Revivals, classical periodicity, and zitterbewegung of electron currents in monolayer graphene

Revivals of electric current in graphene in the presence of an external magnetic field are described. It is shown that when the electrons are prepared in the form of wave packets assuming a Gaussian population of only positive (or negative) energy Landau levels, the presence of the magnetic field induce revivals of the electron currents, besides the classical cyclotron motion. When the population comprises both positive and negative energy Landau levels, revivals of the electric current manifest simultaneously with zitterbewegung and the classical cyclotron motion. We relate the temporal scales of these three effects and discuss to what extent these results hold for real graphene samples

Dangling-bond spin relaxation and magnetic 1/f noise from the amorphous-semiconductor/oxide interface: Theory

We propose a model for magnetic noise based on spin-flips (not electron-trapping) of paramagnetic dangling-bonds at the amorphous-semiconductor/oxide interface. A wide distribution of spin-flip times is derived from the single-phonon cross-relaxation mechanism for a dangling-bond interacting with the tunneling two-level systems of the amorphous interface. The temperature and frequency dependence is sensitive to three energy scales: The dangling-bond spin Zeeman energy delta, as well as the minimum (E_min) and maximum (E_max) values for the energy splittings of the tunneling two-level systems. We compare and fit our model parameters to a recent experiment probing spin coherence of antimony donors implanted in nuclear-spin-free silicon [T. Schenkel {\it et al.}, Appl. Phys. Lett. 88, 112101 (2006)], and conclude that a dangling-bond area density of the order of 10^{14}cm^{-2} is consistent with the data. This enables the prediction of single spin qubit coherence times as a function of the distance from the interface and the dangling-bond area density in a real device structure. We apply our theory to calculations of magnetic flux noise affecting SQUID devices due to their Si/SiO_2 substrate. Our explicit estimates of flux noise in SQUIDs lead to a noise spectral density of the order of 10^{-12}Phi_{0}^{2} {Hz}^{-1} at f=1Hz. This value might explain the origin of flux noise in some SQUID devices. Finally, we consider the suppression of these effects using surface passivation with hydrogen, and the residual nuclear-spin noise resulting from a perfect silicon-hydride surface.Comment: Final published versio

Identifying wave packet fractional revivals by means of information entropy

Wave packet fractional revivals is a relevant feature in the long time scale evolution of a wide range of physical systems, including atoms, molecules and nonlinear systems. We show that the sum of information entropies in both position and momentum conjugate spaces is an indicator of fractional revivals by analyzing three different model systems: $(i)$ the infinite square well, $(ii)$ a particle bouncing vertically against a wall in a gravitational field, and $(iii)$ the vibrational dynamics of hydrogen iodide molecules. This description in terms of information entropies complements the usual one in terms of the autocorrelation function

Ohmic and step noise from a single trapping center hybridized with a Fermi sea

We show that single electron tunneling devices such as the Cooper-pair box or double quantum dot can be sensitive to the zero-point fluctuation of a single trapping center hybridized with a Fermi sea. If the trap energy level is close to the Fermi sea and has line-width \gamma > k_B T, its noise spectrum has an Ohmic Johnson-Nyquist form, whereas for \gamma < k_B T the noise has a Lorentzian form expected from the semiclassical limit. Trap levels above the Fermi level are shown to lead to steps in the noise spectrum that can be used to probe their energetics, allowing the identification of individual trapping centers coupled to the device.Comment: Revised version to appear in Phys. Rev. Let

Phase diagram of hot magnetized two-flavor color superconducting quark matter

A two-flavor color superconducting (2SC) Nambu--Jona-Lasinio (NJL) model is introduced at finite temperature T, chemical potential mu and in the presence of a constant magnetic field eB. The effect of (T,mu,eB) on the formation of chiral and color symmetry breaking condensates is studied. The complete phase portrait of the model in T-mu, mu-eB, and T-eB phase spaces for various fixed eB, T, and mu is explored. A threshold magnetic field eB_t~ 0.5 GeV^2 is found above which the dynamics of the system is solely dominated by the lowest Landau level (LLL) and the effects of T and mu are partly compensated by eB.Comment: V1: 29 pages, 15 figures, 3 tables. V2: Discussions improved. Version accepted for publication in PR

