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外文期刊>Physics Letters, A
>Similarity transformation operators as the images of classical symplectic transformations in coherent state representation
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Similarity transformation operators as the images of classical symplectic transformations in coherent state representation
For the similarity transformation W, WA W~(-1) = AQ + AN, WAW~(-1) = AL + AP, where A = (a_1,a_2,...,a_n), A = (a_1,a_2,...,a_n), a_i(a_i) is the n-mode bosonic creation (annihilation) operator, and Q, L, N. P all complex matrices, we find W's coherent state representation W = sq root det Q integral #PI#_(i = 1)~n (d~2z_i/#pi#) | [_(N)~Q _P~(-L)] (_(Z-tilde)~(Z-tilde))><(_(Z-tilde)~(Z-tilde))|. It turns out that the general exponential quadratic boson operator V = exp{1/2(#ALPHA# #ALPHA#)#GAMMA#(_(A-tilde)~(A-tilde))}, where #GAMMA# is a symmetric matrix, is equal to W provided exp{#GAMMA#[_I~0 _0~(-I)]} is put into the form [_N~Q _P~L]. The Feynman density matrix for V in the coherent state basis can be directly obtained.
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机译：对于相似度变换W，WA W〜（-1）= AQ + AN，WAW〜（-1）= AL + AP，其中A =（a_1，a_2，...，a_n），A =（a_1，a_2 ，...，a_n），a_i（a_i）是n模式玻色生成（an灭）运算符，以及Q，L，N.P是所有复矩阵，我们发现W的相干态表示W = sq root det Q积分＃ PI #_（i = 1）〜n（d〜2z_i /＃pi＃）| [_（N）〜Q _P〜（-L）]（_（Z-波浪号）〜（Z-波浪号））> <（_（Z-波浪号）〜（Z-波浪号））|。事实证明，一般指数二次玻色子算子V = exp {1/2（＃ALPHA＃#ALPHA＃）＃GAMMA＃（_（A-tilde）〜（A-tilde））}}，其中＃GAMMA＃是a如果exp {#GAMMA＃[_ I〜0 _0〜（-I）]}的形式为[_N〜Q _P〜L]，则该对称矩阵等于W。可以直接获得基于相干态的V的费曼密度矩阵。
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