Andrei E. Ruckenstein

A Ratchet Mechanism of Transcription Elongation and Its Control

RNA chain elongation is a highly processive and accurate process that is finely regulated by numerous intrinsic and extrinsic signals. Here we describe a general mechanism that governs RNA polymerase (RNAP) movement and response to regulatory inputs such as pauses, terminators, and elongation factors. We show that E.coli RNAP moves by a complex Brownian ratchet mechanism, which acts prior to phosphodiester bond formation. The incoming substrate and the flexible F bridge domain of the catalytic center serve as two separate ratchet devices that function in concert to drive forward translocation. The adjacent G loop domain controls F bridge motion, thus keeping the proper balance between productive and inactive states of the elongation complex. This balance is critical for cell viability since it determines the rate, processivity, and fidelity of transcription.

Optimal path to epigenetic switching.

We use large deviation methods to calculate rates of noise-induced transitions between states in multistable genetic networks. We analyze a synthetic biochemical circuit, the toggle switch, and compare the results to those obtained from a numerical solution of the master equation.

Long-wavelength behavior, impurity scattering and magnetic excitations in a marginal Fermi liquid

The marginal Fermi liquid hypothesis about the excitation spectrum of the high-temperature superconductors is supplemented to specify the long-wavelength behavior; it is shown that there are no anomalous renormalizations of the compressibility and the uniform paramagnetic susceptibility. Consideration of elastic scattering from impurities leads to the conclusion that as temperature is decreased, the scattering approaches the unitarity limit. We discuss the possibility that at T → 0, a marginal Fermi liquid is either a superconductor or an insulator. Predictions for the magnetic structure factor observable in neutron scattering consistent with the nuclear relaxation rate on copper and on oxygen are also given.

Correlation Induced Insulator to Metal Transitions

We study a spinless two-band model at half-filling in the limit of infinite dimensions. The ground state of this model in the noninteracting limit is a band insulator. We identify transitions to a metal and to a charge Mott insulator, using a combination of analytical, quantum Monte Carlo, and zero temperature recursion methods. The metallic phase is a non-Fermi-liquid state with algebraic local correlation functions with universal exponents over a range of parameters.

Charge- and spin-gap formation in exactly solvable Hubbard chains with long-range hopping.

We discuss the transition from a metal to charge- or spin-insulating phases characterized by the opening of a gap in the charge- or spin-excitation spectra, respectively. These transitions are addressed within the context of two exactly solvable Hubbard and t-J chains with long-range, 1/r hopping. We discuss the specific heat, compressibility, and magnetic susceptibility of these models as a function of temperature, the band filling, and the interaction strength. We then use conformal-field-theory techniques to extract ground-state correlation functions. Finally, by employing the g-ology analysis we show that the charge-insulator transition is accompanied by an infinite discontinuity in the Drude weight of the electrical conductivity. While the magnetic properties of these models reflect the genuine features of strongly correlated electron systems, the charge-transport properties, especially near the Mott-Hubbard transition, display a nongeneric behavior.

SINGLE SPIN FLIP IN THE INFINITE U HUBBARD MODEL: HUBBARD OPERATORS, THREE-BODY FADEEV EQUATIONS AND GUTZWILLER WAVE FUNCTIONS

We investigate a recently proposed many-body theory for composite (Hubbard) operators (A.E. Ruckenstein and S. Schmitt-Rink, Phys. Rev. B38, 7188 (1988)) in the context of the problem of a single spin flip in the saturated ferromagnetic state of the infinite U Hubbard model. We prove that the suitably defined strong coupling Hartree-Fock mean field theory leads to results identical to those obtained from the Gutzwiller wave function through exact evaluation of the kinetic energy. Most interestingly, we also show how exactly the same results can be obtained starting from the weak coupling limit by solving analytically the three-body t-matrix (Fadeev) equations in the infinite U limit. This work also sheds light on the physical content of slave boson approximations to which our approach was previously shown to be equivalent in the limit of large spin or orbital degeneracy. For the single spin flip problem we compare our results with those obtained by Bethe-Goldstone perturbation theory, Bethe Ansatz in one dimension, and exact diagonalization studies.

INTERFERENCE OF THE FERMI EDGE SINGULARITY WITH AN EXCITONIC RESONANCE IN DOPED SEMICONDUCTORS

Low-temperature emission spectra are calculated for an n-doped semiconductor in which the Fermi level is almost degenerate with an exciton of a higher conduction band. It is shown that in such a sample the virtual transitions of electrons from the Fermi surface into the excitonic state can lead to a strong enhancement of the optical oscillator strength. In particular, due to this effect, the Fermi edge singularity, which is usually only seen in absorption, can become visible also in the emission spectrum. This explains the optical spectra recently obtained in experiments on modulation-doped heterostructures.

Squeezing in the weakly interacting uniform Bose-Einstein condensate

We investigate the presence of squeezing in the weakly repulsive uniform Bose gas, in both the condensate mode and in the nonzero opposite-momenta mode pairs, using two different variational formulations. We explore the U(1) symmetry breaking and Goldstones theorem in the context of a squeezed coherent variational wavefunction, and present the associated Ward identity. We show that squeezing of the condensate mode is absent at the mean field Hartree-Fock-Bogoliubov level and emerges as a result of fluctuations about mean field as a finite volume effect, which vanishes in the thermodynamic limit. On the other hand, the squeezing of the excitations about the condensate survives the thermodynamic limit and is interpreted in terms of density-phase variables using a number-conserving formulation of the interacting Bose gas.

Transverse Spin Diffusion in a Dilute Spin-Polarized Degenerate Fermi Gas

We re-examine the calculation of the transverse spin-diffusion coefficient in a dilute degenerate spin-polarized Fermi gas, for the case of s-wave scattering. The special feature of this limit is that the dependence of the spin diffusion coefficient on temperature and field can be calculated explicitly with no further approximations. This exact solution uncovers a novel intermediate behaviour between the high field spin-rotation dominated regime in which D⊥ ∝ H−2, D∥ ∝ T−2, and the low-field isotropic, collision dominated regime with D⊥ = D∥ ∝ T−2. In this intermediate regime, D⊥, ∥ ∝ T−2but D⊥ ≠ D∥. We emphasize that the low-field crossover cannot be described within the relaxation time approximation. We also present an analytical calculation of the self-energy in the s-wave approximation for a dilute spin-polarized Fermi gas, at zero temperature. This emphasizes the failure of the conventional Fermi-liquid phase space arguments for processes involving spin flips. We close by reviewing the evidence for the existence of the intermediate regime in experiments on weakly spin-polarized3He and3He–4He mixtures.

Optical singularities of the one-dimensional electron gas in semiconductor quantum wires

Abstract The optical properties of a one-dimensional (1D) electron gas with only one or two occupied subbands have been studied in semiconductor quantum wires, obtained by electron beam lithography and subsequent low-energy ion bombardment of modulation-doped GaAs quantum wells. Large optical singularities have been observed at the Fermi level, both in optical absorption and emission. They disappear at temperatures comparable to the Fermi energy. The 1D singularities are much larger and sharper than in 2D systems due to the lack of certain hole recoil effects in 1D. The experimental data are in qualitative agreement with theoretical results based on the exact diagonalization of finite chains.