First-Matsubara-frequency rule in a Fermi liquid. Part I: Fermionic self-energy

We analyze in detail the fermionic self-energy \Sigma(\omega, T) in a Fermi liquid (FL) at finite temperature T and frequency \omega. We consider both canonical FLs -- systems in spatial dimension D >2, where the leading term in the fermionic self-energy is analytic [the retarded Im\Sigma^R(\omega,T) = C(\omega^2 +\pi^2 T^2)], and non-canonical FLs in 1<D <2, where the leading term in Im\Sigma^R(\omega,T) scales as T^D or \omega^D. We relate the \omega^2 + \pi^2 T^2 form to a special property of the self-energy -"the first-Matsubara-frequency rule", which stipulates that \Sigma^R(i\pi T,T) in a canonical FL contains an O(T) but no T^2 term. We show that in any D >1 the next term after O(T) in \Sigma^R(i\pi T,T) is of order T^D (T^3\ln T in D=3). This T^D term comes from only forward- and backward scattering, and is expressed in terms of fully renormalized amplitudes for these processes. The overall prefactor of the T^D term vanishes in the "local approximation", when the interaction can be approximated by its value for the initial and final fermionic states right on the Fermi surface. The local approximation is justified near a Pomeranchuk instability, even if the vertex corrections are non-negligible. We show that the strength of the first-Matsubara-frequency rule is amplified in the local approximation, where it states that not only the T^D term vanishes but also that \Sigma^R(i\pi T,T) does not contain any terms beyond O(T). This rule imposes two constraints on the scaling form of the self-energy: upon replacing \omega by i\pi T, Im\Sigma^R(\omega,T) must vanish and Re\Sigma^R (\omega, T) must reduce to O(T). These two constraints should be taken into consideration in extracting scaling forms of \Sigma^R(\omega,T) from experimental and numerical data.Comment: 22 pages, 3 figure

Symmetry Plays a Key Role in the Erasing of Patterned Surface Features

We report on how the relaxation of patterns prepared on a thin film can be controlled by manipu- lating the symmetry of the initial shape. The validity of a lubrication theory for the capillary-driven relaxation of surface profiles is verified by atomic force microscopy measurements, performed on films that were patterned using focused laser spike annealing. In particular, we observe that the shape of the surface profile at late times is entirely determined by the initial symmetry of the perturba- tion, in agreement with the theory. Moreover, in this regime the perturbation amplitude relaxes as a power-law in time, with an exponent that is also related to the initial symmetry. The results have relevance in the dynamical control of topographic perturbations for nanolithography and high density memory storage

The Equilibrium Distribution of Gas Molecules Adsorbed on an Active Surface

We evaluate the exact equilibrium distribution of gas molecules adsorbed on an active surface with an infinite number of attachment sites. Our result is a Poisson distribution having mean $X = {\mu P P_s \over P_e}$, with $\mu$ the mean gas density, $P_s$ the sticking probability, $P_e$ the evaporation probability in a time interval $\tau$, and $P$ Smoluchowski's exit probability in time interval $\tau$ for the surface in question. We then solve for the case of a finite number of attachment sites using the mean field approximation, recovering in this case the Langmuir isotherm.Comment: 14 pages done in late

Weak Field Hall Resistance and Effective Carrier Density Through Metal-Insulator Transition in Si-MOS Structures

We studied the weak field Hall voltage in 2D electron layers in Si-MOS structures with different mobilities, through the metal-insulator transition. In the vicinity of the critical density on the metallic side of the transition, we have found weak deviations (about 6-20 %) of the Hall voltage from its classical value. The deviations do not correlate with the strong temperature dependence of the diagonal resistivity rho_{xx}(T). The smallest deviation in R_{xy} was found in the highest mobility sample exhibiting the largest variation in the diagonal resistivity \rho_{xx} with temperature (by a factor of 5).Comment: 4 pages, 4 figures, RevTe

The impact of a correctional-based parenting program in strengthening parenting skills of incarcerated mothers

Despite a relative paucity of information on the impact that incarceration of a parent has on a child, most literature agrees that the effects are real and profound. Corrective Services NSW (CSNSW) in conjunction with Tresillian Family Care Centres introduced a parenting program, Mothering at a Distance (MAAD), across correctional facilities for female prisoners in New South Wales (NSW), Australia. The central aim of the Program was to provide early parenting education and support intervention to mothers in custody, with the aim of guarding against the intergenerational cycle of crime. The Program intended to enhance a prisoner's ability to provide appropriate and sensitive parenting and reduce the emotional and social impact of separation on their children. An evaluation of the Program's development, implementation, effectiveness, and sustainability was conducted on all groups run between October 2006 and December 2008. This article provides a summary of the evaluation findings

Investigation of electro-optical techniques for controlling the direction of a laser beam. Part one - Beam deflector devices. Part two - Beam deflector systems Interim report

Piezoelectrically powered laser beam waveguide for electro-optical acquisition and trackin

Probing the field-induced variation of the chemical potential in Bi(2)Sr(2)CaCu(2)O(y) via the magneto-thermopower measurements

Approximating the shape of the measured in $Bi_2Sr_2CaCu_2O_y$ magneto-thermopower (TEP) $\Delta S(T,H)$ by asymmetric linear triangle of the form $\Delta S(T,H)\simeq S_p(H)\pm B^{\pm}(H)(T_c-T)$ with positive $B ^{-}(H)$ and $B ^{+}(H)$ defined below and above $T_c$, we observe that $B ^{+}(H)\simeq 2B ^{-}(H)$. In order to account for this asymmetry, we explicitly introduce the field-dependent chemical potential of holes $\mu (H)$ into the Ginzburg-Landau theory and calculate both an average $\Delta S_{av}(T,H)$ and fluctuation $\Delta S_{fl}(T,H)$ contributions to the total magneto-TEP $\Delta S(T,H)$. As a result, we find a rather simple relationship between the field-induced variation of the chemical potential in this material and the above-mentioned magneto-TEP data around $T_c$, viz. $\Delta \mu (H)\propto S_p(H)$.Comment: REVTEX (epsf), 4 pages, 2 PS figures; to be published in JET