Multiquantum eigenstates of a linear chain of coupled qubits

We present a technique to identify exact analytic expressions for the multiquantum eigenstates of a linear chain of coupled qubits. A choice of Hilbert subspaces is described that allows an exact solution of the stationary Schrodinger equation without imposing periodic boundary conditions and without neglecting end effects, fully including the dipole-dipole nearest-neighbor interaction between the atoms. The treatment is valid for an arbitrary coherent excitation in the atomic system, any number of atoms, any size of the chain relative to the resonant wavelength and arbitrary initial conditions of the atomic system. The procedure we develop is general enough to be adopted for the study of excitation in an arbitrary array of atoms including spin chains and one-dimensional Bose-Einstein condensates.

Effect of aspect ratio on thermal convection in open and closed systems

Internally heated fluids are found across the nuclear fuel cycle. In certain situations the motion of the fluid is driven by the decay heat (i.e. corium melt pools in severe accidents, the shutdown of liquid metal reactors, molten salt and the passive control of light water reactors) as well as normal operation (i.e. intermediate waste storage and generation IV reactor designs). This can in the long-term affect reactor vessel integrity or lead to localized hot spots and accumulation of solid wastes that may prompt local increases in activity. Two approaches to the modeling of internally heated convection are presented here. These are based on numerical analysis using codes developed in-house and simulations using widely available computational fluid dynamics solvers. Open and closed fluid layers at around the transition between conduction and convection of various aspect ratios are considered. We determine optimum domain aspect ratio (1:7:7 up to 1:24:24 for open systems and 5:5:1, 1:10:10 and 1:20:20 for closed systems), mesh resolutions and turbulence models required to accurately and efficiently capture the convection structures that evolve when perturbing the conductive state of the fluid layer. Note that the open and closed fluid layers we study here are bounded by a conducting surface over an insulating surface. Conclusions will be drawn on the influence of the periodic boundary conditions on the flow patterns observed. We have also examined the stability of the nonlinear solutions that we found with the aim of identifying the bifurcation sequence of these solutions en route to turbulence.

Dimensional dependence of the Stokes-Einstein relation and its violation

We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical simulations. We then investigate the evolution of the high-density SER violation with dimension in simple hard sphere glass formers. The analysis suggests that this SER violation disappears around dimension du = 8, above which it is not observed. The critical exponent associated with the violation appears to evolve linearly in 8 - d, below d = 8, as predicted by Biroli and Bouchaud [J. Phys.: Condens. Matter 19, 205101 (2007)], but the linear coefficient is not consistent with the prediction. The SER violation with d establishes a new benchmark for theory, and its complete description remains an open problem. © 2013 AIP Publishing LLC.

Formation of helical ion chains

We study the nonequilibrium dynamics of the linear to zigzag structural phase transition exhibited by an ion chain confined in a trap with periodic boundary conditions. The transition is driven by reducing the transverse confinement at a finite quench rate, which can be accurately controlled. This results in the formation of zigzag domains oriented along different transverse planes. The twists between different domains can be stabilized by the topology of the trap and under laser cooling the system has a chance to relax to a helical chain with nonzero winding number. Molecular dynamics simulations are used to obtain a large sample of possible trajectories for different quench rates. The scaling of the average winding number with different quench rates is compared to the prediction of the Kibble-Zurek theory, and a good quantitative agreement is found.

Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary

We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media.

Homogenization in a thin domain with an oscillatory boundary

In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type R(epsilon) = {(x(1), x(2)) is an element of R(2) vertical bar x(1) is an element of (0, 1), 0 < x(2) < epsilon G(x(1), x(1)/epsilon)} where the function G(x, y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter epsilon. (C) 2011 Elsevier Masson SAS. All rights reserved.

Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u equivalent to 1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain. (C) 2009 Elsevier Inc. All rights reserved.

