Acta Scientiarum Naturalium Universitatis Neimongol

SU（2）q—奇偶相干叠加态的非经典效应

张慧慧, 王维玺, 白鲜萍, 李瑞芳, 张艳霞

Published Jan 1, 2003• 0 citations

Abstract

由一维线性谐振子引入q-形变谐振子,构成q-形变谐振子的量子Heisenberg-Weyl代数,构造了SU(2)q-奇偶相干叠加态,计算了在此态下的期望值,通过理论计算作图研究了其非经典效应.发现由于形变参数的影响,其压缩效应和反聚束效应具有丰富的结构.

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Acta Scientiarum Naturalium Universitatis Neimongol

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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.