Hooke's law correlation in two-electron systems

We study the properties of the Hooke's law correlation energy (\Ec), defined as the correlation energy when two electrons interact {\em via} a harmonic potential in a $D$-dimensional space. More precisely, we investigate the $^1S$ ground state properties of two model systems: the Moshinsky atom (in which the electrons move in a quadratic potential) and the spherium model (in which they move on the surface of a sphere). A comparison with their Coulombic counterparts is made, which highlights the main differences of the \Ec in both the weakly and strongly correlated limits. Moreover, we show that the Schr\"odinger equation of the spherium model is exactly solvable for two values of the dimension ($D = 1 \text{and} 3$), and that the exact wave function is based on Mathieu functions.Comment: 7 pages, 5 figure

Invariance of the correlation energy at high density and large dimension in two-electron systems

We prove that, in the large-dimension limit, the high-density correlation energy \Ec of two opposite-spin electrons confined in a $D$-dimensional space and interacting {\em via} a Coulomb potential is given by \Ec \sim -1/(8D^2) for any radial confining potential $V(r)$. This result explains the observed similarity of \Ec in a variety of two-electron systems in three-dimensional space.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Effective one-band electron-phonon Hamiltonian for nickel perovskites

Inspired by recent experiments on the Sr-doped nickelates, $La_{2-x}Sr_xNiO_4$, we propose a minimal microscopic model capable to describe the variety of the observed quasi-static charge/lattice modulations and the resulting magnetic and electronic-transport anomalies. Analyzing the motion of low-spin (s=1/2) holes in a high-spin (S=1) background as well as their their coupling to the in-plane oxygen phonon modes, we construct a sort of generalized Holstein t-J Hamiltonian for the $NiO_2$ planes, which contains besides the rather complex ``composite-hole'' hopping part non-local spin-spin and hole-phonon interaction terms.Comment: 12 pages, LaTeX, submitted to Phys. Rev.

Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, \textit{viz.} the usual one-electron density parameter $\rho$ and a new two-electron parameter $\eta$. We outline a systematic strategy to determine a new density functional $E(\rho,\eta)$ across the spectrum of possible $\rho$ and $\eta$ values.Comment: 8 pages, 2 figures, 5 table

Multipulse operation of a Ti:sapphire laser mode locked by an ion-implanted semiconductor saturable-absorber mirror

Multipulse operation was demonstrated with a Ti:sapphire laser mode-locked by a semiconductor saturable absorber mirror. Widely separated double, triple, and quadruple pulses with irregular spacing were observed. In addition, closely coupled states were also found that could be attributed to interplay between saturable absorber and filter losses, saturated gain and the coherent interaction of solitons. These observations, as well as the mechanisms in the transitions from single to multipulse states are explained within the framework of the generalized complex Ginzburg-Landau equation as the laser master equation.Peer Reviewe

SMT-based Model Checking for Recursive Programs

We present an SMT-based symbolic model checking algorithm for safety verification of recursive programs. The algorithm is modular and analyzes procedures individually. Unlike other SMT-based approaches, it maintains both "over-" and "under-approximations" of procedure summaries. Under-approximations are used to analyze procedure calls without inlining. Over-approximations are used to block infeasible counterexamples and detect convergence to a proof. We show that for programs and properties over a decidable theory, the algorithm is guaranteed to find a counterexample, if one exists. However, efficiency depends on an oracle for quantifier elimination (QE). For Boolean Programs, the algorithm is a polynomial decision procedure, matching the worst-case bounds of the best BDD-based algorithms. For Linear Arithmetic (integers and rationals), we give an efficient instantiation of the algorithm by applying QE "lazily". We use existing interpolation techniques to over-approximate QE and introduce "Model Based Projection" to under-approximate QE. Empirical evaluation on SV-COMP benchmarks shows that our algorithm improves significantly on the state-of-the-art.Comment: originally published as part of the proceedings of CAV 2014; fixed typos, better wording at some place

Space-time versus particle-hole symmetry in quantum Enskog equations

The non-local scattering-in and -out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the -in and -out processes are conjugated by the space and time inversions. Generalisations of the Enskog equation to Fermi liquid systems are hindered by a request of the particle-hole symmetry which contradicts the reversed displacements. We resolve this problem with the help of the optical theorem. It is found that space-time and particle-hole symmetry can only be fulfilled simultaneously for the Bruckner-type of internal Pauli-blocking while the Feynman-Galitskii form allows only for particle-hole symmetry but not for space-time symmetry due to a stimulated emission of Bosons

Correlation energy of anisotropic quantum dots

We study the $D$-dimensional high-density correlation energy \Ec of the singlet ground state of two electrons confined by a harmonic potential with Coulombic repulsion. We allow the harmonic potential to be anisotropic, and examine the behavior of \Ec as a function of the anisotropy $\alpha^{-1}$. In particular, we are interested in the limit where the anisotropy goes to infinity ($\alpha\to0$) and the electrons are restricted to a lower-dimensional space. We show that tuning the value of $\alpha$ from 0 to 1 allows a smooth dimensional interpolation and we demonstrate that the usual model, in which a quantum dot is treated as a two-dimensional system, is inappropriate. Finally, we provide a simple function which reproduces the behavior of \Ec over the entire range of $\alpha$.Comment: 5 pages, 2 figures, 1 table, submitted to Phys. Rev.

Predicting phase equilibria in polydisperse systems

Many materials containing colloids or polymers are polydisperse: They comprise particles with properties (such as particle diameter, charge, or polymer chain length) that depend continuously on one or several parameters. This review focusses on the theoretical prediction of phase equilibria in polydisperse systems; the presence of an effectively infinite number of distinguishable particle species makes this a highly nontrivial task. I first describe qualitatively some of the novel features of polydisperse phase behaviour, and outline a theoretical framework within which they can be explored. Current techniques for predicting polydisperse phase equilibria are then reviewed. I also discuss applications to some simple model systems including homopolymers and random copolymers, spherical colloids and colloid-polymer mixtures, and liquid crystals formed from rod- and plate-like colloidal particles; the results surveyed give an idea of the rich phenomenology of polydisperse phase behaviour. Extensions to the study of polydispersity effects on interfacial behaviour and phase separation kinetics are outlined briefly.Comment: 48 pages, invited topical review for Journal of Physics: Condensed Matter; uses Institute of Physics style file iopart.cls (included

Dynamical Properties of small Polarons

On the basis of the two-site polaron problem, which we solve by exact diagonalization, we analyse the spectral properties of polaronic systems in view of discerning localized from itinerant polarons and bound polaron pairs from an ensemble of single polarons. The corresponding experimental techniques for that concern photoemission and inverse photoemission spectroscopy. The evolution of the density of states as a function of concentration of charge carriers and strength of the electron-phonon interaction clearly shows the opening up of a gap between single polaronic and bi-polaronic states, in analogy to the Hubbard problem for strongly correlated electron systems. The crossover regime between adiabatic and anti-adiabatic small polarons is triggered by two characteristic time scales: the renormalized electron hopping rate and the renormalized vibrational frequency becoming equal. This crossover regime is then characterized by temporarily alternating self- localization and delocalization of the charge carriers which is accompanied by phase slips in the charge and molecular deformation oscillations and ultimately leads to a dephasing between these two dynamical components of the polaron problem. We visualize these features by a study of the temporal evolution of the charge redistribution and the change in molecular deformations. The spectral and dynamical properties of polarons discussed here are beyond the applicability of the standard Lang Firsov approach to the polaron problem.Comment: 31 pages and 23 figs.(eps), accepted in the Phys. Rev.