A family of irreducible free divisors in P^2

An infinite family of irreducible homogeneous free divisors in $K[x, y, z]$ is constructed. Indeed, we identify sets of monomials $X$ such that the general polynomial supported on $X$ is a free divisor.Comment: comments are welcom

Optimal suppression of defect generation during a passage across a quantum critical point

The dynamics of quantum phase transitions are inevitably accompanied by the formation of defects when crossing a quantum critical point. For a generic class of quantum critical systems, we solve the problem of minimizing the production of defects through the use of a gradient-based deterministic optimal control algorithm. By considering a finite size quantum Ising model with a tunable global transverse field, we show that an optimal power law quench of the transverse field across the Ising critical point works well at minimizing the number of defects, in spite of being drawn from a subset of quench profiles. These power law quenches are shown to be inherently robust against noise. The optimized defect density exhibits a transition at a critical ratio of the quench duration to the system size, which we argue coincides with the intrinsic speed limit for quantum evolution.Comment: 5 pages, 4 figures. The first two authors contributed equally to this wor

Rabi oscillations, decoherence, and disentanglement in a qubit-spin-bath system: exact dynamics

We examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one-dimensional spin bath. In contrast to previous studies, both the qubit-bath coupling and the nearest neighbor intrabath couplings are taken as the spin-flip XX-type. We first study the Rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state, finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics. Next, we discuss the bath-induced decoherence of the qubit when the bath is initially in the ground state, and show that the decoherence properties depend on the internal phases of the spin bath. By considering two independent copies of the qubit-bath system, we finally probe the disentanglement dynamics of two noninteracting entangled qubits. We find that entanglement sudden death appears when the spin bath is in its critical phase. We show that the single-qubit decoherence factor is an upper bound for the two-qubit concurrence.Comment: 15 pages, 9 figures. Ning Wu and Arun Nanduri equally contributed to this wor

Entanglement spreading in a many-body localized system

Motivated by the findings of logarithmic spreading of entanglement in a many-body localized system, we more closely examine the spreading of entanglement in the fully many-body localized phase, where all many-body eigenstates are localized. Performing full diagonalizations of an XXZ spin model with random longitudinal fields, we identify two factors contributing to the spreading rate: the localization length ($\xi$), which depends on the disorder strength, and the final value of entanglement per spin ($s_\infty$), which primarily depends on the initial state. We find that the entanglement entropy grows with time as $\sim \xi \times s_\infty \log t$, providing support for the phenomenology of many-body localized systems recently proposed by Huse and Oganesyan [arXiv:1305.4915v1].Comment: 7 pages, 5 figure

Optimization of parameters and study of kinetics in lactulose production by lactose isomerization using strong basic anion exchange resin

In this work, an experimental design was employed to investigate the effects of different operating conditions on the isomerization of lactose to lactulose by using strong basic anion exchange resin (AMBERLITE-IRA 402). Temperature, resin/lactose mass ratio and pH were considered to be the three factors affecting the conversion of lactose. Box-Behnken design was then used to optimize the operating conditions for maximum response and also to study the various interaction and main effects of the factors. The analysis of variance (ANOVA) of the experimental data showed a high correlation coefficient R² (0.99) and a low root mean square error (2.84) values for the second order regression model for the experimental design, indicating the good predictive nature of the model. The results gave an operating condition of temperature = 80.8⁰C, resin/lactose mass ratio = 0.371 and pH = 10.3 for maximum response. A kinetic model was deduced on the basis of Langmuir-Hinshelwood-Hougen-Watson formulation and the experimental data was later fit to the model by using least square approximation to estimate the activation energy (Ea), pre-exponential factor (A0) and the adsorption coefficient (K₁). The effect of resin bead diameter was also studied and the results indicated that the bead diameter of the as-received resin is sufficiently small to eliminate internal diffusion resistances. --Abstract, page iii

Further Understanding the Efficacy of Music-Based Cognitive Remediation Therapy for Patients with Traumatic Brain Injury

Objective To further assess the efficacy of music-based interventions in patients with traumatic brain injury and its therapeutic application to cognitive, motor and sensory deficits due to neurological sequalae Introduction - Traumatic brain injury is a direct result of an external force disabling neurological and neurophysiological functioning - Sensory, motor, emotional, language and cognitive functioning impaired - Treatment is usually cognitive remediation therapy (CR) - In correspondence, music enhances cognitive performance via neural plasticity - Current literature shows preliminary evidence of the positive results of music in parallel with C