Analytically solvable model of an electronic Mach-Zehnder interferometer

We consider a class of models of non-equilibrium electronic Mach-Zehnder interferometers built on integer quantum Hall edges states. The models are characterized by the electron-electron interaction being restricted to the inner part of the interferometer and transmission coefficients of the quantum quantum point contacts, defining the interferometer, which may take arbitrary values from zero to one. We establish an exact solution of these models in terms of single-particle quantities --- determinants and resolvents of Fredholm integral operators. In the general situation, the results can be obtained numerically. In the case of strong charging interaction, the operators acquire the block Toeplitz form. Analyzing the corresponding Riemann-Hilbert problem, we reduce the result to certain singular single-channel determinants (which are a generalization of Toeplitz determinants with Fisher-Hartwig singularities), and obtain an analytic result for the interference current (and, in particular, for the visibility of Aharonov-Bohm oscillations). Our results, which are in good agreement with experimental observations, show an intimate connection between the observed "lobe" structure in the visibility of Aharonov-Bohm oscillations and multiple branches in the asymptotics of singular integral determinants.Comment: 29 pages, 10 figure

Interaction Quench in Nonequilibrium Luttinger Liquids

We study the relaxation dynamics of a nonequilibrium Luttinger liquid after a sudden interaction switch-on ("quench"), focussing on a double-step initial momentum distribution function. In the framework of the non-equilibrium bosonization, the results are obtained in terms of singular Fredholm determinants that are evaluated numerically and whose asymptotics are found analytically. While the quasi-particle weights decay exponentially with time after the quench, this is not a relaxation into a thermal state, in view of the integrability of the model. The steady-state distribution emerging at infinite times retains two edges which support Luttinger-liquid-like power-law singularities smeared by dephasing. The obtained critical exponents and the dephasing length are found to depend on the initial nonequilibrium state.Comment: 11 pages, 5 figure

First-Order Transition in XY Fully Frustrated Simple Cubic Lattice

We study the nature of the phase transition in the fully frustrated simple cubic lattice with the XY spin model. This system is the Villain's model generalized in three dimensions. The ground state is very particular with a 12-fold degeneracy. Previous studies have shown unusual critical properties. With the powerful Wang-Landau flat-histogram Monte Carlo method, we carry out in this work intensive simulations with very large lattice sizes. We show that the phase transition is clearly of first order, putting an end to the uncertainty which has lasted for more than twenty years

Kinetics of Loop Formation in Polymer Chains

We investigate the kinetics of loop formation in flexible ideal polymer chains (Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is $\tau_c\sim \tau_0 N^2$ (where $\tau_0$ is a microscopic time scale and $N$ is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when $a$, the capture radius for contact formation, exceeds $b$, the average distance between two connected beads. Simulations also show that, when $a < b$, $\tau_c\sim N^{\alpha_\tau}$, where $1.5<{\alpha_\tau}\le 2$ in the range $7<N<200$ used in the simulations. By using a diffusion coefficient that is dependent on the length scales $a$ and $b$ (with $a<b$), which captures the two-stage mechanism by which looping occurs when $a < b$, we obtain an analytic expression for $\tau_c$ that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly affected when interactions between monomers are taken into account. Remarkably, for $N < 100$ the values of $\tau_c$ decrease by more than two orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for $\tau_c$ to a power law in $N$ ($\tau_c\sim N^{\alpha_\tau}$) show that $\alpha_\tau$ varies from about 2.4 in a good solvent to about 1.0 in poor solvents. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain.Comment: 30 pages, 9 figures. Revised version includes a new figure (8) and minor changes to the tex

On the origin of the unusual behavior in the stretching of single-stranded DNA

Force extension curves (FECs), which quantify the response of a variety of biomolecules subject to mechanical force ($f$), are often quantitatively fit using worm-like chain (WLC) or freely-jointed chain (FJC) models. These models predict that the chain extension, $x$, normalized by the contour length increases linearly at small $f$ and at high forces scale as $x \sim (1 - f^{-\alpha})$ where $\alpha$= 0.5 for WLC and unity for FJC. In contrast, experiments on ssDNA show that over a range of $f$ and ionic concentration, $x$ scales as $x\sim\ln f$, which cannot be explained using WLC or FJC models. Using theory and simulations we show that this unusual behavior in FEC in ssDNA is due to sequence-independent polyelectrolyte effects. We show that the $x\sim \ln f$ arises because in the absence of force the tangent correlation function, quantifying chain persistence, decays algebraically on length scales on the order of the Debye length. Our theory, which is most appropriate for monovalent salts, quantitatively fits the experimental data and further predicts that such a regime is not discernible in double stranded DNA.Comment: Accepted for publication in JC

Off-fault tensile cracks: A link between geological fault observations, lab experiments, and dynamic rupture models

We examine the local nature of the dynamic stress field in the vicinity of the tip of a semi-infinite sub-Rayleigh (slower than the Rayleigh wave speed, c_R) mode II crack with a velocity-weakening cohesive zone. We constrain the model using results from dynamic photoelastic experiments, in which shear ruptures were nucleated spontaneously in Homalite-100 plates along a bonded, precut, and inclined interface subject to a far-field uniaxial prestress. During the experiments, tensile cracks grew periodically along one side of the shear rupture interface at a roughly constant angle relative to the shear rupture interface. The occurrence and inclination of the tensile cracks are explained by our analytical model. With slight modifications, the model can be scaled to natural faults, providing diagnostic criteria for interpreting velocity, directivity, and static prestress state associated with past earthquakes on exhumed faults. Indirectly, this method also allows one to constrain the velocity-weakening nature of natural ruptures, providing an important link between field geology, laboratory experiments, and seismology

Simple Combined Model for Nonlinear Excitations in DNA

We propose a new simple model for DNA denaturation bases on the pendulum model of Englander\cite{A1} and the microscopic model of Peyrard {\it et al.},\cite{A3} so called "combined model". The main parameters of our model are: the coupling constant $k$ along each strand, the mean stretching $y^\ast$ of the hydrogen bonds, the ratio of the damping constant and driven force $\gamma/F$. We show that both the length $L$ of unpaired bases and the velocity $v$ of kinks depend on not only the coupling constant $k$ but also the temperature $T$. Our results are in good agreement with previous works.Comment: 6 pages, 10 figures, submitted to Phys. Rev.