
Convergence from Atomistic Model to PeierlsNabarro Model for Dislocations in Bilayer System with Complex Lattice
In this paper, we prove the convergence from the atomistic model to the ...
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The IFF Approach to the Lattice of Theories
The IFF approach for the notion of "lattice of theories" uses the idea o...
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Flowbased sampling for fermionic lattice field theories
Algorithms based on normalizing flows are emerging as promising machine ...
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Lattice Packings of Crosspolytopes Constructed from Sidon Sets
A family of lattice packings of ndimensional crosspolytopes (ℓ_1 balls...
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Bending behavior of additively manufactured lattice structures: numerical characterization and experimental validation
Selective Laser Melting (SLM) technology has undergone significant devel...
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Adaptive deep density approximation for FokkerPlanck equations
In this paper we present a novel adaptive deep density approximation str...
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Rapid and deterministic estimation of probability densities using scalefree field theories
The question of how best to estimate a continuous probability density fr...
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On the validity of complex Langevin method for path integral computations
The complex Langevin (CL) method is a classical numerical strategy to alleviate the numerical sign problem in the computation of lattice field theories. Mathematically, it is a simple numerical tool to compute a wide class of highdimensional and oscillatory integrals. However, it is often observed that the CL method converges but the limiting result is incorrect. The literature has several unclear or even conflicting statements, making the method look mysterious. By an indepth analysis of a model problem, we reveal the mechanism of how the CL result turns biased as the parameter changes, and it is demonstrated that such a transition is difficult to capture. Our analysis also shows that the method works for any observables only if the probability density function generated by the CL process is localized. To generalize such observations to lattice field theories, we formulate the CL method on general groups using rigorous mathematical languages for the first time, and we demonstrate that such localized probability density function does not exist in the simulation of lattice field theories for general compact groups, which explains the unstable behavior of the CL method. Fortunately, we also find that the gauge cooling technique creates additional velocity that helps confine the samples, so that we can still see localized probability density functions in certain cases, as significantly broadens the application of the CL method. The limitations of gauge cooling are also discussed. In particular, we prove that gauge cooling has no effect for Abelian groups, and we provide an example showing that biased results still exist when gauge cooling is insufficient to confine the probability density function.
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