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

A scalable, high-speed measurement-based quantum computer using trapped ions

We describe a scalable, high-speed, and robust architecture for measurement-based quantum-computing with trapped ions. Measurement-based architectures offer a way to speed-up operation of a quantum computer significantly by parallelizing the slow entangling operations and transferring the speed requirement to fast measurement of qubits. We show that a 3D cluster state suitable for fault-tolerant measurement-based quantum computing can be implemented on a 2D array of ion traps. We propose the projective measurement of ions via multi-photon photoionization for nanosecond operation and discuss the viability of such a scheme for Ca ions.Comment: 4 pages, 3 figure

Fluctuations in the level density of a Fermi gas

We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe's theory. At low energies oscillatory corrections to the many--body density of states, related to shell effects, are obtained. The fluctuations depend non-trivially on energy and particle number. Universality and connections with Poisson statistics and random matrix theory are established for regular and chaotic single--particle motion.Comment: 4 pages, 1 figur

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

Hierarchical Model for the Evolution of Cloud Complexes

The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment. Based on this picture, a hierarchical model for the evolution of Cloud Complexes, including star formation, is constructed, that follows the mass evolution of each sub-structure by computing its mass exchange (evaporation or condensation) with its parent and children, which depends on the radiation density at the interphase. For the set of parameters used as a reference model, the system produces IMFs with a maximum at too high mass (~2 M_sun) and the characteristic times for evolution seem too long. We show that these properties can be improved by adjusting model parameters. However, the emphasis here is to illustrate some general properties of this nonlinear model for the star formation process. Notwithstanding the simplifications involved, the model reveals an essential feature that will likely remain if additional physical processes are included. That is: the detailed behavior of the system is very sensitive to variations on the initial and external conditions, suggesting that a "universal" IMF is very unlikely. When an ensemble of IMFs corresponding to a variety of initial or external conditions is examined, the slope of the IMF at high masses shows variations comparable to the range derived from observational data. (Abridged)Comment: Latex, 29 pages, 13 figures, accepted for publication in Ap

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

Temperature and salinity tolerances of Stage 1 zoeae predict possible range expansion of an introduced portunid crab, Charybdis japonica, in New Zealand

The successful invasion of a non-native species depends on several factors, including initial colonization and establishment of a self-sustaining population. Populations of the non-native paddle crab Charybdis japonica were first recognized in the Waitemata Harbour, Auckland, New Zealand in 2000, most likely arriving in ballast waters of an Asian merchant vessel. A survey completed in 2003 found C. japonica throughout the Waitemata Harbour, and further sampling in 2009 has revealed several well established populations in estuaries up to 70 km from the putative invasion point. As the potential for further establishment of C. japonica beyond this area may depend on the temperature and salinity tolerances of their free swimming larvae, we quantified the survival of newly-hatched Stage 1 C. japonica zoeae subjected to temperatures ranging from 11 to 43°C or salinities from 5 to 45‰ in the laboratory. Upon hatching, replicate C. japonica zoeae were directly transferred from 21°C and 34.6‰ seawater to either an experimental temperature or salinity level. Behaviour and death rates of the larvae were monitored over a 24 h period in the absence of food. Comparisons of zoeal survival rates to historical sea surface temperatures and salinities show that C. japonica Stage 1 zoeae tolerate a broad range of temperatures and salinities and could survive natural conditions throughout New Zealand. This gives C. japonica the potential to invade many other New Zealand estuaries and harbours