Quantum Physics

    

Schr"odinger-Robertson Uncertainty Relation Which Depends on the Quantum Phase Transition

Authors: Koji Nagata, Do Ngoc Diep, Tadao Nakamura

We derive the Schr"odinger--Robertson uncertainty relation which depends on the quantum phase transition.Our general uncertainty relationasserts, in different times $t$ and $t'$,a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as its position at time $t$ ($hat{x}(t)$) and momentum at time $t'$ ($hat{p}(t')$), can be known. It turns out that the uncertainty relation is valid for different times $t$ and $t'$.Additionally, it turns out that the formula is natural from the understandable upper limit inthe Bloch sphere, in qubits handling,and the meaningful lower limit (exactly zero).We hope the new formula is useful for analyzing for several systems in condensed matter and certain atomic nuclei in which such phase transitions can be observed.

Comments: 7 pages

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Submission history

[v1] 2022-12-23 02:19:18
[v2] 2023-07-21 13:41:51

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