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Complexity and instability of quantum motion near a quantum phase transition
Pinquan Qin1, Wen-ge Wang1, Giuliano Benenti2
1Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.
Summary
The number of harmonics of the Wigner function can identify quantum phase transitions. This quantum complexity measure shows nonanalytic behavior near transitions, similar to quantum Loschmidt echo and fidelity.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
- Quantum Optics
Background:
- Quantum complexity measures are crucial for understanding quantum systems.
- Quantum phase transitions (QPTs) signify abrupt changes in quantum systems.
- The Wigner function's harmonics were recently proposed as a quantum complexity measure.
Purpose of the Study:
- To investigate the utility of Wigner function harmonics for characterizing quantum phase transitions.
- To compare this novel measure with established methods for assessing quantum system stability.
Main Methods:
- Calculating the number of harmonics of the Wigner function.
- Analyzing the nonanalytic behavior of this measure near quantum phase transitions.
- Utilizing the Dicke model as a test case.
- Comparing results with the quantum Loschmidt echo and fidelity.
Main Results:
- The number of Wigner function harmonics effectively characterizes quantum phase transitions.
- Nonanalytic behavior of this measure is observed near QPTs.
- The results align with established measures of quantum motion stability.
Conclusions:
- The number of Wigner function harmonics serves as a viable indicator of quantum phase transitions.
- This measure offers a new perspective on quantum complexity and system dynamics.
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