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Title:

Neuronal coding in the retina

Publisher:

Ludwig-Maximilians-Universität München

Year of Publication:

2012-02-01

Document Type:

Dissertation ; NonPeerReviewed

Subjects:

Fakultät für Physik

Fakultät für Physik Minimize

Relations:

http://edoc.ub.uni-muenchen.de/13901/

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Title:

Towards the Kantorovich dual solution for strictly correlated electrons in atoms and molecules

Publisher:

eScholarship, University of California

Year of Publication:

2014-04-21

Source:

Mendl, Christian. (2014). Towards the Kantorovich dual solution for strictly correlated electrons in atoms and molecules. Physical Review B. Lawrence Berkeley National Laboratory: Lawrence Berkeley National Laboratory. Retrieved from: http://www.escholarship.org/uc/item/1d00k3ww

Mendl, Christian. (2014). Towards the Kantorovich dual solution for strictly correlated electrons in atoms and molecules. Physical Review B. Lawrence Berkeley National Laboratory: Lawrence Berkeley National Laboratory. Retrieved from: http://www.escholarship.org/uc/item/1d00k3ww Minimize

Document Type:

article

Language:

english

Subjects:

Physics ; Mathematics and Computing

Physics ; Mathematics and Computing Minimize

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public

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Title:

Efficient algorithm for many-electron angular momentum and spin diagonalization on atomic subshells

Description:

We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the n-fold antisymmetrized tensor product $\wedge^n V_u$, where n is the number of electrons and u = s, p, d, . denotes the atomic subshell. This is an essential step for dimension reduction in configuration-interaction ...

We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the n-fold antisymmetrized tensor product $\wedge^n V_u$, where n is the number of electrons and u = s, p, d, . denotes the atomic subshell. This is an essential step for dimension reduction in configuration-interaction (CI) methods applied to atomic many-electron quantum systems. The algorithm relies on the observation that each $L_z$ eigenstate with maximal eigenvalue is also an $L^2$ eigenstate (equivalently for $S_z$ and $S^2$), as well as the traversal of LS eigenstates using the lowering operators $L_-$ and $S_-$. Iterative application to the remaining states in $\wedge^n V_u$ leads to an implicit simultaneous diagonalization. A detailed complexity analysis for fixed n and increasing subshell number u yields running time $O(u^{3n-2})$. A symbolic computer algebra implementation is available online. ; Comment: 10 pages, 3 figures Minimize

Year of Publication:

2014-09-24

Document Type:

text

Subjects:

Physics - Atomic Physics ; Physics - Computational Physics ; Quantum Physics

Physics - Atomic Physics ; Physics - Computational Physics ; Quantum Physics Minimize

DDC:

518 Numerical analysis *(computed)*

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Title:

Matrix-valued Quantum Lattice Boltzmann Method

Description:

We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum Boltzmann equation, with the classical Maxwell distribution replaced by Fermi-Dirac functions. To accommodate the spin density matrix, the distribution functions become 2 x 2 matrix-valued. We show that the efficient, commonly used BGK approximation of the collision operator ...

We devise a lattice Boltzmann method (LBM) for a matrix-valued quantum Boltzmann equation, with the classical Maxwell distribution replaced by Fermi-Dirac functions. To accommodate the spin density matrix, the distribution functions become 2 x 2 matrix-valued. We show that the efficient, commonly used BGK approximation of the collision operator is valid in the present setting. The framework could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics. ; Comment: 19 pages Minimize

Year of Publication:

2013-09-06

Document Type:

text

Subjects:

Physics - Computational Physics ; Computer Science - Numerical Analysis ; Physics - Fluid Dynamics ; Quantum Physics ; 65Z05 ; 76Y05 ; 82D40 ; 81-08

Physics - Computational Physics ; Computer Science - Numerical Analysis ; Physics - Fluid Dynamics ; Quantum Physics ; 65Z05 ; 76Y05 ; 82D40 ; 81-08 Minimize

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Title:

Efficient Algorithm for Asymptotics-Based Configuration-Interaction Methods and Electronic Structure of Transition Metal Atoms

Description:

Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schr\"odinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement,...

Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schr\"odinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wavefunctions, and use of Slater-type orbitals (STO's). The required Coulomb integrals for STO's are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to 3d transition metal atoms are in good agreement with experimental data. In particular we reproduce the anomalous magnetic moment and orbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr. ; Comment: 14 pages, 1 figure Minimize

Year of Publication:

2010-09-10

Document Type:

text

Subjects:

Quantum Physics ; Physics - Atomic Physics

Quantum Physics ; Physics - Atomic Physics Minimize

DDC:

539 Modern physics *(computed)*

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Title:

The FermiFab Toolbox for Fermionic Many-Particle Quantum Systems

Description:

This paper introduces the FermiFab toolbox for many-particle quantum systems. It is mainly concerned with the representation of (symbolic) fermionic wavefunctions and the calculation of corresponding reduced density matrices (RDMs). The toolbox transparently handles the inherent antisymmetrization of wavefunctions and incorporates the creation/a...

