Phonon-mediated electron pairing in graphene

The possibility of superconducting pairing of electrons in doped graphene due to in-plane and out-of-plane phonons is studied. Quadratic coupling of electrons with out-of-plane phonons is considered in details, taking into account both deformation potential and bond-stretch contributions. The order parameter of electron-electron pairing can have different structures due to four-component spinor character of electrons wave function. We consider s-wave pairing, diagonal on conduction and valence bands, but having arbitrary structure with respect to valley degree of freedom. The sign and magnitude of contribution of each phonon mode to effective electron-electron interaction turns out to depend on both the symmetry of phonon mode and the structure of the order parameter. Unconventional orbital-spin symmetry of the order parameter is found.     

Slow dynamics and anomalous nonlinear fast dynamics in diverse solids

Results are reported of the first systematic study of anomalous nonlinear fast dynamics and slow dynamics in a number of solids. Observations are presented from seven diverse materials showing that anomalous nonlinear fast dynamics (ANFD) and slow dynamics (SD) occur together, significantly expanding the nonlinear mesoscopic elasticity class. The materials include samples of gray iron, alumina ceramic, quartzite, cracked Pyrex, marble, sintered metal, and perovskite ceramic. In addition, it is shown that materials which exhibit ANFD have very similar ratios of amplitude-dependent internal-friction to the resonance-frequency shift with strain amplitude. The ratios range between 0.28 and 0.63, except for cracked Pyrex glass, which exhibits a ratio of 1.1, and the ratio appears to be a material characteristic. The ratio of internal friction to resonance frequency shift as a function of time during SD is time independent, ranging from 0.23 to 0.43 for the materials studied.     

Zonal-flow dynamics and size scaling of anomalous transport

Nonlinear equations for the slow space-time evolution of the radial drift-wave envelope and zonal flow amplitude have been self-consistently derived for a model nonuniform tokamak equilibrium within the coherent four-wave drift wave-zonal flow modulation interaction model of Chen, Lin, and White [Phys. Plasmas 7, 3129 (2000)]]. Solutions clearly demonstrate turbulence spreading due to nonlinearly enhanced dispersiveness and, consequently, the device-size dependence of the saturated wave intensities and transport coefficients.     

Phonon-mediated electron-spin phase diffusion in a quantum dot

An effective spin relaxation mechanism that leads to electron spin decoherence in a quantum dot is proposed. In contrast with the common calculations of spin-flip transitions between the Kramers doublets, we take into account a process of phonon-mediated fluctuation in the electron spin preces-sion and subsequent spin phase diffusion. Specifically, we consider modulations in the longitudinal g factor and hyperfine interaction induced by the phonon-assisted transitions between the lowest electronic states. Prominent differences in the temperature and magnetic field dependence between the proposed mechanism and the spin-flip transitions are expected to facilitate its experimental verification. Numerical estimation demonstrates highly efficient spin relaxation in typical semiconductor quantum dots.     

Topological defects dynamics and Melnikov's theory

We use Melnikov's analysis to construct recurrence time maps near homoclinic and heteroclinic bifurcations. We show that a method developed by Kawasaki and Ohta in order to study defects dynamics is indeed equivalent to this version of Melnikov's theory.     

Understanding anomalous delays in a model of intracellular calcium dynamics

In many cell types, oscillations in the concentration of free intracellular calcium ions are used to control a variety of cellular functions. It has been suggested [J. Sneyd et al., "A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations," Proc. Natl. Acad. Sci. U.S.A. 103, 1675-1680 (2006)] that the mechanisms underlying the generation and control of such oscillations can be determined by means of a simple experiment, whereby a single exogenous pulse of inositol trisphosphate (IP(3)) is applied to the cell. However, more detailed mathematical investigations [M. Domijan et al., "Dynamical probing of the mechanisms underlying calcium oscillations," J. Nonlinear Sci. 16, 483-506 (2006)] have shown that this is not necessarily always true, and that the experimental data are more difficult to interpret than first thought. Here, we use geometric singular perturbation techniques to study the dynamics of models that make different assumptions about the mechanisms underlying the calcium oscillations. In particular, we show how recently developed canard theory for singularly perturbed systems with three or more slow variables [M. Wechselberger, "A propos de canards (Apropos canards)," Preprint, 2010] applies to these calcium models and how the presence of a curve of folded singularities and corresponding canards can result in anomalous delays in the response of these models to a pulse of IP(3).     

