Large-deviation properties of the extended Moran model

The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta distribution Beta(alpha, 2-alpha) for various choices of alpha. This includes also the classical Moran model (alpha->0) as well as the uniform distribution (alpha=1). Using a statistical mechanics-based large-deviation approach, the distributions can be studied over an extended range of the support, down to probabilities like 10^{-70}, which allowed us to study the change of the tails of the distribution when varying the value of alpha in [0,2]. We find exponential distributions p(t_mrca)~ delta^{t_mrca} in all cases, with systematically varying values for the base delta. Only for the cases alpha=0 and alpha=1, analytical results are known, i.e., delta=\exp(-2/N^2) and delta=2/3, respectively. We recover these values, confirming the validity of our approach. Finally, we also study the correlations between t_mrca and the number of descendants.Comment: 8 pages, 8 figure

Discrete-time output feedback sliding-mode control design for uncertain systems using linear matrix inequalities

An output feedback-based sliding-mode control design methodology for discrete-time systems is considered in this article. In previous work, it has been shown that by identifying a minimal set of current and past outputs, an augmented system can be obtained which permits the design of a sliding surface based upon output information only, if the invariant zeros of this augmented system are stable. In this work, a procedure for realising discrete-time controllers via a particular set of extended outputs is presented for non-square systems with uncertainties. This method is applicable when unstable invariant zeros are present in the original system. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to obtain a Lyapunov matrix, which simultaneously satisfies both a Riccati inequality and a structural constraint, is used to formulate the corresponding control to solve the reachability problem. A numerical method using linear matrix inequalities is suggested to obtain the Lyapunov matrix. Finally, the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated

Non-equilibrium supercurrent through a quantum dot: current harmonics and proximity effect due to a normal metal lead

We consider a Hamiltonian model for a quantum dot which is placed between two superconducting leads with a constant bias imposed between these leads. Using the non-equilibrium Keldysh technique, we focus on the subgap current, where it is known that multiple Andreev reflections (MAR) are responsible for charge transfer through the dot. Attention is put on the DC current and on the first harmonics of the supercurrent. Varying the energy and width of the resonant level on the dot, we first investigate a cross-over from a quantum dot regime to a quantum point contact regime when there is zero coupling to the normal probe. We then study the effect on the supercurrent of the normal probe which is attached to the dot. This normal probe is understood to lead to dephasing, or alternatively to induce reverse proximity effect. We describe the full crossover from zero dephasing to the incoherent case. We also compute the Josephson current in the presence of the normal lead, and find it in excellent agreement with the values of the non-equlibrium current extrapolated at zero voltage

Exact wavefunctions for excitations of the nu=1/3 fractional quantum Hall state from a model Hamiltonian

We study fractional quantum Hall states in the cylinder geometry with open boundaries. By truncating the Coulomb interactions between electrons we show that it is possible to construct infinitely many exact eigenstates including the ground state, quasiholes, quasielectrons and the magnetoroton branch of excited states.Comment: 7 pages, 3 figures, longer published versio

Composite-fermionization of bosons in rapidly rotating atomic traps

The non-perturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. The system of neutral bosons in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic field, which has opened up the possibility of fractional quantum Hall effect for bosons interacting with a short range interaction. Motivated by the composite fermion theory of the fractional Hall effect of electrons, we test the idea that the interacting bosons map into non-interacting spinless fermions carrying one vortex each, by comparing wave functions incorporating this physics with exact wave functions available for systems containing up to 12 bosons. We study here the analogy between interacting bosons at filling factors $\nu=n/(n+1)$ with non-interacting fermions at $\nu^*=n$ for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small $n$, but interactions between fermions become increasingly important with $n$. At $\nu=1$, which is obtained in the limit $n\rightarrow \infty$, the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an {\em attractive} interactions between fermions, as evidenced by a pairing of fermions here.Comment: 8 pages, 3 figures. Submitted to Phys. Rev.