We construct the natural generalization of stochastic quantization (in the Markovian sense) by considering jump-diffusion processes. This class of stochastic processes exhibits non-continuous paths, so-called L\'evy flights. In the presence of jumps, action landscapes with barriers can be efficiently explored, improving and even restoring ergodicity where traditional diffusion approaches become inefficient. We explore different strategies for constructing efficient jump updates, which we deploy to address the benchmark problem of topological freezing in 2d U(1) gauge theory.
Stochastic quantization formulates $d$-dimensional Euclidean QFT as the equilibrium limit of a $(d+1)$-dimensional Langevin system. Using the supersymmetric formulation of stochastic systems, we apply techniques from Morse theory to study Langevin dynamics. We interpret stochastic quantization as the absolutization of...
We consider scaling limits of integer-valued random walks whose transition probabilities are translation-invariant everywhere except on a set that we will call a membrane or an interface. If the jumps outside the membrane are i.i.d. mean-zero random variables with finite variance, then possible examples of the correspo...
A simple symmetric random walk on a one-dimensional lattice is guaranteed to reach any target site, yet its mean first-passage time diverges. Here, we show that stochastic fluctuations in the jump rate can fundamentally alter this classic result. We find a phase transition in the mean first-passage time: sufficiently b...
For a large class of discrete- and continuous-time models satisfying a linear flow property, we prove convergence to the critical $2d$ stochastic heat flow under diffusive scaling of space and time. Convergence is in the sense of finite-dimensional distributions in the space of measure-valued stochastic flows. The clas...
Hindy Drillick, Jonathan Hou, Shalin Parekh· 0 citations
Our recent research on Langevin dynamics with self-harmonic drift and classical spins has revealed a strong connection to ``Stochastic Localization,"a concept attracting attention in the fields of mathematical geometry and data science. Roughly speaking, the former can be viewed as a version of the latter in which the...
In this work we provide numerical evidence that topological freezing in $\mathrm{SU}(3)$ Yang-Mills theory can be mitigated with a flow-based approach, as tested at lattice spacings as fine as 0.03~fm. We do so by analyzing the scaling of the costs of a computational strategy based on the combination of open boundary c...
C. Bonanno, Andrea Bulgarelli, E. Cellini et al.· 0 citations
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