Energy–time and frequency–time uncertainty relations: exact inequalities

Dodonov, V. V.; Додонов, А. В.

doi:10.1088/0031-8949/90/7/074049

Cited by 45 publications

(62 citation statements)

References 301 publications

(556 reference statements)

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“…Nevertheless, the energy-time pair is of significant importance both fundamentally and technologically. Energy-time uncertainty was already discussed by the founders of quantum mechanics: Bohr, Heisenberg, Schrödinger, and Pauli (see [8] for a review). In the special case of the harmonic oscillator, this pair corresponds to number and phase, and number-phase uncertainty is relevant to metrology [9], e.g., phase estimation in interferometry.…”

Section: Introduction-mentioning

confidence: 95%

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Entropic Energy-Time Uncertainty Relation

et al. 2019

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Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Hermitian operator associated with time. Following previous approaches, we quantify time uncertainty by how well one can read off the time from a quantum clock. We then use entropy to quantify the information-theoretic distinguishability of the various time states of the clock. Our main result is an entropic energy-time uncertainty relation for general time-independent Hamiltonians, stated for both the discrete-time and continuous-time cases. Our uncertainty relation is strong, in the sense that it allows for a quantum memory to help reduce the uncertainty, and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry. Due to the operational relevance of entropy, we anticipate that our uncertainty relation will have information-processing applications.arXiv:1805.07772v2 [quant-ph]

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Section: Introduction-mentioning

confidence: 95%

“…We remark that (8) can be generalized to allow for nonuniform probabilities for the various times. As shown in the Supplementary Material (Appendix E), the righthand-side of (8) gets replaced by the entropy S(T ) κ of the time distribution for this generalization.…”

Section: Introduction-mentioning

confidence: 99%

Entropic Energy-Time Uncertainty Relation

et al. 2019

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“…This violation of exponential decay at early times is a special case of the so called quantum Zeno effect [33,34], and it has been verified experimentally [38]. The early time behavior of a decaying system can also be identified by an uncertainty relation for the persistence probability, first derived by Mandelstam and Tamm [35], see, also [36,37]. For a system in a state |ψ and HamiltonianĤ, the Kennard-Robertson uncertainty relation gives, Eq.…”

Section: Beyond Exponential Decaymentioning

confidence: 78%

Decays of Unstable Quantum Systems

Anastopoulos

2018

Int J Theor Phys

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This paper is a pedagogical yet critical introduction to the quantum description of unstable systems, mostly at the level of a graduate quantum mechanics course. Quantum decays appear in many different fields of physics, and their description beyond the exponential approximation is the source of technical and conceptual challenges. In this article, we present both general methods that can be adapted to a large class of problems, and specific elementary models to describe phenomena like photo-emission, beta emission and tunneling-induced decays. We pay particular attention to the emergence of exponential decay; we analyze the approximations that justify it, and we present criteria for its breakdown. We also present a detailed model for non-exponential decays due to resonance, and an elementary model describing decays in terms of particle-detection probabilities. We argue that the traditional methods for treating decays face significant problems outside the regime of exponential decay, and that the exploration of novel regimes of current interest requires new tools. * anastop@physics.upatras.gr arXiv:1808.03798v2 [quant-ph] 8 Dec 2018Probability currents. An alternative elementary description of decays is available, whenever we can associate a probability-current operatorĴ J J(x x x, t) to one of the decay products. For example, for non-relativistic particles of mass m satisfying Schrödinger's equation with HamiltonianĤ, the current operator iŝ J J J(x x x, t) = 1 2m e

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“…But e.g. in the case of the uncertainty relation   b D D p t c even in extensive calculations the rhs is given with β=1 [16] or β=1/2 [34]. We have formulated new bounds for the ratio of important thermophysical properties, namely…”

Section: Discussionmentioning

confidence: 99%

Conjecture of new inequalities for some selected thermophysical properties values

Hohm

2019

J. Phys. Commun.

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In 2005 it was rigorously shown with string theory methods that there is a lower bound for the ratio of the shear viscosity η and the volume density of entropy s=S/V given byHere we extend this result in a heuristic manner to other ratios of thermophysical properties. We conjectured that there are rigorous non-zero lower bounds for the Lorenz number L as well as other combinations of equilibrium and transport properties. We suggest that the lower bounds and the corresponding inequalities can be written in terms of the Planck units. We show that some of the proposed new inequalities set severe constraints on the behavior and properties of ordinary matter.

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Energy–time and frequency–time uncertainty relations: exact inequalities

Cited by 45 publications

References 301 publications

Entropic Energy-Time Uncertainty Relation

Entropic Energy-Time Uncertainty Relation

Decays of Unstable Quantum Systems

Conjecture of new inequalities for some selected thermophysical properties values

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