A Generalized Solution Method to Undamped Constant-Coefficient Second-Order ODEs Using Laplace Transforms and Fourier Series

A generalized method for solving an undamped second order, linear ordinary differential equation with constant coefficients is presented where the non-homogeneous term of the differential equation is represented by Fourier series and a solution is found through Laplace transforms. This method makes use of a particular partial fraction expansion form for finding the inverse Laplace transform. If a non-homogeneous function meets certain criteria for a Fourier series representation, then this technique can be used as a more automated means to solve the differential equation as transforms for specific functions need not be determined. The combined use of the Fourier series and Laplace transforms also reinforces the understanding of function representation through a Fourier series and its potential limitations, the mechanics of finding the Laplace transform of a differential equation and inverse transforms, the operation of an undamped system, and through programming insight into the practical application of both tools including information on the influence of the number of terms in the series solution

Special Case of Partial Fraction Expansion with Laplace Transform Application

Partial fraction expansion is often used with the Laplace Transforms to formulate algebraic expressions for which the inverse Laplace Transform can be easily found. This paper demonstrates a special case for which a linear, constant coefficient, second order ordinary differential equation with no damping term and a harmonic function non-homogeneous term leads to a simplified partial fraction expansion due to the decoupling of the partial fraction expansion coefficients of s and the constant coefficients. Recognizing this special form can allow for quicker calculations and automation of the solution to the differential equation form which is commonly used to model physical systems

Robust gates for holonomic quantum computation

Non Abelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. We study the effects of the environment (modelled as an ensemble of harmonic oscillators) on a holonomic transformation and write the corresponding master equation. The solution is analytically and numerically investigated and the behavior of the fidelity analyzed: fidelity revivals are observed and an optimal finite operation time is determined at which the gate is most robust against noise.Comment: 11 pages, 6 figure

Robustness against parametric noise of non ideal holonomic gates

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the very motivation of this robustness being the geometric character of the transformation achieved in the adiabatic limit. On the other hand, the effects of decoherence are expected to become more and more relevant when the adiabatic limit is approached. Starting from the system described by Florio et al. [Phys. Rev. A 73, 022327 (2006)], here we discuss the behavior of non ideal holonomic gates at finite operational time, i.e., far before the adiabatic limit is reached. We have considered several models of parametric noise and studied the robustness of finite time gates. The obtained results suggest that the finite time gates present some effects of cancellation of the perturbations introduced by the noise which mimic the geometrical cancellation effect of standard holonomic gates. Nevertheless, a careful analysis of the results leads to the conclusion that these effects are related to a dynamical instead of geometrical feature.Comment: 8 pages, 8 figures, several changes made, accepted for publication on Phys. Rev.

Modulation of amyloidogenic peptide aggregation by photoactivatable co-releasing ruthenium(II) complexes

Three Ru(II)-based CO-releasing molecules featuring bidentate benzimidazole and terpyridine derivatives as ligands were investigated for their ability to modulate the aggregation process of the second helix of the C-terminal domain of nucleophosmin 1, namely nucleophosmin 1 (NPM1)264–277, a model amyloidogenic system, before and after irradiation at 365 nm. Thioflavin T (ThT) binding assays and UV/Vis absorption spectra indicate that binding of the compounds to the peptide inhibits its aggregation and that the inhibitory effect increases upon irradiation (half maximal effective concentration (EC50) values in the high micromolar range). Electrospray ionization mass spectrometry data of the peptide in the presence of one of these compounds confirm that the modulation of amyloid aggregation relies on the formation of adducts obtained when the Ru compounds react with the peptide upon releasing of labile ligands, like chloride and carbon monoxide. This mechanism of action explains the subtle different behavior of the three compounds observed in ThT experiments. Overall, data support the hypothesis that metal-based CO releasing molecules can be used to develop metal-based drugs with potential application as anti-amyloidogenic agents

Transitional dynamics in a growth model with government spending, technological progress and population change

Abstract This paper extends public spending-based growth theory along three directions: we assume that exogenous and constant technological progress does exist and that both population change and the ratio of government expenditure to income follow a logistic trajectory. By focusing on the choices of a benevolent social planner we find that, if the inverse of the intertemporal elasticity of substitution in consumption is sufficiently high, the ratio of consumption to private physical capital converges towards zero when time goes to infinity. Through two examples we see that, depending on the form of the underlying aggregate production function and on whether, for given production function, technological progress equals zero or a positive constant, our model may or may not yield an asymptotic balanced growth path (ABGP) equilibrium. When there is no exogenous technological progress, an equilibrium where population size, the ratio of government spending to total income and the ratio of consumption to private physical capital are all constant does exist and the equilibrium is a saddle point. In case of positive technological progress numerical simulations show that the model still exhibits an ABGP equilibriu

Statistical mechanics of multipartite entanglement

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics.Comment: final versio

Robustness of optimal working points for non-adiabatic holonomic quantum computation

Geometric phases are an interesting resource for quantum computation, also in view of their robustness against decoherence effects. We study here the effects of the environment on a class of one-qubit holonomic gates that have been recently shown to be characterized by "optimal" working times. We numerically analyze the behavior of these optimal points and focus on their robustness against noise.Comment: 14 pages, 8 figure

Multipartite Entanglement and Frustration

Some features of the global entanglement of a composed quantum system can be quantified in terms of the purity of a balanced bipartition, made up of half of its subsystems. For the given bipartition, purity can always be minimized by taking a suitable (pure) state. When many bipartitions are considered, the requirement that purity be minimal for all bipartitions can engender conflicts and frustration arises. This unearths an interesting link between frustration and multipartite entanglement, defined as the average purity over all (balanced) bipartitions.Comment: 15 pages, 7 figure