Boundary and internal conditions for adjoint fluid-flow problems

The ever-increasing robustness and reliability of flow-simulation methods have consolidated CFD as a major tool in virtually all branches of fluid mechanics. Traditionally, those methods have played a crucial role in the analysis of flow physics. In more recent years, though, the subject has broadened considerably, with the development of optimization and inverse design applications. Since then, the search for efficient ways to evaluate flow-sensitivity gradients has received the attention of numerous researchers. In this scenario, the adjoint method has emerged as, quite possibly, the most powerful tool for the job, which heightens the need for a clear understanding of its conceptual basis. Yet, some of its underlying aspects are still subject to debate in the literature, despite all the research that has been carried out on the method. Such is the case with the adjoint boundary and internal conditions, in particular. The present work aims to shed more light on that topic, with emphasis on the need for an internal shock condition. By following the path of previous authors, the quasi-1D Euler problem is used as a vehicle to explore those concepts. The results clearly indicate that the behavior of the adjoint solution through a shock wave ultimately depends upon the nature of the objective functional.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Pressure of massless hot scalar theory in the boundary effective theory framework

We use the boundary effective theory approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is essentially nonperturbative. To lowest order, the main ingredient is the solution of the free Euler-Lagrange equation with nontrivial (time) boundary conditions. We derive a resummed pressure, which is in good agreement with recent calculations found in the literature, following a very direct and compact procedure.

Renyi entropy and parity oscillations of anisotropic spin-s Heisenberg chains in a magnetic field

Using the density matrix renormalization group, we investigate the Renyi entropy of the anisotropic spin-s Heisenberg chains in a z-magnetic field. We considered the half-odd-integer spin-s chains, with s = 1/2, 3/2, and 5/2, and periodic and open boundary conditions. In the case of the spin-1/2 chain we were able to obtain accurate estimates of the new parity exponents p(alpha)((p)) and p(alpha)((o)) that gives the power-law decay of the oscillations of the alpha-Renyi entropy for periodic and open boundary conditions, respectively. We confirm the relations of these exponents with the Luttinger parameter K, as proposed by Calabrese et al. [Phys. Rev. Lett. 104, 095701 (2010)]. Moreover, the predicted periodicity of the oscillating term was also observed for some nonzero values of the magnetization m. We show that for s > 1/2 the amplitudes of the oscillations are quite small and get accurate estimates of p(alpha)((p)) and p(alpha)((o)) become a challenge. Although our estimates of the new universal exponents p(alpha)((p)) and p(alpha)((o)) for the spin-3/2 chain are not so accurate, they are consistent with the theoretical predictions.

Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

Inverse analysis FOR two-dimensional structures using the boundary element method

Inverse analysis is currently an important subject of study in several fields of science and engineering. The identification of physical and geometric parameters using experimental measurements is required in many applications. In this work a boundary element formulation to identify boundary and interface values as well as material properties is proposed. In particular the proposed formulation is dedicated to identifying material parameters when a cohesive crack model is assumed for 2D problems. A computer code is developed and implemented using the BEM multi-region technique and regularisation methods to perform the inverse analysis. Several examples are shown to demonstrate the efficiency of the proposed model. (C) 2010 Elsevier Ltd. All rights reserved,

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Gauge P-representations for quantum-dynamical problems: Removal of boundary terms

P-representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum-dynamical many-body calculations such as Bose-Einstein condensation. We introduce a representation called the gauge P representation, which greatly widens the range of tractable problems. Our treatment results in an infinite set of possible time evolution equations, depending on arbitrary gauge functions that can be optimized for a given quantum system. In some cases, previous methods can give erroneous results, due to the usual assumption of vanishing boundary conditions being invalid for those particular systems. Solutions are given to this boundary-term problem for all the cases where it is known to occur: two-photon absorption and the single-mode laser. We also provide some brief guidelines on how to apply the stochastic gauge method to other systems in general, quantify the freedom of choice in the resulting equations, and make a comparison to related recent developments.