Extended Variational Cluster Approximation

The variational cluster approximation (VCA) proposed by M. Potthoff {\it et al.} [Phys. Rev. Lett. {\bf 91}, 206402 (2003)] is extended to electron or spin systems with nonlocal interactions. By introducing more than one source field in the action and employing the Legendre transformation, we derive a generalized self-energy functional with stationary properties. Applying this functional to a proper reference system, we construct the extended VCA (EVCA). In the limit of continuous degrees of freedom for the reference system, EVCA can recover the cluster extension of the extended dynamical mean-field theory (EDMFT). For a system with correlated hopping, the EVCA recovers the cluster extension of the dynamical mean-field theory for correlated hopping. Using a discrete reference system composed of decoupled three-site single impurities, we test the theory for the extended Hubbard model. Quantitatively good results as compared with EDMFT are obtained. We also propose VCA (EVCA) based on clusters with periodic boundary conditions. It has the (extended) dynamical cluster approximation as the continuous limit. A number of related issues are discussed.Comment: 23 pages, 5 figures, statements about DCA corrected; published versio

Towards Distributed Convoy Pattern Mining

Mining movement data to reveal interesting behavioral patterns has gained attention in recent years. One such pattern is the convoy pattern which consists of at least m objects moving together for at least k consecutive time instants where m and k are user-defined parameters. Existing algorithms for detecting convoy patterns, however do not scale to real-life dataset sizes. Therefore a distributed algorithm for convoy mining is inevitable. In this paper, we discuss the problem of convoy mining and analyze different data partitioning strategies to pave the way for a generic distributed convoy pattern mining algorithm.Comment: SIGSPATIAL'15 November 03-06, 2015, Bellevue, WA, US

Higher Order Corrections to Density and Temperature of Fermions from Quantum Fluctuations

A novel method to determine the density and temperature of a system based on quantum Fermionic fluctuations is generalized to the limit where the reached temperature T is large compared to the Fermi energy {\epsilon}f . Quadrupole and particle multiplicity fluctuations relations are derived in terms of T . The relevant Fermi integrals are numerically solved for any values of T and compared to the analytical approximations. The classical limit is obtained, as expected, in the limit of large temperatures and small densities. We propose simple analytical formulas which reproduce the numerical results, valid for all values of T . The entropy can also be easily derived from quantum fluctuations and give important insight for the behavior of the system near a phase transition. A comparison of the quantum entropy to the entropy derived from the ratio of the number of deuterons to neutrons gives a very good agreement especially when the density of the system is very low

Generalization of the Poisson kernel to the superconducting random-matrix ensembles

We calculate the distribution of the scattering matrix at the Fermi level for chaotic normal-superconducting systems for the case of arbitrary coupling of the scattering region to the scattering channels. The derivation is based on the assumption of uniformly distributed scattering matrices at ideal coupling, which holds in the absence of a gap in the quasiparticle excitation spectrum. The resulting distribution generalizes the Poisson kernel to the nonstandard symmetry classes introduced by Altland and Zirnbauer. We show that unlike the Poisson kernel, our result cannot be obtained by combining the maximum entropy principle with the analyticity-ergodicity constraint. As a simple application, we calculate the distribution of the conductance for a single-channel chaotic Andreev quantum dot in a magnetic field.Comment: 7 pages, 2 figure

Statistical study of the conductance and shot noise in open quantum-chaotic cavities: Contribution from whispering gallery modes

In the past, a maximum-entropy model was introduced and applied to the study of statistical scattering by chaotic cavities, when short paths may play an important role in the scattering process. In particular, the validity of the model was investigated in relation with the statistical properties of the conductance in open chaotic cavities. In this article we investigate further the validity of the maximum-entropy model, by comparing the theoretical predictions with the results of computer simulations, in which the Schroedinger equation is solved numerically inside the cavity for one and two open channels in the leads; we analyze, in addition to the conductance, the zero-frequency limit of the shot-noise power spectrum. We also obtain theoretical results for the ensemble average of this last quantity, for the orthogonal and unitary cases of the circular ensemble and an arbitrary number of channels. Generally speaking, the agreement between theory and numerics is good. In some of the cavities that we study, short paths consist of whispering gallery modes, which were excluded in previous studies. These cavities turn out to be all the more interesting, as it is in relation with them that we found certain systematic discrepancies in the comparison with theory. We give evidence that it is the lack of stationarity inside the energy interval that is analyzed, and hence the lack of ergodicity that gives rise to the discrepancies. Indeed, the agreement between theory and numerical simulations is improved when the energy interval is reduced to a point and the statistics is then collected over an ensemble. It thus appears that the maximum-entropy model is valid beyond the domain where it was originally derived. An understanding of this situation is still lacking at the present moment.Comment: Revised version, minor modifications, 28 pages, 7 figure

