Quantum decay and the Mandelstam–Tamm-energy inequality
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The Mandelstam-Tamm time-energy inequality is exploited to obtain a transparent expression of the lifetime-energy uncertainty relation for decaying quantum systems along with some useful features of the quantum non-decay probability.
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In the Landau-Zener model optimized with the Krotov algorithm, there is a minimum elapsed time given by Bhattacharyya's bound below which the algorithm fails to converge, while above it the fidelity approaches one.
“Remarkably they found that there was a minimum value of τ given by Battacharyya's bound [51] (i.e. the Mandelstam-Tamm bound for arbitrary angles), below which the algorithm failed to converge, while for values above this they consistently found F → 1.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [51]
The above expression generalizes in a unified manner previous results derived in Refs. [7-22].
“The above expression generalizes in an unified manner previous results derived in Refs. [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22].”
From Energy–time uncertainty relation for driven quantum systems (2013) · cites this paper as [13]
Equation (5) was previously proven in prior work by employing the general form of the uncertainty relations.
“Equation (5) was previously proven in [1, 2] by employing the general form of the uncertainty relations.”
From Quantum limits to dynamical evolution (2003) · cites this paper as [1]
For γ→0, inequality (14) yields the Mandelstam-Tamm bound, since the process becomes unitary.
“In the extreme cases γ → 0 and ω 0 → 0, inequality (14) yields simple analytical expressions for the bound on the minimal time. For the former, the Mandelstam-Tamm bound [2, 6] is recovered, since the process becomes unitary;”
From Quantum Speed Limit for Physical Processes (2013) · cites this paper as [6]
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Cites
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- Authors
- Bhattacharyya, K.
- Affiliations
- Indian Association for the Cultivation of Science (IN)
- Corresponding author
- Bhattacharyya, K
- ORCID
- Bhattacharyya, K
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1983-09-11
- Volume
- 16
- Issue
- 13
- Pages
- 2993-2996
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1995705985
- Cited by
- 220
- References
- 7
- Citations by year
- 2026: 4 · 2025: 10 · 2024: 9 · 2023: 16 · 2022: 14 · 2021: 14 · 2020: 18 · 2019: 9 · 2018: 11 · 2017: 15 · 2016: 17 · 2015: 15 · 2014: 10 · 2013: 16 · 2012: 6
- FWCI
- 1.64
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- time-energy uncertainty relation, quantum decay, energy uncertainty
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