58,515 research outputs found
The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
First-principles calculations in crystalline structures are often performed
with a planewave basis set. To make the number of basis functions tractable two
approximations are usually introduced: core electrons are frozen and the
diverging Coulomb potential near the nucleus is replaced by a smoother
expression. The norm-conserving pseudopotential was the first successful method
to apply these approximations in a fully ab initio way. Later on, more
efficient and more exact approaches were developed based on the ultrasoft and
the projector augmented wave formalisms. These formalisms are however more
complex and developing new features in these frameworks is usually more
difficult than in the norm-conserving framework. Most of the existing tables of
norm- conserving pseudopotentials, generated long ago, do not include the
latest developments, are not systematically tested or are not designed
primarily for high accuracy. In this paper, we present our PseudoDojo framework
for developing and testing full tables of pseudopotentials, and demonstrate it
with a new table generated with the ONCVPSP approach. The PseudoDojo is an open
source project, building on the AbiPy package, for developing and
systematically testing pseudopotentials. At present it contains 7 different
batteries of tests executed with ABINIT, which are performed as a function of
the energy cutoff. The results of these tests are then used to provide hints
for the energy cutoff for actual production calculations. Our final set
contains 141 pseudopotentials split into a standard and a stringent accuracy
table. In total around 70.000 calculations were performed to test the
pseudopotentials. The process of developing the final table led to new insights
into the effects of both the core-valence partitioning and the non-linear core
corrections on the stability, convergence, and transferability of
norm-conserving pseudopotentials. ...Comment: abstract truncated, 17 pages, 25 figures, 8 table
Contrasting SYK-like Models
We contrast some aspects of various SYK-like models with large- melonic
behavior. First, we note that ungauged tensor models can exhibit symmetry
breaking, even though these are 0+1 dimensional theories. Related to this, we
show that when gauged, some of them admit no singlets, and are anomalous. The
uncolored Majorana tensor model with even is a simple case where gauge
singlets can exist in the spectrum. We outline a strategy for solving for the
singlet spectrum, taking advantage of the results in arXiv:1706.05364, and
reproduce the singlet states expected in . In the second part of the
paper, we contrast the random matrix aspects of some ungauged tensor models,
the original SYK model, and a model due to Gross and Rosenhaus. The latter,
even though disorder averaged, shows parallels with the Gurau-Witten model. In
particular, the two models fall into identical Andreev ensembles as a function
of . In an appendix, we contrast the (expected) spectra of AdS quantum
gravity, SYK and SYK-like tensor models, and the zeros of the Riemann Zeta
function.Comment: 45 pages, 17 figures; v2: minor improvements and rearrangements, refs
adde
Towards an Intelligent Tutor for Mathematical Proofs
Computer-supported learning is an increasingly important form of study since
it allows for independent learning and individualized instruction. In this
paper, we discuss a novel approach to developing an intelligent tutoring system
for teaching textbook-style mathematical proofs. We characterize the
particularities of the domain and discuss common ITS design models. Our
approach is motivated by phenomena found in a corpus of tutorial dialogs that
were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor
for textbook-style mathematical proofs can be built on top of an adapted
assertion-level proof assistant by reusing representations and proof search
strategies originally developed for automated and interactive theorem proving.
The resulting prototype was successfully evaluated on a corpus of tutorial
dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453
Dimension and Dimensional Reduction in Quantum Gravity
A number of very different approaches to quantum gravity contain a common
thread, a hint that spacetime at very short distances becomes effectively two
dimensional. I review this evidence, starting with a discussion of the physical
meaning of "dimension" and concluding with some speculative ideas of what
dimensional reduction might mean for physics.Comment: 33 page draft of solicited review article -- comments and added
references welcome; v2: many added references, minor clean-u
A New Approach to Black Hole Microstates
If one encodes the gravitational degrees of freedom in an orthonormal frame
field there is a very natural first order action one can write down (which in
four dimensions is known as the Goldberg action). In this essay we will show
that this action contains a boundary action for certain microscopic degrees of
freedom living at the horizon of a black hole, and argue that these degrees of
freedom hold great promise for explaining the microstates responsible for black
hole entropy, in any number of spacetime dimensions. This approach faces many
interesting challenges, both technical and conceptual.Comment: 6 pages, 0 figures, LaTeX; submitted to Mod. Phys. Lett. A.; this
essay received "honorable mention" from the Gravity Research Foundation, 199
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