We explore in detail oscillations of the solar $^7$Be neutrinos in the matter of the Earth. The depth of oscillations is about $(0.1 - 0.2)%$ and the length $approx 30$ km. The period of the oscillatory modulations in the energy scale is comparable w
ith the width of the line determined by the temperature in the center of the Sun. The latter means that depending on the length of trajectory (nadir angle) one obtains different degree of averaging of oscillations. Exploring these oscillations it is possible to measure the width of the $^7$Be line and therefore the temperature of the Sun, determine precisely $Delta m^2_{21}$, perform tomography of the Earth, in particular, measure the deviation of its form from sphere, and detect small structures. Studies of the Be neutrinos open up a possibility to test quantum mechanics of neutrino oscillations and search for the sterile neutrinos. Accuracy of these measurements with future scintillator (or scintillator uploaded) detectors of the $sim 100$ kton mass scale is estimated.
Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have built a serie
s of scalable QA processors consisting of networks of manufactured interacting spins (qubits). Here, we use qubit tunneling spectroscopy to measure the energy eigenspectrum of two- and eight-qubit systems within one such processor, demonstrating quantum coherence in these systems. We present experimental evidence that, during a critical portion of QA, the qubits become entangled and that entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that QA is a viable technology for large-scale quantum computing.
We study distances of propagation and the group velocities of the muon neutrinos in the presence of mixing and oscillations assuming that Lorentz invariance holds. Oscillations lead to distortion of the $ u_mu$ wave packet which, in turn, changes the
group velocity and the distance $ u_mu$ travels. We find that the change of the distance, $d_{osc}$, is proportional to the length of the wave packet, $sigma_x$, and the oscillation phase, $phi_p$, acquired by neutrinos in the $pi-$ and $K-$ meson decay tunnel where neutrino wave packet is formed: $d_{osc} propto sigma phi_p$. Although the distance $d_{osc}$ may effectively correspond to the superluminal motion, the effect is too tiny ($sim 10^{- 5}$ cm) to be reconciled with the OPERA result. We analyze various possibilities to increase $d_{osc}$ and discuss experimental setups in which $d_{osc}$ (corresponding to the superluminal motion) can reach an observable value $sim 1$ m.
We present new formalism for description of the neutrino oscillations in matter with varying density. The formalism is based on the Magnus expansion and has a virtue that the unitarity of the S-matrix is maintained in each order of perturbation theor
y. We show that the Magnus expansion provides better convergence of series: the restoration of unitarity leads to smaller deviations from the exact results especially in the regions of large transition probabilities. Various expansions are obtained depending on a basis of neutrino states and a way one splits the Hamiltonian into the self-commuting and non-commuting parts. In particular, we develop the Magnus expansion for the adiabatic perturbation theory which gives the best approximation. We apply the formalism to the neutrino oscillations in matter of the Earth and show that for the solar oscillation parameters the second order Magnus adiabatic expansion has better than 1% accuracy for all energies and trajectories. For the atmospheric $Delta m^2$ and small 1-3 mixing the approximation works well ($< 3 %$ accuracy for $sin^2 theta_{13} = 0.01$) outside the resonance region (2.7 - 8) GeV.
We analyze the dynamics of rotary biomotors within a simple nano-electromechanical model, consisting of a stator part and a ring-shaped rotor having twelve proton-binding sites. This model is closely related to the membrane-embedded F$_0$ motor of ad
enosine triphosphate (ATP) synthase, which converts the energy of the transmembrane electrochemical gradient of protons into mechanical motion of the rotor. It is shown that the Coulomb coupling between the negative charge of the empty rotor site and the positive stator charge, located near the periplasmic proton-conducting channel (proton source), plays a dominant role in the torque-generating process. When approaching the source outlet, the rotor site has a proton energy level higher than the energy level of the site, located near the cytoplasmic channel (proton drain). In the first stage of this torque-generating process, the energy of the electrochemical potential is converted into potential energy of the proton-binding sites on the rotor. Afterwards, the tangential component of the Coulomb force produces a mechanical torque. We demonstrate that, at low temperatures, the loaded motor works in the shuttling regime where the energy of the electrochemical potential is consumed without producing any unidirectional rotation. The motor switches to the torque-generating regime at high temperatures, when the Brownian ratchet mechanism turns on. In the presence of a significant external torque, created by ATP hydrolysis, the system operates as a proton pump, which translocates protons against the transmembrane potential gradient. Here we focus on the F$_0$ motor, even though our analysis is applicable to the bacterial flagellar motor.
We examine the dynamics of biological nanomotors within a simple model of a rotor having three ion-binding sites. It is shown that in the presence of an external dc electric field in the plane of the rotor, the loading of the ion from the positive si
de of a membrane (rotor charging) provides a torque leading to the motor rotation. We derive equations for the proton populations of the sites and solve these equations numerically jointly with the Langevin-type equation for the rotor angle. Using parameters for biological systems, we demonstrate that the sequential loading and unloading of the sites lead to the unidirectional rotation of the motor. The previously unexplained phenomenon of fast direction-switching in the rotation of a bacterial flagellar motor can also be understood within our model.
We propose using semiconductor quantum dots for a simulation of chemical reactions as electrons are redistributed among such artificial atoms. We show that it is possible to achieve various reaction regimes and obtain different reaction products by v
arying the speed of voltage changes applied to the gates forming quantum dots. Considering the simplest possible reaction, $H_2+Hto H+H_2$, we show how the necessary initial state can be obtained and what voltage pulses should be applied to achieve a desirable final product. Our calculations have been performed using the Pechukas gas approach, which can be extended for more complicated reactions.
We define a set of $2^{n-1}-1$ entanglement monotones for $n$ qubits and give a single measure of entanglement in terms of these. This measure is zero except on globally entangled (fully inseparable) states. This measure is compared to the Meyer-Wall
ach measure for two, three, and four qubits. We determine the four-qubit state, symmetric under exchange of qubit labels, which maximizes this measure. It is also shown how the elementary monotones may be computed as a function of observable quantities. We compute the magnitude of our measure for the ground state of the four-qubit superconducting experimental system investigated in [M. Grajcar et al., Phys. Rev. Lett._96_, 047006 (2006)], and thus confirm the presence of global entanglement in the ground state.
We examine electron transport through semiconductor quantum dot subject to a continuous circularly polarized optical irradiation resonant to the electron - heavy hole transition. Electrons having certain spin polarization experience Rabi oscillation
and their energy levels are shifted by the Rabi frequency. Correspondingly, the equilibrium chemical potential of the leads and the lead-to-lead bias voltage can be adjusted so only electrons with spin-up polarization or only electrons with spin-down polarization contribute to the current. The temperature dependence of the spin polarization of the current is also discussed.
We present a formalism for the matter effects in the Earth on low energy neutrino fluxes which is both accurate and has all advantages of a full analytic treatment. The oscillation probabilities are calculated up to second order term in $epsilon(x) e
quiv 2V(x)E/Delta m^2$ where $V(x)$ is the neutrino potential at position $x$. We show the absence of large undamped phases which makes the expansion in $epsilon$ well behaved. An improved expansion is presented in terms of the variation of $V(x)$ around a suitable mean value which allows to treat energies up to those relevant for Supernova neutrinos. We discuss also the case of three-neutrino mixing.
