Exact Diagonalization Dynamical Mean Field Theory for Multi-Band Materials: Effect of Coulomb correlations on the Fermi surface of Na_0.3CoO_2

Dynamical mean field theory combined with finite-temperature exact diagonalization is shown to be a suitable method to study local Coulomb correlations in realistic multi-band materials. By making use of the sparseness of the impurity Hamiltonian, exact eigenstates can be evaluated for significantly larger clusters than in schemes based on full diagonalization. Since finite-size effects are greatly reduced this approach allows the study of three-band systems down to very low temperatures, for strong local Coulomb interactions and full Hund exchange. It is also shown that exact diagonalization yields smooth subband quasi-particle spectra and self-energies at real frequencies. As a first application the correlation induced charge transfer between t2g bands in Na_0.3CoO_2 is investigated. For both Hund and Ising exchange the small eg' Fermi surface hole pockets are found to be slightly enlarged compared to the non-interacting limit, in agreement with previous Quantum Monte Carlo dynamical mean field calculations for Ising exchange, but in conflict with photoemission data.Comment: 9 pages, 7 figure

Quantum Computation of a Complex System : the Kicked Harper Model

The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting phenomena such as fractal spectra, mixed phase space, dynamical localization, anomalous diffusion, or partial delocalization, and can describe electrons in a magnetic field. Three different quantum algorithms are presented and analyzed, enabling to simulate efficiently the evolution operator of this system with different precision using different resources. Depending on the parameters chosen, the system is near-integrable, localized, or partially delocalized. In each case we identify transport or spectral quantities which can be obtained more efficiently on a quantum computer than on a classical one. In most cases, a polynomial gain compared to classical algorithms is obtained, which can be quadratic or less depending on the parameter regime. We also present the effects of static imperfections on the quantities selected, and show that depending on the regime of parameters, very different behaviors are observed. Some quantities can be obtained reliably with moderate levels of imperfection, whereas others are exponentially sensitive to imperfection strength. In particular, the imperfection threshold for delocalization becomes exponentially small in the partially delocalized regime. Our results show that interesting behavior can be observed with as little as 7-8 qubits, and can be reliably measured in presence of moderate levels of internal imperfections

Generalization of the interaction between the Haar approximation and polynomial operators to higher order methods

International audienceIn applications it is useful to compute the local average of a function f(u) of an input u from empirical statistics on u. A very simple relation exists when the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation

Numerically stable computation of CreditRisk+

The CreditRisk+ model launched by CSFB in 1997 is widely used by practitioners in the banking sector as a simple means for the quantification of credit risk, primarily of the loan book. We present an alternative numerical recursion scheme for CreditRisk+, equivalent to an algorithm recently proposed by Giese, based on well-known expansions of the logarithm and the exponential of a power series. We show that it is advantageous to the Panjer recursion advocated in the original CreditRisk+ document, in that it is numerically stable. The crucial stability arguments are explained in detail. Furthermore, the computational complexity of the resulting algorithm is stated

A Finite Element Computation of the Gravitational Radiation emitted by a Point-like object orbiting a Non-rotating Black Hole

The description of extreme-mass-ratio binary systems in the inspiral phase is a challenging problem in gravitational wave physics with significant relevance for the space interferometer LISA. The main difficulty lies in the evaluation of the effects of the small body's gravitational field on itself. To that end, an accurate computation of the perturbations produced by the small body with respect the background geometry of the large object, a massive black hole, is required. In this paper we present a new computational approach based on Finite Element Methods to solve the master equations describing perturbations of non-rotating black holes due to an orbiting point-like object. The numerical computations are carried out in the time domain by using evolution algorithms for wave-type equations. We show the accuracy of the method by comparing our calculations with previous results in the literature. Finally, we discuss the relevance of this method for achieving accurate descriptions of extreme-mass-ratio binaries.Comment: RevTeX 4. 18 pages, 8 figure

Antisymmetrization of a Mean Field Calculation of the T-Matrix

The usual definition of the prior(post) interaction $V(V^\prime )$ between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projector ${\cal A}$ must be included in the definition of the transition operator, $T\equiv V^\prime{\cal A}+V^\prime{\cal A}GV.$ We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate of $T$. The theory is illustrated by a calculation of forward $\alpha$-$\alpha$ scattering, making use of self consistent symmetries.Comment: 30 pages, no figures, plain TeX, SPHT/93/14

Tidal evolution of exo-planetary systems: WASP-50, GJ 1214 and CoRoT-7

We perform numerical simulations to investigate tidal evolution of two single-planet systems, that is, WASP-50 and GJ 1214 and a two-planet system CoRoT-7. The results of orbital evolution show that tidal decay and circularization may play a significant role in shaping their final orbits, which is related to the initial orbital data in the simulations. For GJ 1214 system, different cases of initial eccentricity are also considered as only an upper limit of its eccentricity (0.27) is shown, and the outcome suggests a possible maximum initial eccentricity (0.4) in the adopted dynamical model. Moreover, additional runs with alternative values of dissipation factor $Q^\prime_1$ are carried out to explore tidal evolution for GJ 1214b, and these results further indicate that the real $Q^\prime_1$ of GJ 1214b may be much larger than its typical value, which may reasonably suggest that GJ 1214b bears a present-day larger eccentricity, undergoing tidal circularization at a slow rate. For the CoRoT-7 system, tidal forces make two planets migrating towards their host star as well as producing tidal circularization, and in this process tidal effects and mutual gravitational interactions are coupled with each other. Various scenarios of the initial eccentricity of the outer planet have also been done to investigate final planetary configuration. Tidal decay arising from stellar tides may still work for each system as the eccentricity decreases to zero, and this is in association with the remaining lifetime of each planet used to predict its future.Comment: 9 pages, 12 figures, accepted for publication in "SCIENCE CHINA Physics,Mechanics & Astronomy

Microscopic universality in the spectrum of the lattice Dirac operator

Large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions are calculated for SU(2) lattice gauge theory. The accumulation of eigenvalues near zero is analyzed as a signal of chiral symmetry breaking and compared with parameter-free predictions from chiral random matrix theory. Excellent agreement for the distribution of the smallest eigenvalue and the microscopic spectral density is found. This provides direct evidence for the conjecture that these quantities are universal functions.Comment: 4 pages, 3 figures (included), REVTeX 3.1; updated version to appear in Phys. Rev. Let