Optimal time evolution for pseudo-Hermitian Hamiltonians

Wang, W. H.; Chen, Z. L.; Song, Yun S.; Fan, Yajing

doi:10.1134/s0040577920080048

Cited by 4 publications

(9 citation statements)

References 22 publications

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“…Remark 3.9. Example 3.8 is used in many papers on quantum speed limits (see, e.g., [6,8,4,16]). In particular, this example proves sharpness of both the Mandelstam- where θ , T θ are the same as in Corollary 3.7 and The following proposition is verified by immediate inspection.…”

Section: Bounds For the Speed Of The Subspace Evolutionmentioning

confidence: 99%

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Optimal bounds on the speed of subspace evolution

Albeverio,

Motovilov

2021

Preprint

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By a quantum speed limit one usually understands an estimate on how fast a quantum system can evolve between two distinguishable states. The most known quantum speed limit is given in the form of the celebrated Mandelstam-Tamm inequality that bounds the speed of the evolution of a state in terms of its energy dispersion. In contrast to the basic Mandelstam-Tamm inequality, we are concerned not with a single state but with a (possibly infinite-dimensional) subspace which is subject to the Schrödinger evolution. By using the concept of maximal angle between subspaces we derive optimal bounds on the speed of such a subspace evolution. These bounds may be viewed as further generalizations of the Mandelstam-Tamm inequality. Our study includes the case of unbounded Hamiltonians.

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Section: Bounds For the Speed Of The Subspace Evolutionmentioning

confidence: 99%

“…Probably, the latest among them is a speed limit for evolution of thermal states derived in [9]. Mandelstam-Tamm-type bounds for the orthogonalization time exist even for some non-self-adjoint (so-called pseudo-Hermitian and, in particular, PT -symmetric) Hamiltonians (see [4,16] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Optimal bounds on the speed of subspace evolution

Albeverio,

Motovilov

2021

Preprint

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“…where δ E = Hψ 0 , ψ 0 − min spec(H) (8) is nothing but the average energy for the state ψ 0 measured relative to the lower edge of the spectrum spec(H) of the Hamiltonian H. Both the bounds ( 5) and (7) have been proven to be sharp (see, e.g., [1, p. 7] and [2, p. 3923]).…”

Section: Introductionmentioning

confidence: 99%

“…It is worth to remark that the inequalities ( 5) and ( 7) recall the uncertainty relation for energy and time but are very different from this relation in the essence since both ( 5) and (7) are related not to the standard deviation in the measurement of t but to the well-founded time for a given state to evolve into an orthogonal state.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, there are more detailed evolution speed estimates for particular classes of quantummechanical evolutionary problems (see [1,2]). The existence of Mandelshtam-Tamm-type bounds for the orthogonalization time is discussed even for certain non-self-adjoint (so-called pseudo-Hermitian and, in particular, PT -symmetric) Hamiltonians (see [6,7] and references therein).…”

Section: Introductionmentioning

confidence: 99%

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Quantum speed limits for time evolution of a system subspace

Albeverio,

Motovilov

2020

Preprint

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One of the fundamental physical limits on the speed of time evolution of a quantum state is known in the form of the celebrated Mandelshtam-Tamm inequality. This inequality gives an answer to the question on how fast an isolated quantum system can evolve from its initial state to an orthogonal one. In its turn, the Fleming bound is an extension of the Mandelshtam-Tamm inequality that gives an optimal speed bound for the evolution between non-orthogonal initial and final states. In the present work, we are concerned not with a single state but with a whole (possibly infinite-dimensional) subspace of the system states that are subject to the Schrödinger evolution. By using the concept of maximal angle between subspaces we derive an optimal estimate on the speed of such a subspace evolution that may be viewed as a natural generalization of the Fleming bound.

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Optimal bounds on the speed of subspace evolution*

Albeverio¹,

Мотовилов²

2022

J. Phys. A: Math. Theor.

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By a quantum speed limit one usually understands an estimate on how fast a quantum system can evolve between two distinguishable states. The most known quantum speed limit is given in the form of the celebrated Mandelstam-Tamm inequality that bounds the speed of the evolution of a state in terms of its energy dispersion. In contrast to the basic Mandelstam-Tamm inequality, we are concerned not with a single state but with a (possibly inﬁnite-dimensional) subspace which is subject to the Schroedinger evolution. By using the concept of maximal angle between subspaces we derive optimal bounds on the speed of such a subspace evolution. These bounds may be viewed as further generalizations of the Mandelstam-Tamm inequality. Our study includes the case of unbounded Hamiltonians.

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Optimal time evolution for pseudo-Hermitian Hamiltonians

Cited by 4 publications

References 22 publications

Optimal bounds on the speed of subspace evolution

Optimal bounds on the speed of subspace evolution

Quantum speed limits for time evolution of a system subspace

Optimal bounds on the speed of subspace evolution*

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