Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

Brownian motors: noisy transport far from equilibrium

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

During the past decade, enormous progress has been made in growing ultrathin organic films and multilayer structures with a wide range of exciting optoelectronic properties. This progress has been made possible by several important advances in our understanding of organic films and their modes of growth. Perhaps the single most important advance has been the use of ultrahigh vacuum (UHV) as a means to achieve, for the first time, monolayer control over the growth of organic thin films with extremely high chemical purity and structural precision.1-3 Such monolayer control has been possible for many years using well-known techniques such as Langmuir-Blodgett film deposition,4 and more recently, self-assembled monolayers from solution have also been achieved.5 However, ultrahighvacuum growth, sometimes referred to as organic molecular beam deposition (OMBD) or organic molecular beam epitaxy (OMBE), has the advantage of providing both layer thickness control and an atomically clean environment and substrate. When combined with the ability to perform in situ highresolution structural diagnostics of the films as they are being deposited, techniques such as OMBD have provided an entirely new prospect for understanding many of the fundamental structural and optoelectronic properties of ultrathin organic film systems. Since such systems are both of intrinsic as well as practical interest, substantial effort worldwide has been invested in attempting to grow and investigate the properties of such thin-film systems. This paper is a review of recent progress made in organic thin films grown in ultrahigh vacuum or using other vapor-phase deposition methods. We will describe the most important work which has been published in this field since the emergence of OMBD in the mid-1980s. Both the nature of thin-film growth and structural ordering will be discussed, as well as some of the more interesting consequences to the physical properties of such organic thin-film systems will be considered both from a theoretical as well as an experimental viewpoint. Indeed, it will 1793 Chem. Rev. 1997, 97, 1793−1896

Ultrathin Organic Films Grown by Organic Molecular Beam Deposition and Related Techniques.

Random-matrix theories in quantum physics : common concepts

Systems with dielectric pairing of spatially separated electrons and holes are considered. Superfluid motion of the charges, corresponding to undamped electric currents, is possible in such systems. The role of interband transitions is discussed. (AIP)

Feasibility of superfluidity of paired spatially separated electrons and holes; a new superconductivity mechanism

We consider chiral electrons moving along the one-dimensional helical edge of a two-dimensional topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states.

Localization at the edge of a 2D topological insulator by Kondo impurities with random anisotropies.

Superconductivity at dielectric pairing of spatially separated quasiparticles

We study multiphoton scattering inside a one-dimensional waveguide caused by a number of resonant two-level atoms located in a region small compared to the photon wavelength. Applying powerful methods of the theory of integrable quantum systems, we analyze photon correlations caused by scattering. In particular, for the important case of two-photon scattering, we describe explicitly the dependence of the scattering parameters on the number of two-level atoms. Also, we outline the method of describing scattering of an arbitrary number of photons and present explicit expressions for the scattering of three photons in the effective chiral one-dimensional model. The photon wave function is represented as a sum of terms of a different degree of ``entanglement.'' We discuss qualitative distinctions in photon correlations for the single two-level atom case and the case of several atoms.

Multiphoton scattering in a one-dimensional waveguide with resonant atoms

While it is well-known that the electron-electron (ee) interaction cannot affect the resistivity of a Galilean-invariant Fermi liquid (FL), the reverse statement is not necessarily true: the resistivity of a non-Galilean-invariant FL does not necessarily follow a T 2 behavior. The T 2 behavior is guaranteed only if Umklapp processes are allowed; however, if the Fermi surface (FS) is small or the electron-electron interaction is of a very long range, Umklapps are suppressed. In this case, a T 2 term can result only from a combined – but distinct from quantum-interference corrections – effect of the electron-impurity and ee interactions. Whether the T 2 term is present depends on (i) dimensionality [two dimensions (2D) vs three dimensions (3D)], (ii) topology (simply- vs multiply-connected), and (iii) shape (convex vs concave) of the FS. In particular, the T 2 term is absent for any quadratic (but not necessarily isotropic) spectrum both in 2D and 3D. The T 2 term is also absent for a convex and simply-connected but otherwise arbitrarily anisotropic FS in 2D. The origin of this nullification is approximate integrability of the electron motion on a 2D FS, where the energy and momentum conservation laws do not allow for current relaxation to leading – second – order in T /EF (EF is the Fermi energy). If the T 2 term is nullified by the conservation law, the first non-zero term behaves as T 4 . The same applies to a quantum-critical metal in the vicinity of a Pomeranchuk instability, with a proviso that the leading (first non-zero) term in the resistivity scales as T^(D+2)/3 (T^(D+8)/3). We discuss a number of situations when integrability is weakly broken, e. g., by inter-plane hopping in a quasi-2D metal or by warping of the FS as in the surface states of topological insulators of the Bi2 Te3 family. The paper is intended to be self-contained and pedagogical; review of the existing results is included along with the original ones wherever deemed necessary for completeness.

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V.I. Yudson

Papers

Feasibility of superfluidity of paired spatially separated electrons and holes; a new superconductivity mechanism

Localization at the edge of a 2D topological insulator by Kondo impurities with random anisotropies.

Superconductivity at dielectric pairing of spatially separated quasiparticles

Multiphoton scattering in a one-dimensional waveguide with resonant atoms

Resistivity of non-galilean-invariant fermi- and non-fermi liquids