Dimensional Crossover of the Dephasing Time in Disordered Mesoscopic Rings: From Diffusive through Ergodic to 0D Behavior

We analyze dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads, where we recently predicted a crossover for the dephasing time \tPh(T) from diffusive or ergodic 1D (\tPh^{-1} \propto T^{2/3}, T^{1}) to $0D$ behavior (\tPh^{-1} \propto T^{2}) as $T$ drops below the Thouless energy \ETh. We provide a detailed derivation of our results, based on an influence functional for quantum Nyquist noise, and calculate all leading and subleading terms of the dephasing time in the three regimes. Explicitly taking into account the Pauli blocking of the Fermi sea in the metal allows us to describe the $0D$ regime on equal footing as the others. The crossover to $0D$, predicted by Sivan, Imry and Aronov for 3D systems, has so far eluded experimental observation. We will show that for T \ll \ETh, $0D$ dephasing governs not only the $T$-dependence for the smooth part of the magnetoconductivity but also for the amplitude of the Altshuler-Aronov-Spivak oscillations, which result only from electron paths winding around the ring. This observation can be exploited to filter out and eliminate contributions to dephasing from trajectories which do not wind around the ring, which may tend to mask the $T^{2}$ behavior. Thus, the ring geometry holds promise of finally observing the crossover to $0D$ experimentally.Comment: in "Perspectives of Mesoscopic Physics - Dedicated to Yoseph Imry's 70th Birthday", edited by Amnon Aharony and Ora Entin-Wohlman (World Scientific, 2010), chap. 20, p. 371-396, ISBN-13 978-981-4299-43-

Thermal noise and dephasing due to electron interactions in non-trivial geometries

We study Johnson-Nyquist noise in macroscopically inhomogeneous disordered metals and give a microscopic derivation of the correlation function of the scalar electric potentials in real space. Starting from the interacting Hamiltonian for electrons in a metal and the random phase approximation, we find a relation between the correlation function of the electric potentials and the density fluctuations which is valid for arbitrary geometry and dimensionality. We show that the potential fluctuations are proportional to the solution of the diffusion equation, taken at zero frequency. As an example, we consider networks of quasi-1D disordered wires and give an explicit expression for the correlation function in a ring attached via arms to absorbing leads. We use this result in order to develop a theory of dephasing by electronic noise in multiply-connected systems.Comment: 9 pages, 6 figures (version submitted to PRB

Non-equilibrium Luttinger liquid: Zero-bias anomaly and dephasing

A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left- and right-movers, yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.Comment: 5 pages, 2 figure

Magnetic-Field Dependence of the Localization Length in Anderson Insulators

Using the conventional scaling approach as well as the renormalization group analysis in $d=2+\epsilon$ dimensions, we calculate the localization length $\xi(B)$ in the presence of a magnetic field $B$. For the quasi 1D case the results are consistent with a universal increase of $\xi(B)$ by a numerical factor when the magnetic field is in the range \ell\ll{\ell_{\!{_H}}}\alt\xi(0), $\ell$ is the mean free path, ${\ell_{\!{_H}}}$ is the magnetic length $\sqrt{\hbar c/eB}$. However, for $d\ge 2$ where the magnetic field does cause delocalization there is no universal relation between $\xi(B)$ and $\xi(0)$. The effect of spin-orbit interaction is briefly considered as well.Comment: 4 pages, revtex, no figures; to be published in Europhysics Letter

Synthesis and Characterization of Electro-Explosive Magnetic Nanoparticles for Biomedical Applications

Nowadays there are new magnetic nanostructures based on bioactive metals with low toxicity and high efficiency for a wide range of biomedical applications including drugs delivery, antimicrobial drugs design, cells' separation and contrasting. For such applications it is necessary to develop highly magnetic particles with less than100 nm in size. In the present study magnetic nanoparticles Fe, Fe[3]O[4] and bimetallic Cu/Fe with the average size of 60- 90 nm have been synthesized by electrical explosion of wire in an oxygen or argon atmosphere. The produced nanoparticles have been characterized with transmission electron microscopy, X-ray phase analysis, and nitrogen thermal desorption. The synthesized particles have shown antibacterial activity to gram-positive (S. aureus, MRSA) and gramnegative (E. coli, P. aeruginosa) bacteria. According to the cytological data Fe, Fe[3]O[4]and Cu/Fe nanoparticles have effectively inhibited viability of cancer cell lines Neuro-2a and J774. The obtained nanoparticles are promising for new antimicrobial drugs and antitumor agents' developmen

Synthesis and Characterization of Electro-Explosive Magnetic Nanoparticles for Biomedical Applications

Nowadays there are new magnetic nanostructures based on bioactive metals with low toxicity and high efficiency for a wide range of biomedical applications including drugs delivery, antimicrobial drugs design, cells' separation and contrasting. For such applications it is necessary to develop highly magnetic particles with less than100 nm in size. In the present study magnetic nanoparticles Fe, Fe[3]O[4] and bimetallic Cu/Fe with the average size of 60- 90 nm have been synthesized by electrical explosion of wire in an oxygen or argon atmosphere. The produced nanoparticles have been characterized with transmission electron microscopy, X-ray phase analysis, and nitrogen thermal desorption. The synthesized particles have shown antibacterial activity to gram-positive (S. aureus, MRSA) and gramnegative (E. coli, P. aeruginosa) bacteria. According to the cytological data Fe, Fe[3]O[4]and Cu/Fe nanoparticles have effectively inhibited viability of cancer cell lines Neuro-2a and J774. The obtained nanoparticles are promising for new antimicrobial drugs and antitumor agents' developmen

Duality of weak and strong scatterer in a Luttinger liquid coupled to massless bosons

We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, ?WS?WL=1, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering

The Causal Relationship between Patent Growth and Growth of GDP with Quarterly Data in the G7 Countries: Cointegration, ARDL and Error Correction Models

This empirical study investigates the dynamic link between patent growth and GDP growth in G7 economies. ARDL model showed that there exist positive relationship in long run between quarterly growth of patents and quarterly GDP growth. The error correction term suggests that 20,6 percent of the adjustment back to long run equilibrium of industrial production in G7 countries is corrected by 20,6% a year, following a shock like the one in 1974 , which in our study is controlled by a dummy variable D74. In the short run however at one or two lags there exist negative relationship between quarterly patents growth and quarterly growth of GDP. Johansen’s procedure for cointegration showed that long run multipliers are positive between the patent growth and GDP growth in G7 economies. Granger causality test showed that patent growth Granger cause GDP growth in G7 countries. Unrestricted VAR showed that there exists positive relationship between patent growth and GDP growth at two or three lags

Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model

A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.Comment: 9 pages, Latex, 6 PostScript figures in uuencoded compressed tar file are appende