Faster than Hermitian Time Evolution
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Faster than Hermitian Time Evolution
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| Creator |
Bender, C.M.
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| Description |
For any pair of quantum states, an initial state |Iñ and a final quantum state |Fñ, in a Hilbert space, there are many Hamiltonians H under which |Iñ evolves into |Fñ. Let us impose the constraint that the difference between the largest and smallest eigenvalues of H, Emax and Emin, is held fixed. We can then determine the Hamiltonian H that satisfies this constraint and achieves the transformation from the initial state to the final state in the least possible time τ. For Hermitian Hamiltonians, τ has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, τ can be made arbitrarily small without violating the time-energy uncertainty principle. The minimum value of τ can be made arbitrarily small because for PT-symmetric Hamiltonians the path from the vector |Iñ to the vector |Fñ, as measured using the Hilbert-space metric appropriate for this theory, can be made arbitrarily short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.
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| Date |
2019-02-11T21:16:26Z
2019-02-11T21:16:26Z 2007 |
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| Type |
Article
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| Identifier |
Faster than Hermitian Time Evolution / C.M. Bender // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 26 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 81Q10; 81S99 http://dspace.nbuv.gov.ua/handle/123456789/146898 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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