34,079 research outputs found
Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
We discuss an Ising spin glass where each spin is coupled
antiferromagnetically to three other spins (3-regular graphs). Inducing quantum
fluctuations by a time-dependent transverse field, we use out-of-equilibrium
quantum Monte Carlo simulations to study dynamic scaling at the quantum glass
transition. Comparing the dynamic exponent and other critical exponents with
those of the classical (temperature-driven) transition, we conclude that
quantum annealing is less efficient than classical simulated annealing in
bringing the system into the glass phase. Quantum computing based on the
quantum annealing paradigm is therefore inferior to classical simulated
annealing for this class of problems. We also comment on previous simulations
where a parameter is changed with the simulation time, which is very different
from the true Hamiltonian dynamics simulated here.Comment: 5 pages, 3 figure
On the Leibniz rule and Laplace transform for fractional derivatives
Taylor series is a useful mathematical tool when describing and constructing
a function. With the series representation, some properties of fractional
calculus can be revealed clearly. This paper investigates two typical
applications: Lebiniz rule and Laplace transform. It is analytically shown that
the commonly used Leibniz rule cannot be applied for Caputo derivative.
Similarly, the well-known Laplace transform of Riemann-Liouville derivative is
doubtful for n-th continuously differentiable function. By the aid of this
series representation, the exact formula of Caputo Leibniz rule and the
explanation of Riemann-Liouville Laplace transform are presented. Finally,
three illustrative examples are revisited to confirm the obtained results
Impurity-induced frustration in correlated oxides
Using the example of Zn-doped La2CuO4, we demonstrate that a spinless
impurity doped into a non-frustrated antiferromagnet can induce substantial
frustrating interactions among the spins surrounding it. This counterintuitive
result is the key to resolving discrepancies between experimental data and
earlier theories. Analytic and quantum Monte Carlo studies of the
impurity-induced frustration are in a close accord with each other and
experiments. The mechanism proposed here should be common to other correlated
oxides as well.Comment: 4 pages, updated figures, accepted versio
An optimized analytical method for the simultaneous detection of iodoform, iodoacetic acid, and other trihalomethanes and haloacetic acids in drinking water
An optimized method is presented using liquid-liquid extraction and derivatization for the extraction of iodoacetic acid (IAA) and other haloacetic acids (HAA9) and direct extraction of iodoform (IF) and other trihalomethanes (THM4) from drinking water, followed by detection by gas chromatography with electron capture detection (GC-ECD). A Doehlert experimental design was performed to determine the optimum conditions for the five most significant factors in the derivatization step: namely, the volume and concentration of acidic methanol (optimized values  = 15%, 1 mL), the volume and concentration of Na2SO4 solution (129 g/L, 8.5 mL), and the volume of saturated NaHCO3 solution (1 mL). Also, derivatization time and temperature were optimized by a two-variable Doehlert design, resulting in the following optimized parameters: an extraction time of 11 minutes for IF and THM4 and 14 minutes for IAA and HAA9; mass of anhydrous Na2SO4 of 4 g for IF and THM4 and 16 g for IAA and HAA9; derivatization time of 160 min and temperature at 40°C. Under optimal conditions, the optimized procedure achieves excellent linearity (R2 ranges 0.9990–0.9998), low detection limits (0.0008–0.2 µg/L), low quantification limits (0.008–0.4 µg/L), and good recovery (86.6%–106.3%). Intra- and inter-day precision were less than 8.9% and 8.8%, respectively. The method was validated by applying it to the analysis of raw, flocculated, settled, and finished waters collected from a water treatment plant in China
Vacuum induced Berry phases in single-mode Jaynes-Cummings models
Motivated by the work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the
vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we
show here that, for a parameter-dependent single-mode JCM, certain atom-field
states also acquire the photon-number-dependent Berry phases after the
parameter slowly changed and eventually returned to its initial value. This
geometric effect related to the field quantization still exists, even the filed
is kept in its vacuum state. Specifically, a feasible Ramsey interference
experiment with cavity quantum electrodynamics (QED) system is designed to
detect the vacuum-induced Berry phase.Comment: 10 pages, 4 figures
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