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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2405.14410 |
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| _version_ | 1866908458226286592 |
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| author | Pal, Kunal Pal, Kuntal |
| author_facet | Pal, Kunal Pal, Kuntal |
| contents | We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we calculate the bi-invariant cost associated with these time-dependent Hamiltonians by suitably regularising their norms and obtain analytical expressions of the costs for several well-known time-dependent quantum mechanical systems. Specifically, we show that an equivalence exists between the total costs of obtaining an operator through time evolution generated by a unit mass harmonic oscillator whose frequency depends on time, and a harmonic oscillator whose both mass and frequency are functions of time. These results are illustrated with several examples, including a specific smooth quench protocol where the comparison of time variation of the cost with other information theoretic quantities, such as the Shannon entropy, is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-dependent Hamiltonians and Geometry of Operators Generated by Them Pal, Kunal Pal, Kuntal Quantum Physics We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we calculate the bi-invariant cost associated with these time-dependent Hamiltonians by suitably regularising their norms and obtain analytical expressions of the costs for several well-known time-dependent quantum mechanical systems. Specifically, we show that an equivalence exists between the total costs of obtaining an operator through time evolution generated by a unit mass harmonic oscillator whose frequency depends on time, and a harmonic oscillator whose both mass and frequency are functions of time. These results are illustrated with several examples, including a specific smooth quench protocol where the comparison of time variation of the cost with other information theoretic quantities, such as the Shannon entropy, is discussed. |
| title | Time-dependent Hamiltonians and Geometry of Operators Generated by Them |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.14410 |