full master equation for sufficiently weak SSET-resonator coupling. The mean field equations also give a good qualitative description of the set of dynamical transitions in the resonator state that occur as the coupling is progressively increased.Comment: 23 pages, 6 Figures, Accepted for NJ

The Einstein-Hilbert Lagrangian Density in a 2-dimensional Spacetime is an Exact Differential

Recently Kiriushcheva and Kuzmin claimed to have shown that the Einstein-Hilbert Lagrangian cannot be written in any coordinate gauge as an exact differential in a 2-dimensional spacetime. Since this is contrary to other statements on the subject found in the literature, as e.g., by Deser and Jackiw, Jackiw, Grumiller, Kummer and Vassilevich it is necessary to do decide who has reason. This is done in this paper in a very simply way using the Clifford bundle formalism. In this version we added Section 18 which discusses a recent comment on our paper just posted by Kiriushcheva and Kuzmin.Comment: 11 pages, Misprints in some equations have been corrected; four new references have been added, Section 18 adde