二次哈密顿量的不变量子态
Invariant Quantum States of Quadratic Hamiltonians.
作者信息
Dodonov Viktor V
机构信息
Institute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, DF, Brazil.
International Center for Physics, University of Brasilia, Brasilia 70919-970, DF, Brazil.
出版信息
Entropy (Basel). 2021 May 19;23(5):634. doi: 10.3390/e23050634.
Abstract
The problem of finding covariance matrices that remain constant in time for arbitrary multi-dimensional quadratic Hamiltonians (including those with time-dependent coefficients) is considered. General solutions are obtained.
摘要
考虑了寻找对于任意多维二次哈密顿量（包括那些具有时间依赖系数的哈密顿量）在时间上保持恒定的协方差矩阵的问题。得到了一般解。
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本文引用的文献
1
Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States.
Entropy (Basel). 2020 May 23;22(5):586. doi: 10.3390/e22050586.
2
Quantum Fidelity for Arbitrary Gaussian States.
Phys Rev Lett. 2015 Dec 31;115(26):260501. doi: 10.1103/PhysRevLett.115.260501. Epub 2015 Dec 22.
3
Universal invariants of quantum-mechanical and optical systems.
J Opt Soc Am A Opt Image Sci Vis. 2000 Dec;17(12):2403-10. doi: 10.1364/josaa.17.002403.
4
Generalized uncertainty relations and characteristic invariants for the multimode states.
Phys Rev A. 1995 Jul;52(1):43-54. doi: 10.1103/physreva.52.43.
5
Quantum-noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms.
Phys Rev A. 1994 Mar;49(3):1567-1583. doi: 10.1103/physreva.49.1567.
6
Invariants and geometric phase for systems with non-Hermitian time-dependent Hamiltonians.
Phys Rev A. 1992 Oct 1;46(7):3626-3630. doi: 10.1103/physreva.46.3626.
7
General moment invariants for linear Hamiltonian systems.
Phys Rev A. 1992 Feb 15;45(4):2572-2585. doi: 10.1103/physreva.45.2572.
8
Geometric phase and the generalized invariant formulation.
Phys Rev A. 1991 Dec 1;44(11):7016-7021. doi: 10.1103/physreva.44.7016.
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