This paper introduces the FermiFab toolbox for many-particle quantum systems. It is mainly concerned with the representation of (symbolic) fermionic wavefunctions and the calculation of corresponding reduced density matrices (RDMs). The toolbox transparently handles the inherent antisymmetrization of wavefunctions and incorporates the creation/annihilation formalism. Thus, it aims at providing a solid base for a broad audience to use fermionic wavefunctions with the same ease as matrices in Matlab, say. Leveraging symbolic computation, the toolbox can greatly simply tedious pen-and-paper calculations for concrete quantum mechanical systems, and serves as "sandbox" for theoretical hypothesis testing. FermiFab (including full source code) is freely available as a plugin for both Matlab and Mathematica. ; Comment: 17 pages, 5 figures Minimize

Year of Publication:

2011-03-04

Document Type:

text

Subjects:

Quantum Physics ; Physics - Computational Physics ; 81-08 ; 81-04

Quantum Physics ; Physics - Computational Physics ; 81-08 ; 81-04 Minimize

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Title:

Efficient Algorithm for Two-Center Coulomb and Exchange Integrals of Electronic Prolate Spheroidal Orbitals

Description:

We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach employs Neumann's expansion of the Coulomb repulsion 1/|x-y|, solves the resulting integrals symbolically in cl...

We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach employs Neumann's expansion of the Coulomb repulsion 1/|x-y|, solves the resulting integrals symbolically in closed form and subsequently performs a numeric Taylor expansion for efficiency. Thanks to the general form of the integrals, the obtained coefficients are independent of the particular wavefunctions and can thus be reused later. Key features of our algorithm include complete avoidance of numeric integration, drafting of the individual steps as fast matrix operations and high accuracy due to the exponential convergence of the expansions. Application to the diatomic molecules O2 and CO exemplifies the developed methods, which can be relevant for a quantitative understanding of chemical bonds in general. ; Comment: 27 pages, 9 figures Minimize

Year of Publication:

2012-03-28

Document Type:

text

Subjects:

Quantum Physics

Quantum Physics Minimize

DDC:

541 Physical chemistry *(computed)*

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Title:

Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation

Description:

We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are 2 x 2 matrix-valued to accommodate the spin degree of freedom, and the scalar quantum Boltzmann equation is recovered as special case when all matrices are proportional to the ide...

We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are 2 x 2 matrix-valued to accommodate the spin degree of freedom, and the scalar quantum Boltzmann equation is recovered as special case when all matrices are proportional to the identity. We use Fourier discretization and fast Fourier transform to efficiently evaluate the collision kernel with spectral accuracy, and numerically investigate periodic, Dirichlet and Maxwell boundary conditions. Model simulations quantify the convergence to local and global thermal equilibrium. ; Comment: 10 figures Minimize

Year of Publication:

2014-08-08

Document Type:

text

Subjects:

Physics - Computational Physics ; Condensed Matter - Mesoscale and Nanoscale Physics

Physics - Computational Physics ; Condensed Matter - Mesoscale and Nanoscale Physics Minimize

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Title:

Equilibrium time-correlation functions for one-dimensional hard-point systems

Description:

As recently proposed, the long-time behavior of equilibrium time-correlation functions for one-dimensional systems are expected to be captured by a nonlinear extension of fluctuating hydrodynamics. We outline the predictions from the theory aimed at the comparison with molecular dynamics. We report on numerical simulations of a fluid with a hard...

As recently proposed, the long-time behavior of equilibrium time-correlation functions for one-dimensional systems are expected to be captured by a nonlinear extension of fluctuating hydrodynamics. We outline the predictions from the theory aimed at the comparison with molecular dynamics. We report on numerical simulations of a fluid with a hard-shoulder potential and of a hard-point gas with alternating masses. These models have in common that the collision time is zero and their dynamics amounts to iterating collision by collision. The theory is well confirmed, with the twist that the non-universal coefficients are still changing at longest accessible times. ; Comment: 5 figures Minimize

Year of Publication:

2014-03-02

Document Type:

text

Subjects:

Condensed Matter - Statistical Mechanics ; Physics - Computational Physics

Condensed Matter - Statistical Mechanics ; Physics - Computational Physics Minimize

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Title:

Towards the Kantorovich dual solution for strictly correlated electrons in atoms and molecules

Description:

The many-body Coulomb repulsive energy of strictly correlated electrons provides direct information of the exact Hohenberg-Kohn exchange-correlation functional in the strong interaction limit. Until now the treatment of strictly correlated electrons is based on the calculation of co-motion functions with the help of semi-analytic formulations. T...

The many-body Coulomb repulsive energy of strictly correlated electrons provides direct information of the exact Hohenberg-Kohn exchange-correlation functional in the strong interaction limit. Until now the treatment of strictly correlated electrons is based on the calculation of co-motion functions with the help of semi-analytic formulations. This procedure is system specific and has been limited to spherically symmetric atoms and strictly 1D systems. We develop a nested optimization method which solves the Kantorovich dual problem directly, and thus facilitates a general treatment of strictly correlated electrons for systems including atoms and small molecules. ; Comment: 3 figures Minimize

Year of Publication:

2012-10-26

Document Type:

text

Subjects:

Physics - Chemical Physics ; Physics - Computational Physics ; Quantum Physics

Physics - Chemical Physics ; Physics - Computational Physics ; Quantum Physics Minimize

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