Bootstrapping time-evolution in quantum mechanics

Fuente: arXiv
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Main Authors: Lawrence, Scott, McPeak, Brian, Neill, Duff
Format: Preprint
Published: 2024
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author Lawrence, Scott
McPeak, Brian
Neill, Duff
author_facet Lawrence, Scott
McPeak, Brian
Neill, Duff
contents We present a method for obtaining a hierarchy of rigorous bounds on the time-evolution of a quantum mechanical system from an arbitrary initial state, systematically generalizing Mandelstam-Tamm-like relations. For any fixed level in the hierarchy, the bounds are tightest after short time-evolution and gradually loosen over time; we present evidence that for any fixed amount of time-evolution, the bounds can be made arbitrarily tight by moving up in the hierarchy. The computational effort to obtain the bounds scales polynomially with the number of degrees of freedom in the system being simulated. We demonstrate the method on both a single anharmonic oscillator and a system of two coupled anharmonic oscillators.
format Preprint
id arxiv_https___arxiv_org_abs_2412_08721
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Bootstrapping time-evolution in quantum mechanics
Lawrence, Scott
McPeak, Brian
Neill, Duff
High Energy Physics - Theory
High Energy Physics - Lattice
Quantum Physics
We present a method for obtaining a hierarchy of rigorous bounds on the time-evolution of a quantum mechanical system from an arbitrary initial state, systematically generalizing Mandelstam-Tamm-like relations. For any fixed level in the hierarchy, the bounds are tightest after short time-evolution and gradually loosen over time; we present evidence that for any fixed amount of time-evolution, the bounds can be made arbitrarily tight by moving up in the hierarchy. The computational effort to obtain the bounds scales polynomially with the number of degrees of freedom in the system being simulated. We demonstrate the method on both a single anharmonic oscillator and a system of two coupled anharmonic oscillators.
title Bootstrapping time-evolution in quantum mechanics
topic High Energy Physics - Theory
High Energy Physics - Lattice
Quantum Physics
url https://arxiv.org/abs/2412.08721