1,111 research outputs found
Density-Matrix Algorithm for Phonon Hilbert Space Reduction in the Numerical Diagonalization of Quantum Many-Body Systems
Combining density-matrix and Lanczos algorithms we propose a new optimized
phonon approach for finite-cluster diagonalizations of interacting
electron-phonon systems. To illustrate the efficiency and reliability of our
method, we investigate the problem of bipolaron band formation in the extended
Holstein Hubbard model.Comment: 14 pages, 6 figures, Workshop on High Performance Computing in
Science and Engineering, Stuttgart 200
The wave-matching boundary integral equation - an energy approach to Galerkin BEM for acoustic wave propagation problems
In this paper, a new Boundary Integral Equation (BIE) is proposed for solution of the scalar Helmholtz equation. Applications include acoustic scattering problems, as occur in room acoustics and outdoor and underwater sound propagation. It draws together ideas from the study of time-harmonics and transient BIEs and spatial audio sensing and rendering, to produce an energy-inspired Galerkin BEM that is intended for use with oscillatory basis functions. Pivotal is the idea that waves at a boundary may be decomposed into incoming and outgoing components. When written in its admittance form, it can be thought of setting the Burton-Miller coupling parameter differently for each basis function based on its oscillation; this is a discrete form of the Dirichlet-to-Neumann map. It is also naturally expressed in a reflectance form, which can be solved by matrix inversion or by marching on in reflection order. Consideration of this leads to an orthogonality relation between the incoming and outgoing waves, which makes the scheme immune to interior cavity eigenmodes. Moreover, the scheme is seen to have two remarkable properties when solution is performed over an entire obstacle: i) it has a condition number of 1 for all positive-real wavenumber k on any closed geometry when a specific choice of cylindrical basis functions are used; ii) when modelling two domains separated by a barrier domain, the two problems are numerical uncoupled when plane wave basis functions are used - this is the case in reality but is not achieved by any other BIE representation that the authors are aware of. Normalisation and envelope functions, as would be required to build a Partition-of-Unity or Hybrid-Numerical-Asymptotic scheme, are introduced and the above properties are seen to become approximate. The modified scheme is applied successfully to a cylinder test case: accuracy of the solution is maintained and the BIE is still immune to interior cavity eigenmodes, gives similar conditioning to the Burton-Miller method and iterative solution is stable. It is seen that for this test case the majority of values in the interaction matrices are extremely small and may be set to zero without affecting conditioning or accuracy, thus the linear system become sparse - a property uncommon in BEM formulations
Variational Schrieffer-Wolff transformations for quantum many-body dynamics
Building on recent results for adiabatic gauge potentials, we propose a variational approach for computing the generator of Schrieffer-Wolff transformations. These transformations consist of block diagonalizing a Hamiltonian through a unitary rotation, which leads to effective dynamics in a computationally tractable reduced Hilbert space. The generators of these rotations are computed variationally and thus go beyond standard perturbative methods, with error controlled by the locality of the variational ansatz. The method is demonstrated on two models. First, in the attractive Fermi-Hubbard model with onsite disorder, we find indications of a lack of observable many-body localization in the thermodynamic limit due to the inevitable mixture of different spinon sectors. Second, in the low-energy sector of the XY spin model with a broken U(1) symmetry, we analyze ground-state response functions by combining the variational Schrieffer-Wolf transformation with the truncated spectrum approach.Published versio
Statistical Fourier Analysis: Clarifications and Interpretations
This paper expounds some of the results of Fourier theory that are essential to the statistical analysis of time series. It employs the algebra of circulant matrices to expose the structure of the discrete Fourier transform and to elucidate the filtering operations that may be applied to finite data sequences. An ideal filter with a gain of unity throughout the pass band and a gain of zero throughout the stop band is commonly regarded as incapable of being realised in finite samples. It is shown here that, to the contrary, such a filter can be realised both in the time domain and in the frequency domain. The algebra of circulant matrices is also helpful in revealing the nature of statistical processes that are band limited in the frequency domain. In order to apply the conventional techniques of autoregressive moving-average modelling, the data generated by such processes must be subjected to antialiasing filtering and sub sampling. These techniques are also described. It is argued that band-limited processes are more prevalent in statistical and econometric time series than is commonly recognised.
Overview of Neutron-Proton Pairing
The role of neutron-proton pairing correlations on the structure of nuclei
along the line is reviewed. Particular emphasis is placed on the
competition between isovector () and isoscalar ) pair fields. The
expected properties of these systems, in terms of pairing collective motion,
are assessed by different theoretical frameworks including schematic models,
realistic Shell Model and mean field approaches. The results are contrasted
with experimental data with the goal of establishing clear signals for the
existence of neutron-proton () condensates. We will show that there is
clear evidence for an isovector condensate as expected from isospin
invariance. However, and contrary to early expectations, a condensate of
deuteron-like pairs appears quite elusive and pairing collectivity in the
channel may only show in the form of a phonon. Arguments are presented for the
use of direct reactions, adding or removing an pair, as the most promising
tool to provide a definite answer to this intriguing question.Comment: 89 pages, 59 figures. Accepted for publication in Progress in
Particle and Nuclear Physics (ELSEVIER
Microscopic Clustering in Light Nuclei
We review recent experimental and theoretical progress in understanding the
microscopic details of clustering in light nuclei. We discuss recent
experimental results on -conjugate systems, molecular structures in
neutron-rich nuclei, and constraints for ab initio theory. We then examine
nuclear clustering in a wide range of theoretical methods, including the
resonating group and generator coordinate methods, antisymmetrized molecular
dynamics, Tohsaki-Horiuchi-Schuck-R\"opke wave function and container model,
no-core shell model methods, continuum quantum Monte Carlo, and lattice
effective field theory.Comment: Accepted for publication in Review of Modern Physics, 50 pages, 28
figures, minor change to titl
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