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arXiv:quant-ph/0507194

On decaying rate of a quantum state

Fardin Kheirandish

Published Jul 20, 2005• 0 citations
arXivHTMLPDF

Abstract

Decaying rate of a quantum system investigated using the Fubini-Study definition of distance between states.
DOI
10.48550/arxiv.quant-ph/0507194

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We compute the time-dependent complexity of the thermofield double states by four different proposals: two holographic proposals based on the "complexity-action" (CA) conjecture and "complexity-volume" (CV) conjecture, and two quantum field theoretic proposals based on the Fubini-Study metric (FS) and Finsler geometry (FG). We find that four different proposals yield both similarities and differences, which will be useful to deepen our understanding on the complexity and sharpen its definition. In particular, at early time the complexity linearly increase in the CV and FG proposals, linearly decreases in the FS proposal, and does not change in the CA proposal. In the late time limit, the CA, CV and FG proposals all show that the growth rate is 2E/(πℏ)2E/(π\hbar)2E/(πℏ) saturating the Lloyd's bound, while the FS proposal shows the growth rate is zero. It seems that the holographic CV conjecture and the field theoretic FG method are more correlated.
We compute the time-dependent complexity of the thermofield double states by four different proposals: two holographic proposals based on the complexity-action (CA) conjecture and complexity-volume (CV) conjecture, and two quantum field theoretic proposals based on the Fubini-Study metric (FS) and Finsler geometry (FG). We find that four different proposals yield both similarities and differences, which will be useful to deepen our understanding on the complexity and sharpen its definition. In particular, at early time the complexity linearly increase in the CV and FG proposals, linearly decreases in the FS proposal, and does not change in the CA proposal. In the late time limit, the CA, CV and FG proposals all show that the growth rate is 2E/(πℏ)2E/(\pi\hbar)2E/(πℏ) saturating the Lloyd's bound, while the FS proposal shows the growth rate is zero. It seems that the holographic CV conjecture and the field theoretic FG method are more correlated.
The neoclassical theory of radiation predicts that the decay rate of an excited atomic state depends on the population density of the lower state. Experimental evidence is presented here which shows that in the case of 39K^{39}\mathrm{K}39K the decay rate is in agreement with the predictions of quantum electrodynamics and definitely in disagreement with the neoclassical theory.