arXiv 0704.13592007-04-11quant-ph

具有可分性约束的哈密顿量子动力学

Hamiltonian Quantum Dynamics With Separability Constraints

Nikola Buric

DOI：: 10.1016/j.aop.2007.04.019

摘要：

希尔伯特空间${\cal H}$上的薛定谔方程，表示量子纯态空间，即射影希尔伯特空间$P {\cal H}$上的线性哈密顿动力系统。二分量子系统的可分态构成了$P {\cal H}$的一个特殊子流形。我们分析的哈密顿动力学，对应于量子系统的可分离状态的流形上的约束，作为一个重要的例子，系统的两个相互作用的量子比特。的约束引入非线性，使非平凡的动态。我们表明，约束动力学的定性性质清楚地表明了量子比特系统的对称性。特别地，如果量子Hamilton算符没有足够的对称性，则约束动力学是不可积的，并显示出混合相空间的Hamilton动力学系统的典型特征。讨论了分离性约束的可能物理实现。

英文摘要：

Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a special submanifold of $P {\cal H}$. We analyze the Hamiltonian dynamics that corresponds to the quantum system constrained on the manifold of separable states, using as an important example the system of two interacting qubits. The constraints introduce nonlinearities which render the dynamics nontrivial. We show that the qualitative properties of the constrained dynamics clearly manifest the symmetry of the qubits system. In particular, if the quantum Hamilton's operator has not enough symmetry, the constrained dynamics is nonintegrable, and displays the typical features of a Hamiltonian dynamical system with mixed phase space. Possible physical realizations of the separability constraints are discussed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文