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k玻色子q相干态的反聚束效应 总被引:3,自引:0,他引:3
研究了q变形湮没算符高次幂(akq,k≥3)本征态的反聚束效应,并就k=3的情况用数值计算方法研究了q变形参数对该效应的影响.结果表明,当q变形相干态中谐振子的强度x=|z|2在某些区间内取值时,akq的本征态将呈现反聚束效应,并且这一效应明显地受到q参数的影响.当参数q取定时,随着q变形光场强度的变大,该光场的光子数涨落在经典(或量子)和量子(或经典)特性之间交替地变化. 相似文献
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Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok (p, q) with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 (p - P) (q - Q), (q - Q) 3 (p - P), and (p, q), which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of (p, q) are also derived, which helps us to put the operators into their - and - ordering, respectively. 相似文献
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Wigner算符的正规乘积形式和相干态形式的应用 总被引:1,自引:0,他引:1
本文导出了Wigner算符的正规乘积形式和相干态形式及其若干应用, 其中包括若干新量子算符公式的导出, Moyal定理的相干态推广, 计算以前文献未曾得到的若干与经典函数对应的量子Weyl算符以及若干与量子算符对应的Weyl经典函数. 相似文献
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众所周知,量子态的演化可用与其相应的Wigner函数演化来代替.因为量子态的Wigner函数和量子态的密度矩阵一样,都包含了概率分布和相位等信息,因此对量子态的Wigner函数进行研究,可以更加快速有效地获取量子态在演化过程的重要信息.本文从经典扩散方程出发,利用密度算符的P表示,导出了量子态密度算符的扩散方程.进一步通过引入量子算符的Weyl编序记号,给出了其对应的Weyl量子化方案.另外,借助于密度算符的另一相空间表示-Wigner函数,建立了Wigner算符在扩散通道中演化方程,并给出了其Wigner算符解的形式.本文推导出了Wigner算符在量子扩散通道中的演化规律,即演化过程中任意时刻Wigner算符的形式.在此结论的基础上,讨论了相干态经过量子扩散通道的演化情况. 相似文献
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介绍经典菲涅耳变换的量子力学对应,它是相干态在相空间中的代表点做辛运动所对应的量子菲涅耳算符. 相似文献
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研究了q变形湮没算符高次幂(αq^k,κ≥3)本征态的反聚束效应,并就κ=3的情况用数值计算方法研究了q变形参数对该效应的影响。结果表明,当q变形相干态中谐振子的强度x=|z|^2在某些区间内取值时,αq^k的本征态将呈现反聚束效应,并且这一效应明显地受到q参数的影响。当参数q取定时,随着q变形光场强度的变大,该光场的光子数涨落在经典(或量子)和量子(或经典)特性之间交替地变化。 相似文献
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Vladimir A. Marchenko 《Letters in Mathematical Physics》1994,31(3):179-193
For the Weyl solutions(z, x) of the Schrödinger and Dirac equations, asymptotics for |z| are obtained. This gives a possibility of selecting Weyl solutions by their behaviour when |z| . Some applications are given. 相似文献
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态|ψ3(3)〉q中广义磁场分量的等幂次高次和压缩 总被引:3,自引:0,他引:3
根据量子力学中态的线性叠加原理,构造了由多模复共轭相干态|{Zj*〉q(j=1,2,……q)、多模复共轭虚相干态|{iZj*〉q和多模真空态|{0j}〉q的线性叠加组成的第Ⅲ类三态叠加多模叠加态光场|ψ3(3)〉q.利用多模压缩态理论,研究了态|ψ3(3)〉q广义磁场分量(即第一正交相位分量)的广义非线性等幂次高次和压缩特性结果发现:当腔模总数q与压缩次数N之积qN取偶数时,态|ψ3(3)〉q广义磁场分量在一定条件下可分别呈现出周期性变化的、广义非线性等幂次奇数模—偶数次、偶数模—奇数次或偶数模—偶数次的高次和压缩效应. 相似文献
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构造了由多模复共轭相干态|{iZj*}〉q、多模复共轭虚相干态|{iZj*}〉q(j=1,2,…q)和多模真空态|{0j}〉q线性叠加所组成的第Ⅲ类三态叠加多模叠加态光场|ψ3(3)〉q.利用多模压缩态理论,研究了态|ψ3(3)〉q中广义电场分量(即第二正交相位分量)的广义非线性等幂次N次方H压缩特性.发现:态|ψ3(3)〉q是一种典型的三态叠加多模非经典光场;当腔模总数q与压缩次数N之积q·N为偶数时,在一定条件下,态|ψ3(3)〉q的广义电场分量可分别呈现出周期性变化的广义非线性等幂次奇数模-偶数次、偶数模-奇数次、偶数模-偶数次N次方H压缩效应. 相似文献
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A. Khodakovsky 《Communications in Mathematical Physics》2000,210(2):399-411
The Schrödinger operator -d2/dx2+q(x)-d^2/dx^2+q(x) is considered on the real axis. We discuss the inverse spectral problem where discrete spectrum and the potential on the positive half-axis determine the potential completely. We do not impose any restrictions on the growth of the potential but only assume that the operator is bounded from below, has discrete spectrum, and the potential obeys q(-|x|) 3 q(|x|)q(-|x|)\geq q(|x|). Under these assertions we prove that the potential for xS 0 and the spectrum of the problem uniquely determine the potential on the whole real axis. Also, we study the uniqueness under slightly different conditions on the potential. The method employed uses Weyl m-function techniques and asymptotic behavior of the Herglotz functions. 相似文献
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P. Pirooznia P. Kopietz 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(3):291-296
We calculate the damping γq of collective density oscillations
(zero sound) in a
one-dimensional Fermi gas
with dimensionless forward scattering interaction
F and quadratic energy dispersion
k2 / 2 m at zero temperature.
