Molecular Dynamics for Fermions

The time-dependent variational principle for many-body trial states is used to discuss the relation between the approaches of different molecular dynamics models to describe indistinguishable fermions. Early attempts to include effects of the Pauli principle by means of nonlocal potentials as well as more recent models which work with antisymmetrized many-body states are reviewed under these premises. Keywords: Many-body theory; Fermion system; Molecular dynamics; Wave-packet dynamics; Time-dependent variational principle; Statistical properties; Canonical ensemble; Ergodicity; Time averagingComment: 97 pages, 13 postscript figures. To be published in July 2000 issue of Reviews of Modern Physics. More information at http://www-aix.gsi.de/~fmd

Quantum Cosmology will need to become a Numerical Subject

The inhomogeneous fluctuations that underlie structure formation - galaxies and CMB hotspots - might have been seeded by quantum cosmological fluctuations, as magnified by some inflationary mechanism. The Halliwell-Hawking model for these, as a lower-energy semiclassical limit, is expected to be shared by many theories. E.g. an O((H/m_pl)^2) suppression of power at large scales results from this. This model contains/suppresses very many terms; we want a qualitative understanding of the meaning of these terms and of different regimes resulting from different combinations of them. I study this with toy models that have tractable mathematics: minisuperspace and, especially, relational particle mechanics. In the present Seminar, I consider in particular averaged terms with some lessons from Hartree-Fock approach to Atomic and Molecular Physics. One needs to anchor this on variational principles; treating the subsequent equations is a numerical venture.Comment: 9 pages, 1 Figure. Invited Seminar at 'XXIX-th International Workshop on High Energy Physics: New Results and Actual Problems in Particle & Astroparticle Physics and Cosmology' (Moscow 2013). 1 reference added and minor typos correcte

Ab initio quantum dynamics using coupled-cluster

The curse of dimensionality (COD) limits the current state-of-the-art {\it ab initio} propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schr\"odinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster (OATDCC), and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given.Comment: 5 figure

Time-Dependent Density Matrix Renormalization Group Algorithms for Nearly Exact Absorption and Fluorescence Spectra of Molecular Aggregates at Both Zero and Finite Temperature

We implement and apply time-dependent density matrix renormalization group (TD-DMRG) algorithms at zero and finite temperature to compute the linear absorption and fluorescence spectra of molecular aggregates. Our implementation is within a matrix product state/operator framework with an explicit treatment of the excitonic and vibrational degrees of freedom, and uses the locality of the Hamiltonian in the zero-exciton space to improve the efficiency and accuracy of the calculations. We demonstrate the power of the method by calculations on several molecular aggregate models, comparing our results against those from multi-layer multiconfiguration time- dependent Hartree and n-particle approximations. We find that TD-DMRG provides an accurate and efficient route to calculate the spectrum of molecular aggregates.Comment: 10 figure