Fermion Resonances on a Thick Brane with a Piecewise Warp Factor

In this paper, we mainly investigate the problems of resonances of massive KK fermions on a single scalar constructed thick brane with a piecewise warp factor matching smoothly. The distance between two boundaries and the other parameters are determined by one free parameter through three junction conditions. For the generalized Yukawa coupling $\eta\bar{\Psi}\phi^{k}\Psi$ with odd $k=1,3,5,...$, the mass eigenvalue $m$, width $\Gamma$, lifetime $\tau$, and maximal probability $P_{max}$ of fermion resonances are obtained. Our numerical calculations show that the brane without internal structure also favors the appearance of resonant states for both left- and right-handed fermions. The scalar-fermion coupling and the thickness of the brane influence the resonant behaviors of the massive KK fermions.Comment: V3: 15 pages, 7 figures, published versio

Virial Expansion of the Nuclear Equation of State

We study the equation of state (EOS) of nuclear matter as function of density. We expand the energy per particle (E/A) of symmetric infinite nuclear matter in powers of the density to take into account 2,3,. . .,N-body forces. New EOS are proposed by fitting ground state properties of nuclear matter (binding energy, compressibility and pressure) and assuming that at high densities a second order phase transition to the Quark Gluon Plasma (QGP) occurs. The latter phase transition is due to symmetry breaking at high density from nuclear matter (locally color white) to the QGP (globally color white). In the simplest implementation of a second order phase transition we calculate the critical exponent ? by using Landau's theory of phase transition. We find ? = 3. Refining the properties of the EOS near the critical point gives ? = 5 in agreement with experimental results. We also discuss some scenarios for the EOS at finite temperatures

Theoretical analysis of dynamic chemical imaging with lasers using high-order harmonic generation

We report theoretical investigations of the tomographic procedure suggested by Itatani {\it et al.} [Nature, {\bf 432} 867 (2004)] for reconstructing highest occupied molecular orbitals (HOMO) using high-order harmonic generation (HHG). Using the limited range of harmonics from the plateau region, we found that under the most favorable assumptions, it is still very difficult to obtain accurate HOMO wavefunction, but the symmetry of the HOMO and the internuclear separation between the atoms can be accurately extracted, especially when lasers of longer wavelengths are used to generate the HHG. We also considered the possible removal or relaxation of the approximations used in the tomographic method in actual applications. We suggest that for chemical imaging, in the future it is better to use an iterative method to locate the positions of atoms in the molecule such that the resulting HHG best fits the macroscopic HHG data, rather than by the tomographic method.Comment: 13 pages, 14 figure

Thick branes with a nonminimally coupled bulk-scalar field

In this paper, we investigate thick branes with a nonminimally coupled background scalar field, whose solution is a single-kink or a double-kink. The effects of the nonminimal coupling constant $\xi$ on the structure of the thick branes and the localization of gravity, fermions, scalars and vectors are discussed. It is shown that each brane will split into two sub-branes as increasing the nonminimal coupling constant $\xi$. By investigating the tensor perturbation equations of gravity and the general covariant Dirac equation of fermions, we find that both the gravity zero mode and left-chiral fermion zero mode are localized at the center of the single-kink branes and localized between the two sub-branes generated by the double-kink, which indicates that the constant $\xi$ does not effect the localization of these zero modes. However, the zero mode of scalars is localized on each sub-brane (for both single-kink and double-kink branes) when $\xi$ is larger than its critical value $\xi_0$. The effects of the nonminimal coupling constant $\xi$ on the resonances of gravity and fermions with finite lifetime on the branes are also discussed.Comment: V2: 33 pages, 17 figures, 3 tables, published versio