Properties of neutral mesons in a hot and magnetized quark matter

The properties of non-interacting $\sigma$ and $\pi^{0}$ mesons are studied at finite temperature, chemical potential and in the presence of a constant magnetic field. To do this, the energy dispersion relations of these particles, including nontrivial form factors, are derived using a derivative expansion of the effective action of a two-flavor, hot and magnetized Nambu--Jona-Lasinio (NJL) model up to second order. The temperature dependence of the pole and screening masses as well as the directional refraction indices of magnetized neutral mesons are explored for fixed magnetic fields and chemical potentials. It is shown that, because of the explicit breaking of the Lorentz invariance by the magnetic field, the refraction index and the screening mass of neutral mesons exhibit a certain anisotropy in the transverse and longitudinal directions with respect to the direction of the external magnetic field. In contrast to their longitudinal refraction indices, the transverse indices of the neutral mesons are larger than unity.Comment: V1: 26 pages, 15 figures; V2: Discussions improved, references added. Version accepted for publication in PR

Polynomial Realization of sℓq(2)s\ell_q(2) and Fusion Rules at Exceptional Values of qq

Representations of the $s\ell_q(2)$ algebra are constructed in the space of polynomials of real (complex) variable for $q^N=1$. The spin addition rule based on eigenvalues of Casimir operator is illustrated on few simplest cases and conjecture for general case is formulated

Radiative transfer theory for vacuum fluctuations

A semiclassical kinetic theory is presented for the fluctuating photon flux emitted by a disordered medium in thermal equilibrium. The kinetic equation is the optical analog of the Boltzmann-Langevin equation for electrons. Vacuum fluctuations of the electromagnetic field provide a new source of fluctuations in the photon flux, over and above the fluctuations due to scattering. The kinetic theory in the diffusion approximation is applied to the super-Poissonian noise due to photon bunching and to the excess noise due to beating of incident radiation with the vacuum fluctuations.Comment: 4 pages, 2 figures, revised version according to referee's comment

Neuron dynamics in the presence of 1/f noise

Interest in understanding the interplay between noise and the response of a non-linear device cuts across disciplinary boundaries. It is as relevant for unmasking the dynamics of neurons in noisy environments as it is for designing reliable nanoscale logic circuit elements and sensors. Most studies of noise in non-linear devices are limited to either time-correlated noise with a Lorentzian spectrum (of which the white noise is a limiting case) or just white noise. We use analytical theory and numerical simulations to study the impact of the more ubiquitous "natural" noise with a 1/f frequency spectrum. Specifically, we study the impact of the 1/f noise on a leaky integrate and fire model of a neuron. The impact of noise is considered on two quantities of interest to neuron function: The spike count Fano factor and the speed of neuron response to a small step-like stimulus. For the perfect (non-leaky) integrate and fire model, we show that the Fano factor can be expressed as an integral over noise spectrum weighted by a (low pass) filter function. This result elucidates the connection between low frequency noise and disorder in neuron dynamics. We compare our results to experimental data of single neurons in vivo, and show how the 1/f noise model provides much better agreement than the usual approximations based on Lorentzian noise. The low frequency noise, however, complicates the case for information coding scheme based on interspike intervals by introducing variability in the neuron response time. On a positive note, the neuron response time to a step stimulus is, remarkably, nearly optimal in the presence of 1/f noise. An explanation of this effect elucidates how the brain can take advantage of noise to prime a subset of the neurons to respond almost instantly to sudden stimuli.Comment: Phys. Rev. E in pres

Parameterized Compilation Lower Bounds for Restricted CNF-formulas

We show unconditional parameterized lower bounds in the area of knowledge compilation, more specifically on the size of circuits in decomposable negation normal form (DNNF) that encode CNF-formulas restricted by several graph width measures. In particular, we show that - there are CNF formulas of size $n$ and modular incidence treewidth $k$ whose smallest DNNF-encoding has size $n^{\Omega(k)}$, and - there are CNF formulas of size $n$ and incidence neighborhood diversity $k$ whose smallest DNNF-encoding has size $n^{\Omega(\sqrt{k})}$. These results complement recent upper bounds for compiling CNF into DNNF and strengthen---quantitatively and qualitatively---known conditional low\-er bounds for cliquewidth. Moreover, they show that, unlike for many graph problems, the parameters considered here behave significantly differently from treewidth