# Real-Time Corrections to the Effective Potential

## TL;DR

This paper develops a real-time approach to understanding non-perturbative effects in quantum systems, revealing significant corrections to effective potentials that standard equilibrium methods miss, with implications for string and inflationary models.

## Contribution

It introduces a new real-time framework for analyzing non-perturbative effects, deriving an effective Schrödinger equation that captures out-of-equilibrium dynamics.

## Key findings

- Large corrections to effective potentials in non-equilibrium settings
- Quantitative criteria for when corrections are significant
- Demonstration on toy quantum mechanical models

## Abstract

Non-perturbatively generated effective potentials play an extremely useful and often critical role in string and inflationary model building. These potentials are typically computed by methods that assume the system is in equilibrium. For systems out of equilibrium, like an inflaton rolling down its potential, there are corrections to the semi-classical evolution due to transient phenomena. We provide a new qualitative and quantitative understanding of non-perturbative effects in real time for a wide class of toy quantum mechanical models. We derive an effective Schr\"{o}dinger equation that does not rely on any notion of equilibrium and captures the low-energy dynamics supposedly described by the effective potential. We find that there are potentially large corrections to this potential that are not captured by standard equilibrium techniques, and quantify when these corrections significantly alter the effective dynamics.