Adsorbate vibrational dynamics in the anomalous skin effect frequency region

It is shown that in surface infrared reflectance at low frequencies, dipole forbidden parallel adsorbate vibrations give rise to anti-absorption resonances, whose asymmetry is independent of the nature of the adsorbate-substrate bond. The theory is compared with new absolute IR measurements for CO/Cu(100) and (111) over the frequency range 180–2500 cm⁻¹ at high resolution (1 cm⁻¹). The linewidth of the CO frustrated rotation is dominated by energy relaxation via electron-hole pair exitations. The deduced lifetimes (~ 1 ps) are in good agreement with theory.     

Effective spin-glass Hamiltonian for the anomalous dynamics of the HMF model

We discuss an effective spin-glass Hamiltonian which can be used to study the glassy-like dynamics observed in the metastable states of the Hamiltonian mean field (HMF) model. By means of the Replica formalism, we were able to find a self-consistent equation for the glassy order parameter which reproduces, in a restricted energy region below the phase transition, the microcanonical simulations for the polarization order parameter recently introduced in the HMF model.     

UCN anomalous losses and the UCN capture cross section on material defects

Experimental data shows anomalously large ultra cold neutrons (UCN) reflection losses and that the process of UCN reflection is not completely coherent. UCN anomalous losses under reflection cannot be explained in the context of neutron optics calculations. UCN losses by means of incoherent scattering on material defects are considered and cross-section values calculated. The UCN capture cross section on material defects is enhanced by a factor of 10⁴ due to localization of UCN around defects. This phenomenon can explain anomalous losses of UCN.     

Noncontact friction and relaxational dynamics of surface defects

The motion of a cantilever near sample surfaces exhibits additional friction even before two bodies come into mechanical contact. Called noncontact friction (NCF), this friction is of great practical importance to the ultrasensitive force detection measurements. The observed large NCF of a micron-scale cantilever found an anomalously large damping that exceeds theoretical predictions by 8-11 orders of magnitude. This finding points to a contribution beyond fluctuating electromagnetic fields within the van der Waals approach. Recent experiments reported by Saitoh et al. [Phys. Rev. Lett. 105, 236103 (2010)] also found a nontrivial distance dependence of NCF. Motivated by these observations, we propose a mechanism based on the coupling of a cantilever to the relaxation dynamics of surface defects. We assume that the surface defects couple to the cantilever tip via spin-spin coupling and their spin relaxation dynamics gives rise to the backaction terms and modifies both the friction coefficient and the spring constant. We explain the magnitude, as well as the distance dependence of the friction due to these backaction terms. Reasonable agreement is found with the experiments.     

Critical dynamics in the presence of relaxing defects

The influence of defects coupling linearly to the order parameter on the critical behaviour of structural phase transitions is studied. A continuum model for the statics and dynamics is introduced and is investigated by the renormalization group theory. If the defects are slow a central peak is found, the characteristic width of which is determined by the defects. Concerning the critical behaviour the dynamical model belongs to the same universality class as the one studied previously by Grinstein, MA, and Mazenko. The concentration dependence of the central peak response is discussed inside and outside the critical region.     

Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics

Most biochemical processes in cells are usually modeled by reaction–diffusion(RD) equations. In these RD models,the diffusive process is assumed to be Gaussian. However, a growing number of studies have noted that intracellular diffusion is anomalous at some or all times, which may result from a crowded environment and chemical kinetics. This work aims to computationally study the effects of chemical reactions on the diffusive dynamics of RD systems by using both stochastic and deterministic algorithms. Numerical method to estimate the mean-square displacement(MSD) from a deterministic algorithm is also investigated. Our computational results show that anomalous diffusion can be solely due to chemical reactions. The chemical reactions alone can cause anomalous sub-diffusion in the RD system at some or all times.The time-dependent anomalous diffusion exponent is found to depend on many parameters, including chemical reaction rates, reaction orders, and chemical concentrations.     

Phonon-mediated coupling of InGaAs/GaAs quantum-dot excitons to photonic crystal cavities

We demonstrate that the emission characteristics of site-controlled InGaAs/GaAs single quantum dots embedded in photonic crystal slab cavities correspond to single confined excitons coupled to cavity modes, unlike previous reports of similar systems based on self-assembled quantum dots. By using polarization-resolved photoluminescence spectroscopy at different temperatures and a theoretical model, we show that the exciton-cavity interaction range is limited to the phonon sidebands. Photon-correlation and pump-power dependence experiments under nonresonant excitation conditions further establish that the cavity is fed only by a single exciton.