Related papers: Lefschetz-thimble techniques for path integral of …
Off-shell supersymmetry, which restricts sparticles to appear only off-shell, solves the gauge hierarchy problem and unifies the gauge couplings in the usual way. Without introducing any new interactions or exacerbating the naturalness,…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
We study the vacuum stability of a model of massless scalar and fermionic fields minimally coupled to a Chern-Simons field. The classical Lagrangian only involves dimensionless parameters, and the model can be thought as a (2+1) dimensional…
We have considered the corrections to the finite-size-scaling functions for a general class of $O(N)$ $\sigma$-models with two-spin interactions in two dimensions for $N=\infty$. We have computed the leading corrections finding that they…
We process snapshots of trajectories of evolution equations with intrinsic symmetries, and demonstrate the use of recently developed eigenvector-based techniques to successfully quotient out the degrees of freedom associated with the…
Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. These factorizations in turn reduce the labor and improve the…
Two-dimensional Stokes flow through a periodic channel is considered. The channel walls need only be Lipschitz continuous, in other words they are allowed to have corners. Boundary integral methods are an attractive tool for numerically…
The Teichm\"uller harmonic map flow is a gradient flow for the harmonic map energy of maps from a closed surface to a general closed Riemannian target manifold of any dimension, where both the map and the domain metric are allowed to…
Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the…
We show how one may perform a stochastic unraveling which respects weak permutation symmetry for models of $N$ emitters coupled to a common system (e.g. a cavity mode). For problems involving 2-level emitters, such an unravelling reduces…
We develop several non-perturbative approximations for studying the dynamics of a supersymmetric O(N) model which preserve supersymmetry. We study the phase structure of the vacuum in both the leading order in large-N approximation as well…
A supersymmetric path integral representation is developed for stochastic processes whose Langevin equation contains any number N of time derivatives, thus generalizing the Langevin equation with inertia studied by Kramers, where N=2. The…
We develop a way of improving complex Langevin dynamics motivated by the Lefschetz-thimble decomposition of integrals. In our method, arbitrary observables of an original model with multiple Lefschetz thimbles are computed by a modified…
It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the…
Discrete gradient methods are geometric integration techniques that can preserve the dissipative structure of gradient flows. Due to the monotonic decay of the function values, they are well suited for general convex and nonconvex…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…
We present a simple, new method for the 1-loop renormalization of integrable $\sigma$-models. By treating equations of motion and Bianchi identities on an equal footing, we derive 'universal' formulae for the 1-loop on-shell divergences,…
This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the…
First, we consider the problem of hedging in complete binomial models. Using the discrete-time F\"ollmer-Schweizer decomposition, we demonstrate the equivalence of the backward induction and sequential regression approaches. Second, in…
Building on insights from the theory of integrable lattices, the integrability is claimed for nonlinear replica sigma models derived in the context of real symmetric random matrices. Specifically, the fermionic and the bosonic replica…