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arXiv quant-ph/0511007quant-ph
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关联费米子的高斯算子基

Gaussian operator bases for correlated fermions

J. F. Corney, P. D. Drummond

摘要:

我们制定了一个通用的多模高斯算子的基础费米子,使一个积极的相空间表示的相关费米态。高斯基将现有的玻色子相空间方法扩展到费米系统,从而使量子多体费米系统的第一性原理动力学或平衡计算成为可能。我们证明的基础上的完整性和积极性,并推导出微分形式的产品与一个和两个身体的运营商。由于基满足费米子超选择规则,因此所得到的相空间只涉及c-数,而不需要反交换格拉斯曼变量。

英文摘要:

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus enables first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness and positivity of the basis, and derive differential forms for products with one- and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c-numbers, without requiring anti-commuting Grassmann variables.

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