170,959 research outputs found
The Divine Clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state
We consider the Bohr correspondence limit of the Schrodinger wave function
for an atomic elliptic state. We analyse this limit in the context of Nelson's
stochastic mechanics, exposing an underlying deterministic dynamical system in
which trajectories converge to Keplerian motion on an ellipse. This solves the
long standing problem of obtaining Kepler's laws of planetary motion in a
quantum mechanical setting. In this quantum mechanical setting, local mild
instabilities occur in the Kelperian orbit for eccentricities greater than
1/\sqrt{2} which do not occur classically.Comment: 42 pages, 18 figures, with typos corrected, updated abstract and
updated section 6.
Strong-Coupling Perturbation Theory of the Hubbard Model
The strong-coupling perturbation theory of the Hubbard model is presented and
carried out to order (t/U)^5 for the one-particle Green function in arbitrary
dimension. The spectral weight A(k,omega) is expressed as a Jacobi continued
fraction and compared with new Monte-Carlo data of the one-dimensional,
half-filled Hubbard model. Different regimes (insulator, conductor and
short-range antiferromagnet) are identified in the temperature--hopping
integral (T,t) plane. This work completes a first paper on the subject (Phys.
Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and
higher-order results. In addition, the non half-filled case, infinite
resummations of diagrams and the double occupancy are discussed. Various tests
of the method are also presented.Comment: 28 pages, 19 figure
Big-Data-Driven Materials Science and its FAIR Data Infrastructure
This chapter addresses the forth paradigm of materials research -- big-data
driven materials science. Its concepts and state-of-the-art are described, and
its challenges and chances are discussed. For furthering the field, Open Data
and an all-embracing sharing, an efficient data infrastructure, and the rich
ecosystem of computer codes used in the community are of critical importance.
For shaping this forth paradigm and contributing to the development or
discovery of improved and novel materials, data must be what is now called FAIR
-- Findable, Accessible, Interoperable and Re-purposable/Re-usable. This sets
the stage for advances of methods from artificial intelligence that operate on
large data sets to find trends and patterns that cannot be obtained from
individual calculations and not even directly from high-throughput studies.
Recent progress is reviewed and demonstrated, and the chapter is concluded by a
forward-looking perspective, addressing important not yet solved challenges.Comment: submitted to the Handbook of Materials Modeling (eds. S. Yip and W.
Andreoni), Springer 2018/201
Analyzing the success of T-matrix diagrammatic theories in representing a modified Hubbard model
We present a systematic study of various forms of renormalization that can be
applied in the calculation of the self-energy of the Hubbard model within the
T-matrix approximation. We compare the exact solutions of the attractive and
repulsive Hubbard models, for linear chains of lengths up to eight sites, with
all possible taxonomies of the T-matrix approximation. For the attractive
Hubbard model, the success of a minimally self-consistent theory found earlier
in the atomic limit (Phys. Rev. B 71, 155111 (2005)) is not maintained for
finite clusters unless one is in the very strong correlation limit. For the
repulsive model, in the weak correlation limit at low electronic densities --
that is, where one would expect a self-consistent T-matrix theory to be
adequate -- we find the fully renormalized theory to be most successful. In our
studies we employ a modified Hubbard interaction that eliminates all Hartree
diagrams, an idea which was proposed earlier (Phys. Rev. B 63, 035104 (2000)).Comment: Includes modified discussion of 1st-order phase transition. Accepted
for publication in J. Phys.: Condensed Matte
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