Search results for "QUANTUM MECHANICS"
showing 10 items of 2468 documents
Spatial Search by Quantum Walk is Optimal for Almost all Graphs.
2015
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erd\"os-Renyi random graphs, i.e.\ graphs of $n$ vertices where each edge exists with probability $p$, search by CTQW is \textit{almost surely} optimal as long as $p\geq \log^{3/2}(n)/n$. Consequently, we show that quantum spatial search is in fact optimal for \emph{almost all} graphs, meaning that the fraction of graphs of $n$ vertices for which this optimality holds tends to one in the asymptotic limit. We obtain this result by provin…
Studying the phosphoryl transfer mechanism of the E. coli phosphofructokinase-2: from X-ray structure to quantum mechanics/molecular mechanics simula…
2019
Phosphofructokinases (Pfks) catalyze the ATP-dependent phosphorylation of fructose-6-phosphate (F6P) and they are regulated in a wide variety of organisms. Although numerous aspects of the kinetics and regulation have been characterized for Pfks, the knowledge about the mechanism of the phosphoryl transfer reaction and the transition state lags behind. In this work, we describe the X-ray crystal structure of the homodimeric Pfk-2 from E. coli, which contains products in one site and reactants in the other, as well as an additional ATP molecule in the inhibitory allosteric site adjacent to the reactants. This complex was previously predicted when studying the kinetic mechanism of ATP inhibit…
Theoretical Modeling on the Reaction Mechanism of p-Nitrophenylmethylphosphate Alkaline Hydrolysis and its Kinetic Isotope Effects
2015
We have studied the alkaline hydrolysis of p-nitrophenylmethylphosphate (p-NPmP) in aqueous solution by means of polarizable continuum models and by hybrid quantum-mechanical/molecular-mechanical (QM/MM) methods. The theoretical predictions of kinetic isotope effects (KIEs) are in very good agreement with the experimental data, confirming a concerted asynchronous molecular mechanism. In addition, comparison of high level DFT theory with semiempirical AM1/d Hamiltonian has allowed checking the reliability of the later to be used in modeling very large molecular models containing phosphorus atoms.
Measurement of theE2/M1Ratio in theN→ΔTransition Using the Reactionp(γ→,p)π0[Phys. Rev. Lett. 78, 606 (1997)]
1997
The small electric quadrupole $E2$ amplitude of the predominantly magnetic dipole $M1$ $p\ensuremath{\rightarrow}\ensuremath{\Delta}(1232)$ transition has been measured using 270 to 420 MeV tagged linearly polarized photons in the $p(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}},p){\ensuremath{\pi}}^{o}$ reaction at the Mainz Microtron MAMI. Differential cross sections and photon asymmetries were determined by measuring the recoil proton in the cylindrically symmetric $4\ensuremath{\pi}$ detector DAPHNE. From the proton angular distributions the ratio $E2/M1\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}(2.5\ifmmode\pm\else\textpm\fi{}0.2\ifmmode\pm\else\textpm\…
Energy-weighted M1 sum rule with explicit δ degrees of freedom
1985
Abstract The influence of Δ degrees of freedom on the energy-weighted M1 sum rule is investigated and applied to 2 H and 4 He. Using π- and ρ-exchange potentials a reduction of the potential contribution of the order of 50% is obtained. The absolute value of the sum rule is strongly dependent on the short-range behaviour of the nuclear wave function. Furthermore, the contribution of c.m. effects is evaluated and found to be of the order of 5–10%.
Molecular mode-coupling theory applied to a liquid of diatomic molecules
2000
We study the molecular mode coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters ${\bf F}_{ll'}^m(q)$ and the critical amplitudes of the $\beta$ - relaxation ${\bf H}_{ll'}^m(q)$ are solved up to a cut off $l_{co}$ = 2 without any further approximations. Here $l,m$ are indices of spherical harmonics. Contrary to previous studies, where additional approximations were applied, we find in agreement with simulations, that all molecular degrees of freedom vitrify at a single temperature $T_c$. The theoretical results for the non ergodicity parameters and the critical amplitudes are compared with those from simulations. The qualitat…
Geometry of the theory space in the exact renormalization group formalism
2018
We consider the theory space as a manifold whose coordinates are given by the couplings appearing in the Wilson action. We discuss how to introduce connections on this theory space. A particularly intriguing connection can be defined directly from the solution of the exact renormalization group (ERG) equation. We advocate a geometric viewpoint that lets us define straightforwardly physically relevant quantities invariant under the changes of a renormalization scheme.
Renormalization-group analysis for the transition to chaos in Hamiltonian systems
2002
Abstract We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of…
Is massless quantum electrodynamics a free-field theory?
1976
It is shown that if the photon wave-function renormalization constant is finite, then in the limit of zero fermion mass, quantum electrodynamics is a free- field theory.
Nonlocal chiral quark models with wavefunction renormalization: Sigma properties andπ−πscattering parameters
2008
We analyze the sigma meson mass and width together with the pion-pion scattering parameters in the context of nonlocal chiral quark models with wave function renormalization (WFR). We consider both nonlocal interactions based on the frequently used exponential form factor, and on fits to the quark mass and renormalization functions obtained in lattice calculations. In the case of the sigma properties, we obtain results which are less dependent on the parametrization than in the standard local Nambu-Jona-Lasinio model, and which are in reasonable agreement with the recently reported empirical values. We also show that the inclusion of the WFR tend to improve the description of the $\ensurema…