Quantum chaos with spin-chains in pulsed magnetic fields

Recently it was found that the dynamics in a Heisenberg spin-chain subjected to a sequence of periodic pulses from an external, parabolic, magnetic field can have a close correspondence with the quantum kicked rotor (QKR). The QKR is a key paradigm of quantum chaos; it has as its classical limit the well-known Standard Map. It was found that a single spin excitation could be converted into a pair of non-dispersive, counter-propagating spin coherent states equivalent to the accelerator modes of the Standard Map. Here we consider how other types of quantum chaotic systems such as a double-kicked quantum rotor or a quantum rotor with a double-well potential might be realized with spin chains; we discuss the possibilities regarding manipulation of the one-magnon spin waves.Comment: 10 pages, 4 figures. Submitted to PTP special issue for QMC200

Periodically-driven cold atoms: the role of the phase

Numerous theoretical and experimental studies have investigated the dynamics of cold atoms subjected to time periodic fields. Novel effects dependent on the amplitude and frequency of the driving field, such as Coherent Destruction of Tunneling have been identified and observed. However, in the last year or so, three distinct types of experiments have demonstrated for the first time, interesting behaviour associated with the driving phase: i.e. for systems experiencing a driving field of general form $V(x)\sin (\omega t + \phi)$, different types of large scale oscillations and directed motion were observed. We investigate and explain the phenomenon of Super-Bloch Oscillations (SBOs) in relation to the other experiments and address the role of initial phase in general. We analyse and compare the role of $\phi$ in systems with homogeneous forces ($V'(x)= const$), such as cold atoms in shaken or amplitude-modulated optical lattices, as well as non-homogeneous forces ($V'(x)\neq const$), such as the sloshing of atoms in driven traps, and clarify the physical origin of the different $\phi$-dependent effects.Comment: 10 pages, 1 figur

Optimal control of a dengue epidemic model with vaccination

We present a SIR+ASI epidemic model to describe the interaction between human and dengue fever mosquito populations. A control strategy in the form of vaccination, to decrease the number of infected individuals, is used. An optimal control approach is applied in order to find the best way to fight the disease.Comment: This is a preprint of a paper accepted for presentation at ICNAAM 2011, Halkidiki, Greece, 19-25 September 2011, and to appear in AIP Conference Proceedings, volume 138

Modeling and Optimal Control Applied to a Vector Borne Disease

A model with six mutually-exclusive compartments related to Dengue disease is presented. In this model there are three vector control tools: insecticides (larvicide and adulticide) and mechanical control. The problem is studied using an Optimal Control (OC) approach. The human data for the model is based on the Cape Verde Dengue outbreak. Some control measures are simulated and their consequences analyzed

Insecticide control in a Dengue epidemics model

A model for the transmission of dengue disease is presented. It consists of eight mutually-exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquitoes. The main goal of this work is to investigate the best way to apply the control in order to effectively reduce the number of infected humans and mosquitoes. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.Comment: Accepted 28/07/2010 in the special session "Numerical Optimization" of the 8th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2010), Rhodes, Greece, 19-25 September 201

Doubly excited ferromagnetic spin-chain as a pair of coupled kicked rotors

We show that the dynamics of a doubly-excited 1D Heisenberg ferromagnetic chain, subject to short pulses from a parabolic magnetic field may be analyzed as a pair of quantum kicked rotors. By focusing on the two-magnon dynamics in the kicked XXZ model we investigate how the anisotropy parameter - which controls the strength of the magnon-magnon interaction - changes the nature of the coupling between the two "image" coupled Kicked Rotors. We investigate quantum state transfer possibilities and show that one may control whether the spin excitations are transmitted together, or separate from each other.Comment: 8 pages, 4 figures; extended appendix and corrected typo

Classical diffusion in double-delta-kicked particles

We investigate the classical chaotic diffusion of atoms subjected to {\em pairs} of closely spaced pulses (`kicks) from standing waves of light (the $2\delta$-KP). Recent experimental studies with cold atoms implied an underlying classical diffusion of type very different from the well-known paradigm of Hamiltonian chaos, the Standard Map. The kicks in each pair are separated by a small time interval $\epsilon \ll 1$, which together with the kick strength $K$, characterizes the transport. Phase space for the $2\delta$-KP is partitioned into momentum `cells' partially separated by momentum-trapping regions where diffusion is slow. We present here an analytical derivation of the classical diffusion for a $2\delta$-KP including all important correlations which were used to analyze the experimental data. We find a new asymptotic ($t \to \infty$) regime of `hindered' diffusion: while for the Standard Map the diffusion rate, for $K \gg 1$, $D \sim K^2/2[1- J_2(K)..]$ oscillates about the uncorrelated, rate $D_0 =K^2/2$, we find analytically, that the $2\delta$-KP can equal, but never diffuses faster than, a random walk rate. We argue this is due to the destruction of the important classical `accelerator modes' of the Standard Map. We analyze the experimental regime $0.1\lesssim K\epsilon \lesssim 1$, where quantum localisation lengths $L \sim \hbar^{-0.75}$ are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate $D\propto K^3\epsilon$, in correspondence to a $D\propto K^3$ regime in the Standard Map associated with 'golden-ratio' cantori.Comment: 14 pages, 10 figures, error in equation in appendix correcte