1,678 research outputs found
The 4-loop beta-function in the 2D Non-Abelian Thirring model, and comparison with its conjectured "exact" form
Recently, B. Gerganov, A. LeClair and M. Moriconi [Phys. Rev. Lett. 86 (2001)
4753] have proposed an "exact" (all orders) beta-function for 2-dimensional
conformal field theories with Kac-Moody current-algebra symmetry at any level
k, based on a Lie group G, which are perturbed by a current-current
interaction. This theory is also known as the Non-Abelian Thirring model. We
check this conjecture with an explicit calculation of the beta-function to
4-loop order, for the classical groups G= SU(N), SO(N) and SP(N). We find a
contribution at 4-loop order, proportional to a higher-order group-theoretical
invariant, which is incompatible with the proposed beta-function in all
possible regularization schemes.Comment: 26 pages, 24 figures, latex2
Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
We introduce a class of interatomic potential models that can be
automatically generated from data consisting of the energies and forces
experienced by atoms, derived from quantum mechanical calculations. The
resulting model does not have a fixed functional form and hence is capable of
modeling complex potential energy landscapes. It is systematically improvable
with more data. We apply the method to bulk carbon, silicon and germanium and
test it by calculating properties of the crystals at high temperatures. Using
the interatomic potential to generate the long molecular dynamics trajectories
required for such calculations saves orders of magnitude in computational cost.Comment: v3-4: added new material and reference
Exact Renormalisation Group Equations and Loop Equations for Tensor Models
In this paper, we review some general formulations of exact renormalisation
group equations and loop equations for tensor models and tensorial group field
theories. We illustrate the use of these equations in the derivation of the
leading order expectation values of observables in tensor models. Furthermore,
we use the exact renormalisation group equations to establish a suitable
scaling dimension for interactions in Abelian tensorial group field theories
with a closure constraint. We also present analogues of the loop equations for
tensor models
2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions
We compute transition amplitudes between two spin networks with dipole
graphs, using the Lorentzian EPRL model with up to two (non-simplicial)
vertices. We find power-law decreasing amplitudes in the large spin limit,
decreasing faster as the complexity of the foam increases. There are no
oscillations nor asymptotic Regge actions at the order considered, nonetheless
the amplitudes still induce non-trivial correlations. Spin correlations between
the two dipoles appear only when one internal face is present in the foam. We
compute them within a mini-superspace description, finding positive
correlations, decreasing in value with the Immirzi parameter. The paper also
provides an explicit guide to computing Lorentzian amplitudes using the
factorisation property of SL(2,C) Clebsch-Gordan coefficients in terms of SU(2)
ones. We discuss some of the difficulties of non-simplicial foams, and provide
a specific criterion to partially limit the proliferation of diagrams. We
systematically compare the results with the simplified EPRLs model, much faster
to evaluate, to learn evidence on when it provides reliable approximations of
the full amplitudes. Finally, we comment on implications of our results for the
physics of non-simplicial spin foams and their resummation.Comment: 27 pages + appendix, many figures. v2: one more numerical result,
plus minor amendment
A Survey of Symbolic Execution Techniques
Many security and software testing applications require checking whether
certain properties of a program hold for any possible usage scenario. For
instance, a tool for identifying software vulnerabilities may need to rule out
the existence of any backdoor to bypass a program's authentication. One
approach would be to test the program using different, possibly random inputs.
As the backdoor may only be hit for very specific program workloads, automated
exploration of the space of possible inputs is of the essence. Symbolic
execution provides an elegant solution to the problem, by systematically
exploring many possible execution paths at the same time without necessarily
requiring concrete inputs. Rather than taking on fully specified input values,
the technique abstractly represents them as symbols, resorting to constraint
solvers to construct actual instances that would cause property violations.
Symbolic execution has been incubated in dozens of tools developed over the
last four decades, leading to major practical breakthroughs in a number of
prominent software reliability applications. The goal of this survey is to
provide an overview of the main ideas, challenges, and solutions developed in
the area, distilling them for a broad audience.
The present survey has been accepted for publication at ACM Computing
Surveys. If you are considering citing this survey, we would appreciate if you
could use the following BibTeX entry: http://goo.gl/Hf5FvcComment: This is the authors pre-print copy. If you are considering citing
this survey, we would appreciate if you could use the following BibTeX entry:
http://goo.gl/Hf5Fv
Future-based Static Analysis of Message Passing Programs
Message passing is widely used in industry to develop programs consisting of
several distributed communicating components. Developing functionally correct
message passing software is very challenging due to the concurrent nature of
message exchanges. Nonetheless, many safety-critical applications rely on the
message passing paradigm, including air traffic control systems and emergency
services, which makes proving their correctness crucial. We focus on the
modular verification of MPI programs by statically verifying concrete Java
code. We use separation logic to reason about local correctness and define
abstractions of the communication protocol in the process algebra used by
mCRL2. We call these abstractions futures as they predict how components will
interact during program execution. We establish a provable link between futures
and program code and analyse the abstract futures via model checking to prove
global correctness. Finally, we verify a leader election protocol to
demonstrate our approach.Comment: In Proceedings PLACES 2016, arXiv:1606.0540
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