GENERALIZED P-REPRESENTATIONS IN QUANTUM OPTICS
GENERALIZED P-REPRESENTATIONS IN QUANTUM OPTICS
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DOI：
10.1088/0305-4470/13/7/018
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发表时间：
1980-01-01
期刊：
影响因子：
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通讯作者：
GARDINER, CW
中科院分区：
文献类型：
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作者：
DRUMMOND, PD;GARDINER, CW
引入了一类量子算符的正规序表示，它用非对角相干态投影算符推广了Glauber-suarshan P表示。这些结果对量子力学主方程的求解具有实际应用价值。在通常的正则相空间的复杂扩展上，不同的表示具有不同的积分范围。“复P-表示”是指解析P-函数在复平面的等高线上被定义和归一化的情况。在这种情况下，通常可以得到精确的稳态解，即使在使用Glauber-Sudarshan P-表示时这是不可能的。正P-表示是指区域是整个复相空间的情况。在这种情况下，P-函数总是可以选择为正的，并且任何产生的福克-普朗克方程都可以选择为具有正的半定扩散阵列。因此，“正P-表示”是一个真实的概率分布。新的表示法在非经典统计的情况下特别有用。
A class of normal ordering representations of quantum operators is introduced, that generalises the Glauber-Sudarshan P-representation by using nondiagonal coherent state projection operators. These are shown to have practical application to the solution of quantum mechanical master equations. Different representations have different domains of integration, on a complex extension of the usual canonical phase-space. The'complex P-representation'is the case in which analytic P-functions are defined and normalised on contours in the complex plane. In this case, exact steady-state solutions can often be obtained, even when this is not possible using the Glauber-Sudarshan P-representation. The'positive P-representation'is the case in which the domain is the whole complex phase-space. In this case the P-function may always be chosen positive, and any Fokker-Planck equation arising can be chosen to have a positive-semidefinite diffusion array. Thus the'positive P-representation'is a genuine probability distribution. The new representations are especially useful in cases of nonclassical statistics.