Using standard many-body perturbation theory,
we obtain γq from the expansion
of the
inverse irreducible polarization to first order
in the effective screened (RPA) interaction.
For wave-vectors | q| /kF ≪F (where kF = m vF is the Fermi wave-vector)
we find to leading order γq ∝| q |3 /(vF m2).
On the other hand, for F ≪| q| /kF most of the spectral weight
is carried by the particle-hole continuum, which is
distributed over a frequency interval of the order of q2/m.
We also show that zero sound damping
leads to a finite maximum proportional to
|k - kF | -2 + 2 η
of the charge peak in the single-particle
spectral function, where η is the anomalous
dimension. Our prediction agrees with photoemission data for
the blue bronze K0.3MoO3.
We comment on other recent calculations of γq. 相似文献
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We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the
projective superalgebra
\mathfrakpgl(p+1|q){\mathfrak{pgl}(p+1|q)} is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the
quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of
\mathfrakpgl(n|n)\not @ \mathfraksl(n|n){\mathfrak{pgl}(n|n)\not\cong \mathfrak{sl}(n|n)}), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms
of a generalized divergence operator acting on supersymmetric tensor fields. 相似文献
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构造了由多模复共轭相干态|{Zj*}〉q、多模复共轭相干态的相反态|{-Zj*}〉q以及多模虚相干态|{iZj*}〉q的线性叠加所组成的第Ⅴ类三态叠加多模叠加态光场|ψ5(3)〉q.利用多模压缩态理论研究了态|ψ5(3)〉q中广义磁场分量的等幂次N次方Y压缩特性.结果发现:当压缩次数N=2p且p=2m(m=1,2,3,…,…)时,只要各模的初始相位φj(j=1,2,…,…,q)、态间的初始相位差(θ1-θ2)、(θ1-θ3)和(θ2-θ3)以及受各模的初始相位φj调制的各单模相干态光场的平均光子数之和 等分别满足一定的取值条件,则态|ψ5(3)〉q的广义磁场分量就可呈现出周期性变化的广义非线性等幂次4m次方Y压缩效应. 相似文献
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It is shown that the elliptic algebra
at the critical level c = –2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and containing the q-deformed Virasoro algebra is constructed on this center. We show also that t(z) close an exchange algebra when p
m = q
c+2 for
, they commute when in addition p = q
2k
for k integer non-zero, and they belong to the center of
when k is odd. The Poisson structures obtained for t(z) in these classical limits contain the q-deformed Virasoro algebra, characterizing the structures at p q
2k
as new
algebras. 相似文献
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四态叠加多模叠加态光场|Ψe(4),Ⅲ〉q的等阶N次方Y压缩 总被引:7,自引:1,他引:6
根据量子力学的线性叠加原理,构造了由多模偶相干态与多模虚偶相干态组成的第Ⅲ种四态叠加多模叠加态光场态|Ψe(4),Ⅲ〉q的等阶N次方Y压缩特性.结果发现:1) 当压缩阶数N=4m,(m=1,2,3,…)时,态|Ψe(4),Ⅲ〉q恒处于等阶数N-Y最小测不准态;2) 当压缩阶数N=4m′+2,(m′=0,1,2,…)时,在(θ1-θ2),q,Rj,r1,r2等取不同的组合定值下,态|Ψe(4),Ⅲ〉q可分别呈现出等阶N次方Y压缩效应与"半相干态"效应;3) 当压缩阶数N为奇数时,在(θ1-θ2),q,Rj,r1,r2等取不同的组合定值下,态|Ψe(4),Ⅲ〉q可呈现出等阶N次方Y压缩效应. 相似文献
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构造了由多模复共轭相干态|{Zj*}〉q、多模复共轭虚相干态|{iZj*}〉q和多模真空态|{Qj} 〉q这三态的线性叠加所组成的第Ⅲ类三态叠加多模叠加态光场|ψ3(3)〉q.利用多模压缩态理论研究了态|ψ3(3)〉q中广义磁场分量的任意偶数次广义非线性等幂次N次方Y压缩特性.结果发现:在压缩次数N取偶数,只要各模的初始相位φj(j=1,2,3,…,…,q),态间的初始相位差(θi-θ2)(i=1,3)和各单模相干态光场平均光子数Rj2之和 分别满足各自的取值条件,态|ψ3(3)〉q的广义磁场分量(即第一正交相位分量)就可呈现出周期性变化的、任意偶数次的广义非线性等幂次N次方Y压缩效应. 相似文献