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Quantum Speed Limit is Not Quantum.
Manaka Okuyama1, Masayuki Ohzeki2
1Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan.
Physical Review Letters
|March 16, 2018
Summary
Researchers discovered a classical speed limit, mirroring the quantum speed limit (QSL). This finding reveals that fundamental speed limits are universal dynamical properties of Hilbert space, not exclusive to quantum mechanics.
Area of Science:
- Physics
- Quantum Mechanics
- Classical Mechanics
Background:
- The quantum speed limit (QSL), related to the energy-time uncertainty relation, defines the maximum rate of quantum time evolution.
- Previously, the QSL was considered a unique characteristic of quantum mechanics.
Purpose of the Study:
- To investigate the existence of a classical speed limit analogous to the QSL.
- To determine if fundamental speed limits are exclusive to quantum phenomena.
Main Methods:
- Utilized Hilbert space formalism to analyze the classical Liouville equation.
- Derived speed limits for classical systems within this framework.
- Extended the analysis to imaginary-time Schrödinger equations and classical master equations.
Main Results:
- A classical speed limit, corresponding to the QSL, was successfully derived.
- Demonstrated that the QSL is not solely a quantum phenomenon.
- Identified similar speed limits applicable to classical master equations.
Conclusions:
- Classical mechanics possesses a fundamental speed limit.
- The quantum speed limit represents a universal dynamical property inherent to Hilbert space.
- The concept of speed limits extends to various formulations of quantum and classical dynamics.
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