The purpose of this Lecture is to demonstrate how the well-known results on Luttinger Liquid can ... more The purpose of this Lecture is to demonstrate how the well-known results on Luttinger Liquid can be obtained with the use of the coherent state integral.
Duality in multi-channel Luttinger Liquid with local scatterer
EPL (Europhysics Letters), 2013
ABSTRACT We have devised a general scheme that provides exact results for the scaling dimensions ... more ABSTRACT We have devised a general scheme that provides exact results for the scaling dimensions of all allowed in multi-channel Luttinger Liquids local perturbations. The technique developed provides universal description and establishes relations between scaling dimensions of perturbations in different phases of Luttinger Liquid. These multiple relations between scaling dimensions are universal. They are valid for all Luttinger Liquids with arbitrary current-current and density-density interactions. We have also established duality transformation between different subsets of Luttinger Liquid phases known for single-channel liquid as duality between weak link and weak scatterer limits.
Polarization of light scattered from slightly rough dielectric film
Optics Letters, 1994
We found that a slightly rough thin dielectric film polarizes diffusely scattered light. There is... more We found that a slightly rough thin dielectric film polarizes diffusely scattered light. There is a discrete set of angles of incidence and observation for which the intensity of a nonspecular diffuse P-polarized component is significantly greater than that for S polarization.
We consider data losses in a single node of a packet-switched Internet-like network. We employ tw... more We consider data losses in a single node of a packet-switched Internet-like network. We employ two distinct models, one with discrete and the other with continuous one-dimensional random walks, representing the state of a queue in a router. Both models {have} a built-in critical behavior with {a sharp} transition from exponentially small to finite losses. It turns out that the finite capacity of a buffer and the packet-dropping procedure give rise to specific boundary conditions which lead to strong loss rate fluctuations at the critical point even in the absence of such fluctuations in the data arrival process.
We calculate the tunnelling density of states (TDoS) for a quantum dot in the Coulomb-blockade re... more We calculate the tunnelling density of states (TDoS) for a quantum dot in the Coulomb-blockade regime, using a functional integral representation with allowing correctly for the charge quantisation. We show that in addition to the well-known gap in the TDoS in the Coulomb-blockade valleys, there is a suppression of the TDoS at the peaks. We show that such a suppression is necessary in order to get the correct result for the peak of the differential conductance through an almost close quantum dot.
We calculate the moments of transmittance, <Tn>, through an open disordered 1D system with an ima... more We calculate the moments of transmittance, <Tn>, through an open disordered 1D system with an imaginary vector potential, ih. It turns out that the critical curves on the complex energy plane, Cn, where an exponential decay of the appropriate quantity is changed by a power-law one, are all different. They also differ from the corresponding curves for <lnT> and that of the averaged one-particle Green's function; the latter defines the density of states support for the open system. This results from the absence of self-averaging in disordered 1D systems and reflects higher-order correlations in localized eigenstates of the non-Hermitian model.
We suggest a variant of the nonlinear σ model for the description of disordered superconductors. ... more We suggest a variant of the nonlinear σ model for the description of disordered superconductors. The main distinction from existing models lies in the fact that the saddle point equation is solved nonperturbatively in the superconducting pairing field. It allows one to use the model both in the vicinity of the metal-superconductor transition and well below its critical temperature with full account for the self-consistency conditions. We show that the model reproduces a set of known results in different limiting cases, and apply it for a self-consistent description of the proximity effect at the superconductor-metal interface.
It is shown that the quasilocalized states in weakly disordered systems can lead to the nonanalyt... more It is shown that the quasilocalized states in weakly disordered systems can lead to the nonanalytical distribution of level curvatures. In 2D systems the distribution function P\(K\) has a branching point at K = 0, while in quasi-1D systems the nonanalyticity is very weak and in 3D metals it is absent. It was shown earlier within the similar saddle-point method that for weak disorder the wave functions possess a (weak) multifractality only in 2D systems. This allows us to conjecture that the branching in P\(K\) at K = 0 is a generic feature of all critical eigenstates with multifractal statistics. A relationship between the branching power and the fractal dimensionality D2 is suggested.
Enhanced carrier-carrier interaction in optically pumped hydrogenated nanocrystalline silicon
Applied Physics Letters, Oct 1, 2012
ABSTRACT A femtosecond pump-probe setup was used to measure the time resolved reflectivity of hyd... more ABSTRACT A femtosecond pump-probe setup was used to measure the time resolved reflectivity of hydrogenated amorphous silicon containing crystalline silicon nanoparticles at eight different incidence angles. Results fitted with the Drude model found a scattering rate of Gamma = 2(-1)(+1.2) x 10(15) s(-1) at a corresponding carrier concentration of similar to 10(20) cm(-3). The observed scattering rate is attributed to enhanced carrier-carrier interaction in optically pumped nanocrystals. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4755760]
We show that electron-phonon coupling strongly affects transport properties of the Luttinger liqu... more We show that electron-phonon coupling strongly affects transport properties of the Luttinger liquid hybridized with a resonant level. Namely, this coupling significantly modifies the effective energy-dependent width of the resonant level in two different geometries, corresponding to the resonant or antiresonant transmission in the Fermi gas. This leads to a rich phase diagram for a metal-insulator transition induced by the hybridization with the resonant level.
We show that for all the three standard symmetry classes (unitary, orthogonal and symplectic), th... more We show that for all the three standard symmetry classes (unitary, orthogonal and symplectic), the conventional replica nonlinear sigma model gives the correct non-perturbative result for the two-level correlation functions R_2(\omega) of electrons in disordered metals in the limit of large \omega. In this limit, non-perturbative oscillatory contributions arise from a degenerate saddle-point manifold within this sigma model which corresponds to the replica-symmetry breaking. Moreover, we demonstrate that in the unitary case the very same results can be extracted from the well known exact integral representation for R_2(\omega).
We study the influence of electron-phonon coupling on electron transport through a Luttinger liqu... more We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations, which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in a rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.
We study electronic transport in a Luttinger liquid (LL) with an embedded impurity, which is eith... more We study electronic transport in a Luttinger liquid (LL) 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, $\Delta_{ws}\Delta_{wl}=1 $, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard LL, 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.
We suggest a variant of the nonlinear σ model for the description of disordered superconductors. ... more We suggest a variant of the nonlinear σ model for the description of disordered superconductors. The main distinction from existing models lies in the fact that the saddle point equation is solved nonperturbatively in the superconducting pairing field. It allows one to use the model both in the vicinity of the metal-superconductor transition and well below its critical temperature with full account for the self-consistency conditions. We show that the model reproduces a set of known results in different limiting cases, and apply it for a self-consistent description of the proximity effect at the superconductor-metal interface.
We have found an exact expression for the decoherence rate of a Josephson charge qubit coupled to... more We have found an exact expression for the decoherence rate of a Josephson charge qubit coupled to fluctuating background charges. At low temperatures T the decoherence rate Γ is linear in T while at high temperatures it saturates in agreement with a known classical solution which, however, reached at surprisingly high T . In contrast to the classical picture, impurity states spread in a wide interval of energies (≫T) may essentially contribute to Γ .
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Papers by Igor Yurkevich