Bootstrapping time-evolution in quantum mechanics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929626856554496 |
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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 |
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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 |