132 research outputs found
Many-Body Density Matrices for Free Fermions
Building upon an analytical technique introduced by Chung and Peschel [M.
Chung and I. Peschel, Phys. Rev. B 64, art. 064412 (2001)], we calculated the
density matrix rho_B of a finite block of B sites within an infinite system of
free spinless fermions. In terms of the block Green function matrix G (whose
elements are G_ij = , where c_i^+ and c_j are fermion creation and
annihilation operators acting on sites i and j within the block respectively),
the density matrix can be written as rho_B = det(1 - G) exp[ sum_ij (log G(1 -
G^{-1})_ij c_i^+ c_j]. Implications of such a result to Hilbert space
truncation for real-space renormalization schemes is discussed.Comment: 12 pages in RevTeX4 format. Uses amsmath, bbold, dcolumn and mathrsfs
package
Knowledge Evolution in Physics Research: An Analysis of Bibliographic Coupling Networks
Even as we advance the frontiers of physics knowledge, our understanding of
how this knowledge evolves remains at the descriptive levels of Popper and
Kuhn. Using the APS publications data sets, we ask in this letter how new
knowledge is built upon old knowledge. We do so by constructing year-to-year
bibliographic coupling networks, and identify in them validated communities
that represent different research fields. We then visualize their evolutionary
relationships in the form of alluvial diagrams, and show how they remain intact
through APS journal splits. Quantitatively, we see that most fields undergo
weak Popperian mixing, and it is rare for a field to remain isolated/undergo
strong mixing. The sizes of fields obey a simple linear growth with
recombination. We can also reliably predict the merging between two fields, but
not for the considerably more complex splitting. Finally, we report a case
study of two fields that underwent repeated merging and splitting around 1995,
and how these Kuhnian events are correlated with breakthroughs on BEC, quantum
teleportation, and slow light. This impact showed up quantitatively in the
citations of the BEC field as a larger proportion of references from during and
shortly after these events.Comment: 14 pages, 14 figures, 1 tabl
Using Machine Learning to Predict the Evolution of Physics Research
The advancement of science as outlined by Popper and Kuhn is largely
qualitative, but with bibliometric data it is possible and desirable to develop
a quantitative picture of scientific progress. Furthermore it is also important
to allocate finite resources to research topics that have growth potential, to
accelerate the process from scientific breakthroughs to technological
innovations. In this paper, we address this problem of quantitative knowledge
evolution by analysing the APS publication data set from 1981 to 2010. We build
the bibliographic coupling and co-citation networks, use the Louvain method to
detect topical clusters (TCs) in each year, measure the similarity of TCs in
consecutive years, and visualize the results as alluvial diagrams. Having the
predictive features describing a given TC and its known evolution in the next
year, we can train a machine learning model to predict future changes of TCs,
i.e., their continuing, dissolving, merging and splitting. We found the number
of papers from certain journals, the degree, closeness, and betweenness to be
the most predictive features. Additionally, betweenness increases significantly
for merging events, and decreases significantly for splitting events. Our
results represent a first step from a descriptive understanding of the Science
of Science (SciSci), towards one that is ultimately prescriptive.Comment: 24 pages, 10 figures, 4 tables, supplementary information is include
Stochastic boundary conditions for molecular dynamics simulations
In this paper we develop a stochastic boundary conditions (SBC) for
event-driven molecular dynamics simulations of a finite volume embedded within
an infinite environment. In this method, we first collect the statistics of
injection/ejection events in periodic boundary conditions (PBC). Once
sufficient statistics are collected, we remove the PBC and turn on the SBC. In
the SBC simulations, we allow particles leaving the system to be truly ejected
from the simulation, and randomly inject particles at the boundaries by
resampling from the injection/ejection statistics collected from the current or
previous simulations. With the SBC, we can measure thermodynamic quantities
within the grand canonical ensemble, based on the particle number and energy
fluctuations. To demonstrate how useful the SBC algorithm is, we simulated a
hard disk gas and measured the pair distribution function, the compressibility
and the specific heat, comparing them against literature values.Comment: 24 pages, 16 figure
Correlation density matrix: an unbiased analysis of exact diagonalizations
Given the ground state wavefunction for an interacting lattice model, we
define a "correlation density matrix"(CDM) for two disjoint, separated clusters
and , to be the density matrix of their union, minus the direct product
of their respective density matrices. The CDM can be decomposed systematically
by a numerical singular value decomposition, to provide a systematic and
unbiased way to identify the operator(s) dominating the correlations, even
unexpected ones.Comment: (4pp, 2 figures
Exact ground states and correlation functions of chain and ladder models of interacting hardcore bosons or spinless fermions
By removing one empty site between two occupied sites, we map the ground
states of chains of hardcore bosons and spinless fermions with infinite
nearest-neighbor repulsion to ground states of chains of hardcore bosons and
spinless fermions without nearest-neighbor repulsion respectively, and
ultimately in terms of the one-dimensional Fermi sea. We then introduce the
intervening-particle expansion, where we write correlation functions in such
ground states as a systematic sum over conditional expectations, each of which
can be ultimately mapped to a one-dimensional Fermi-sea expectation. Various
ground-state correlation functions are calculated for the bosonic and fermionic
chains with infinite nearest-neighbor repulsion, as well as for a ladder model
of spinless fermions with infinite nearest-neighbor repulsion and correlated
hopping in three limiting cases. We find that the decay of these correlation
functions are governed by surprising power-law exponents.Comment: 20 pages, 18 figures, RevTeX4 clas
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