Simulation of quantum zero-point effects in water using a frequency-dependent thermostat

Molecules like water have vibrational modes with a zero-point energy well above room temperature. As a consequence, classical molecular dynamics simulations of their liquids largely underestimate the energy of modes with a higher zero-point temperature, which translates into an underestimation of covalent interatomic distances due to anharmonic effects. Zero-point effects can be recovered using path integral molecular dynamics simulations, but these are computationally expensive, making their combination with ab initio molecular dynamics simulations a challenge. As an alternative to path integral methods, from a computationally simple perspective, one would envision the design of a thermostat capable of equilibrating and maintaining the different vibrational modes at their corresponding zero-point temperatures. Recently, Ceriotti et al. (Phys. Rev. Lett. 102 020601 (2009)) introduced a framework to use a custom-tailored Langevin equation with correlated noise that can be used to include quantum fluctuations in classical molecular dynamics simulations. Here we show that it is possible to use the generalized Langevin equation with suppressed noise in combination with Nose-Hoover thermostats to efficiently impose a zero-point temperature on independent modes in liquid water. Using our simple and inexpensive method, we achieve excellent agreement for all atomic pair correlation functions compared to the path integral molecular dynamics simulation.Comment: 27 pages, 12 figs, Published versio

FQHE interferometers in strong tunneling regime. The role of compactness of edge fields

We consider multiple-point tunneling in the interferometers formed between edges of electron liquids with in general different filling factors in the regime of the Fractional Quantum Hall effect (FQHE). We derive an effective matrix Caldeira-Leggett models for the multiple tunneling contacts connected by the chiral single-mode FQHE edges. It is shown that the compactness of the Wen- Fr\"ohlich chiral boson fields describing the FQHE edge modes plays a crucial role in eliminating the spurious non-locality of the electron transport properties of the FQHE interferometers arising in the regime of strong tunneling.Comment: 5 page

Structure and Rheology of the Defect-gel States of Pure and Particle-dispersed Lyotropic Lamellar Phases

We present important new results from light-microscopy and rheometry on a moderately concentrated lyotropic smectic, with and without particulate additives. Shear-treatment aligns the phase rapidly, except for a striking network of oily-streak defects, which anneals out much more slowly. If spherical particles several microns in diameter are dispersed in the lamellar medium, part of the defect network persists under shear-treatment, its nodes anchored on the particles. The sample as prepared has substantial storage and loss moduli, both of which decrease steadily under shear-treatment. Adding particles enhances the moduli and retards their decay under shear. The data for the frequency-dependent storage modulus after various durations of shear-treatment can be scaled to collapse onto a single curve. The elasticity and dissipation in these samples thus arises mainly from the defect network, not directly from the smectic elasticity and hydrodynamics.Comment: 19 pages inclusive of 12 PostScript figures, uses revtex, psfrag and epsfig. Revised version, accepted for publication in Euro. Phys. J. B, with improved images of defect structure and theoretical estimates of network elasticity and scalin

Phase relations and gibbs energies in the system Mn-Rh-O

Phase relations in the system Mn-Rh-O are established at 1273 K by equilibrating different compositions either in evacuated quartz ampules or in pure oxygen at a pressure of 1.01 × 105 Pa. The quenched samples are examined by optical microscopy, X-ray diffraction, and energy-dispersive X-ray analysis (EDAX). The alloys and intermetaUics in the binary Mn-Rh system are found to be in equilibrium with MnO. There is only one ternary compound, MnRh204, with normal spinel structure in the system. The compound Mn304 has a tetragonal structure at 1273 K. A solid solution is formed between MnRh204 and Mn304. The solid solution has the cubic structure over a large range of composition and coexists with metallic rhodium. The partial pressure of oxygen corresponding to this two-phase equilibrium is measured as a function of the composition of the spinel solid solution and temperature. A new solid-state cell, with three separate electrode compartments, is designed to measure accurately the chemical potential of oxygen in the two-phase mixture, Rh + Mn3-2xRh2xO4, which has 1 degree of freedom at constant temperature. From the electromotive force (emf), thermodynamic mixing properties of the Mn304-MnRh204 solid solution and Gibbs energy of formation of MnRh204 are deduced. The activities exhibit negative deviations from Raoult's law for most of the composition range, except near Mn304, where a two-phase region exists. In the cubic phase, the entropy of mixing of the two Rh3+ and Mn3+ ions on the octahedral site of the spinel is ideal, and the enthalpy of mixing is positive and symmetric with respect to composition. For the formation of the spinel (sp) from component oxides with rock salt (rs) and orthorhombic (orth) structures according to the reaction, MnO (rs) + Rh203 (orth) → MnRh204 (sp), ΔG° = -49,680 + 1.56T (±500) J mol-1. The oxygen potentials corresponding to MnO + Mn304 and Rh + Rh203 equilibria are also obtained from potentiometric measurements on galvanic cells incorporating yttria-stabilized zirconia as the solid electrolyte. From these results, an oxygen potential diagram for the ternary system is developed

Schematic Models for Active Nonlinear Microrheology

We analyze the nonlinear active microrheology of dense colloidal suspensions using a schematic model of mode-coupling theory. The model describes the strongly nonlinear behavior of the microscopic friction coefficient as a function of applied external force in terms of a delocalization transition. To probe this regime, we have performed Brownian dynamics simulations of a system of quasi-hard spheres. We also analyze experimental data on hard-sphere-like colloidal suspensions [Habdas et al., Europhys. Lett., 2004, 67, 477]. The behavior at very large forces is addressed specifically

A Class of Parameter Dependent Commuting Matrices

We present a novel class of real symmetric matrices in arbitrary dimension $d$, linearly dependent on a parameter $x$. The matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such matrices for all $x$, and an intuitive sufficiency condition for the solvability of certain linear equations that arise therefrom. This class of matrices generically violate the Wigner von Neumann non crossing rule, and is argued to be intimately connected with finite dimensional Hamiltonians of quantum integrable systems.Comment: Latex, Added References, Typos correcte

Explicit MBR All-Symbol Locality Codes

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously

The Origin of Degeneracies and Crossings in the 1d Hubbard Model

The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyze in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated that in these systems there are crossings of levels of the same parameter independent symmetry. We show that this apparent violation of the Wigner-von Neumann noncrossing rule follows directly from the existence of nontrivial conservation laws and is a characteristic signature of quantum integrability. The energy spectra of Hubbard chains display many instances of permanent (at all values of the coupling) twofold degeneracies that cannot be explained by parameter independent symmetries. We relate these degeneracies to the different transformation properties of the conserved currents under spatial reflections and the particle-hole transformation and estimate the fraction of doubly degenerate states. We also discuss multiply degenerate eigenstates of the Hubbard Hamiltonian. The wave functions of many of these states do not depend on the coupling, which suggests the existence of an additional parameter independent symmetry.Comment: 25 pages, 12 figure

A Dynamic Renormalization Group Study of Active Nematics

We carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady state with uniaxial, apolar orientational order. Using the dynamical renormalization group, we show that the leading nonlinearities in this equation are marginally \textit{irrelevant}. We discover a special limit of parameters in which the equation of motion for the angle field of bears a close relation to the 2d stochastic Burgers equation. We find nevertheless that, unlike for the Burgers problem, the nonlinearity is marginally irrelevant even in this special limit, as a result of of a hidden fluctuation-dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterpartsComment: 31 pages 6 figure