Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions

We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing ``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metal-insulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.Comment: 17 pages, 4 figures, REVTe

Measurement of long‐pulse relativistic electron beam perpendicular‐ to‐parallel velocity ratio by Cerenkov emission and radiation darkening on a glass plate

We report measurements of the ratio of the perpendicular velocity to the parallel velocity, α= v⊥ /v∥, of a relativistic electron beam gyrating in a magnetic field by the use of (1) Cerenkov emission from a glass plate, detected by a gated microchannel plate image intensifier camera, and (2) electron‐beam‐induced radiation darkening pattern on the same glass plate. The measurements are based on a direct determination of the Larmor radius of an electron beam of known energy. Experiments were performed on a long‐pulse electron beam accelerator with e‐beam diode parameters: VD = 0.6–0.9 MV, pulse length=0.5–1 μs, ID = 1–10 kA. The experimental value of α agrees with simulation results from particle trajectory codes as well as theoretical predictions from Busch’s theorem and adiabatic theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70360/2/RSINAK-63-2-1671-1.pd

Exact Critical Exponents for Pseudo-Particles in the Kondo Problem

Exact critical exponents of the Green functions for pseudo-fermions and slave bosons in the SU($N$) Anderson model with $U\rightarrow\infty$ are obtained by using the Bethe ansatz solution and boundary conformal field theory. They are evaluated exactly for mixed valence systems and Kondo systems with crystalline fields. The results agree with the prediction of Menge and M\"uller-Hartmann, which coincide with those of the X-ray problem. Some implication of our results in one-dimensional chiral systems is also discussed.Comment: 9 pages, no figure

Dynamical correlations in multiorbital Hubbard models: Fluctuation-exchange approximations

We study the two band degenerate Hubbard model using the Fluctuation Exchange approximation (FLEX) method and compare the results with Quantum Monte-Carlo calculations. Both the self-consistent and the non-self-consistent versions of the FLEX scheme are investigated. We find that, contrary to the one band case, in the multiband case, good agreement with the Quantum Monte-Carlo results is obtained within the electron-electron T-matrix approximation using the full renormalization of the one-particle propagators. The crossover to strong coupling and the formation of satellites is more clearly visible in the non-self-consistent scheme. Finally we discuss the behavior of the FLEX for higher orbital degeneracy.Comment: 18 pages with 12 PS figure

Significant Expansion of Real-Time PCR Multiplexing with Traditional Chemistries using Amplitude Modulation

The real time polymerase chain reaction (rtPCR) is an essential method for detecting nucleic acids that has a wide range of clinical and research applications. Current multiplexed rtPCR is capable of detecting four to six nucleic acid targets in a single sample. However, advances in clinical medicine are driving the need to measure many more targets at once. We demonstrate a novel method which significantly increases the multiplexing capability of any existing rtPCR instrument without new hardware, software, or chemistry. The technique works by varying the relative TaqMan probe concentrations amongst targets that are measured in a single fluorometric channel. Our fluorescent amplitude modulation method generates a unique rtPCR signature for every combination of targets present in a reaction. We demonstrate this technique by measuring nine different targets across three color channels with TaqMan reporting probes, yielding a detection accuracy of 98.9% across all combinations of targets. In principle this method could be extended to measure 6 or more targets per color channel across any number of color channels without loss in specificity

Gas diffusion through columnar laboratory sea ice: implications for mixed-layer ventilation of CO₂ in the seasonal ice zone

Gas diffusion through the porous microstructure of sea ice represents a pathway for ocean–atmosphere exchange and for transport of biogenic gases produced within sea ice. We report on the experimental determination of the bulk gas diffusion coefficients, D, for oxygen (O2) and sulphur hexafluoride (SF6) through columnar sea ice under constant ice thickness conditions for ice surface temperatures between -4 and -12 °C. Profiles of SF6 through the ice indicate decreasing gas concentration from the ice/water interface to the ice/air interface, with evidence for solubility partitioning between gas-filled and liquid-filled pore spaces. On average, DSF6 inline image was 1.3 × 10-4 cm2 s-1 (±40%) and DO2 was 3.9 × 10-5 cm2 s-1 (±41%). The preferential partitioning of SF6 to the gas phase, which is the dominant diffusion pathway produced the greater rate of SF6 diffusion. Comparing these estimates of D with an existing estimate of the air–sea gas transfer through leads indicates that ventilation of the mixed layer by diffusion through sea ice may be negligible, compared to air–sea gas exchange through fractures in the ice pack, even when the fraction of open water is less than 1%

Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons

A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling the expansion represents a universal and comprehensive tool for systematic improvements of static mean-field theories. As an example of the general formalism we investigate in detail an analytically tractable series of ring diagrams that correctly capture dynamical fluctuations at weak coupling. We introduce renormalizations of the diagrammatic expansion at various levels and show how the resultant theories are related to other approximations of similar origin. We demonstrate that only fully self-consistent approximations produce global and thermodynamically consistent extensions of static mean field theories. A fully self-consistent theory for the ring diagrams is reached by summing the so-called noncrossing diagrams.Comment: 17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate file