Acta Scientiarum Naturalium Universitatis Neimongol

SU（2）q—奇偶相干叠加态的高阶压缩效应和高阶反聚束效应

张慧慧, 白鲜萍, 王维玺, 李瑞芳, 张艳霞

Published Jan 1, 2003• 0 citations

Abstract

运用q代数进一步计算了在SU(2)q-奇偶相干叠加态下的高阶期望值,通过理论计算与实验研究了其非经典效应.发现其二阶压缩效应无论q取什么值都存在;其高阶反聚束效应由于形变参数的影响具有更加丰富的结构.

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Published Jan 1, 2003• 0 citations

OpenAlex

Abstract

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Algebraic solutions for

SU(2)\otimes SU(2)

Hamiltonian eigensystems: generic statistical ensembles and a mesoscopic system application

Solutions of generic

SU(2)\otimes SU(2)

Hamiltonian eigensystems are obtained through systematic manipulations of quartic polynomial equations. An {\em ansatz} for constructing separable and entangled eigenstate basis, depending on the quartic equation coefficients, is proposed. Besides the quantum concurrence for pure entangled states, the associated thermodynamic statistical ensembles, their partition function, quantum purity and quantum concurrence are shown to be straightforwardly obtained. Results are specialized to a

SU(2)\otimes SU(2)

structure emulated by lattice-layer degrees of freedom of the Bernal stacked graphene, in a context that can be extended to several mesoscopic scale systems for which the onset from

SU(2)\otimes SU(2)

Hamiltonians has been assumed.

We discuss the entanglement properties of two qubits in terms of polynomial invariants of the adjoint action of SU(2) ⊕ SU(2) group on the space of density matrices

\mathfrak{P}_ +

. Since elements of

\mathfrak{P}_ +

are Hermitian, non-negative fourth-order matrices with unit trace, the space of density matrices represents a semi-algebraic subset,

\mathfrak{P}_ + \in \mathbb{R}^{15}

. We define

\mathfrak{P}_ +

explicitly with the aid of polynomial inequalities in the Casimir operators of the enveloping algebra of SU(4) group. Using this result the optimal integrity basis for polynomial SU(2) ⊕ SU(2) invariants is proposed and the well-known Peres-Horodecki separability criterion for 2-qubit density matrices is given in the form of polynomial inequalities in three SU(4) Casimir invariants and two SU(2) ⊕ SU(2) scalars; namely, determinants of the so-called correlation and the Schlienz-Mahler entanglement matrices.