Exactness of the Original Grover Search Algorithm

It is well-known that when searching one out of four, the original Grover's search algorithm is exact; that is, it succeeds with certainty. It is natural to ask the inverse question: If we are not searching one out of four, is Grover's algorithm definitely not exact? In this article we give a complete answer to this question through some rationality results of trigonometric functions.Comment: 8 pages, 2 figure

Equation-free dynamic renormalization in a glassy compaction model

Combining dynamic renormalization with equation-free computational tools, we study the apparently self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time.Comment: 4 pages, 4 figures (Minor Modifications; Submitted Version

Early Time Dynamics of Gluon Fields in High Energy Nuclear Collisions

Nuclei colliding at very high energy create a strong, quasi-classical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromo-electric and chromo-magnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. For example, we find that the ratio of longitudinal to transverse pressure very early in the system behaves as $p_L/p_T = -[1-\frac{3}{2a}(Q\tau)^2]/[1-\frac{1}{a}(Q\tau)^2]+\mathcal{O}(Q\tau)^4$ where $\tau$ is the longitudinal proper time, $Q$ is related to the saturation scales $Q_s$ of the two nuclei, and $a = \ln (Q^2/\hat{m}^2)$ with $\hat m$ a scale to be defined later. Our results are generally applicable if $\tau \lesssim 1/Q$. As already discussed in a previous paper, the transverse energy flow $S^i$ of the gluon field exhibits hydrodynamic-like contributions that follow transverse gradients of the energy density $\nabla^i \varepsilon$. In addition, a rapidity-odd energy flow also emerges from the non-abelian analog of Gauss' Law and generates non-vanishing angular momentum of the field. We will discuss the space-time picture that emerges from our analysis and its implications for observables in heavy ion collisions.Comment: 26 pages, 9 figure

Shortcut to adiabatic passage in two and three level atoms

We propose a method to transfer the population and control the state of two-level and three-level atoms speeding-up Adiabatic Passage techniques while keeping their robustness versus parameter variations. The method is based on supplementing the standard laser beam setup of Adiabatic Passage methods with auxiliary steering laser pulses of orthogonal polarization. This provides a shortcut to adiabaticity driving the system along the adiabatic path defined by the standard setup.Comment: 4 pages, 4 figure

Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator

There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to reproduce the initial populations at some predetermined final frequency and time, providing lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.Comment: 7 pages, 6 figure

Strange sea distributions of the nucleon

The strange and antistrange quark distributions of the nucleon are less constrained by experimental data than the non-strange quark sea. The combination of light quark sea distributions, \Delta(x)=\dbar(x)+\ubar(x)-s(x)-\sbar(x), originates mainly from non-perturbative processes and can be calculated using non-perturbative models of the nucleon. We have calculated $\Delta(x)$ using the meson cloud model, which, when combined with the relatively well known non-strange light antiquark distributions obtained from global analysis of available experimental data, enables us to make new estimates of the total strange sea distributions of the nucleon and the strange sea suppression factor.Comment: version published in J. Phys. G, 14 pages, 3 figure

Strongly nonlinear waves in capillary electrophoresis

In capillary electrophoresis, sample ions migrate along a micro-capillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background.Under such conditions, the local migration velocity of sample ions becomes concentration dependent resulting in a nonlinear wave that exhibits shock like features. If the nonlinearity is weak, the sample concentration profile, under certain simplifying assumptions, can be shown to obey Burgers' equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which has an exact analytical solution for arbitrary initial condition.In this paper, we use a numerical method to study the problem in the more general case where the sample concentration is not small in comparison to the concentration of background ions. In the case of low concentrations, the numerical results agree with the weakly nonlinear theory presented earlier, but at high concentrations, the wave evolves in a way that is qualitatively different.Comment: 7 pages, 5 figures, 1 Appendix, 2 videos (supplementary material

All-electrical injection and detection of a spin polarized current using 1D conductors

All-electrical control of spin transport in nanostructures has been the central interest and chal- lenge of spin physics and spintronics. Here we demonstrate on-chip spin polarizing/filtering actions by driving the gate-defined one dimensional (1D) conductor, one of the simplest geometries for integrated quantum devices, away from the conventional Ohmic regime. Direct measurement of the spin polarization of the emitted current was performed when the momentum degeneracy was lifted, wherein both the 1D polarizer for spin injection and the analyzer for spin detection were demonstrated. The results showed that a configuration of gates and applied voltages can give rise to a tunable spin polarization, which has implications for the development of spintronic devices and future quantum information processing.Comment: 5 pages, 3 figure