共查询到20条相似文献,搜索用时 218 毫秒
1.
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
2.
FAN Hong-Yi 《理论物理通讯》2003,40(10)
By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for derivingmiscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can alsobe easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transformsand the squeezing transforms in quantum optics is investigated. 相似文献
3.
FANHong-Yi 《理论物理通讯》2003,40(4):409-414
By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving miscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can also be easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transforms and the squeezing transforms in quantum optics is investigated. 相似文献
4.
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. Analogs of Wick’s theorem for the Weyl ordering are verified. Using the Bose–Hubbard chain as an example, we show how these may be applied to constructing a mapping of the system in question to phase space. Regularisation issues and the reordering problem for the Heisenberg operators are addressed. 相似文献
5.
By making use of the coherent state representation of the Wigner operator we present a simple approach for deriving the Weyl correspondence product formula in complex phase space. The formula tells us how to express the Weyl classical function corresponding to an operator F = AB in terms of the Weyl functions corresponding to A and B. 相似文献
6.
7.
Hong-yi Fan 《Optics Communications》2010,283(17):3296-3300
We discuss what happens to the Radon transformation of signal's Wigner functions (i.e., signal's Wigner transformation (WT)) if the signal function undergoes various optical processes, such as Fraunhofer diffraction, lens transformation and Fresnel diffraction, etc. Because the usual Wigner transforms can be studied via their corresponding transforms of the Wigner operator, we use the Weyl ordered form of the Wigner operator and the Weyl ordering invariance under similar transformations to derive the result, we find that the alteration of Radon transformation of signal's Wigner function (or named the variation of tomogram function), through these optical processes, can be ascribed to the variation of Radon transformation parameters once the parameter of WT is given. 相似文献
8.
We find a new complex integration-transform which can establish a new relationship between a two-mode operator's matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience. 相似文献
9.
Jun-hua Chen Hong-yi Fan Xu-bing Tang 《International Journal of Theoretical Physics》2012,51(1):14-22
It is known that beamsplitter can be used to produce quantum entanglement, in this paper we examine this topic from the point
of view of Wigner operators. Using Weyl-ordering of the Wigner operator and the Weyl ordering invariance of Weyl ordered operators
under similarity transformation we derive the entanglement rule of Wigner operators at a beamsplitter. 相似文献
10.
In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl–Wigner–Groenewold–Moyal formalism of phase space quantization, with perfect fluid as a matter source. The corresponding quantum cosmology is described by the Moyal–Wheeler-DeWitt equation which has exact solutions in Moyal phase space, resulting in Wigner quasiprobability distribution functions peaking around the classical paths for large values of scale factor. We show that the Wigner functions of these models are peaked around the non-singular universes with quantum modified density parameter of radiation. 相似文献
11.
In this paper, two-mode displaced excited squeezed vacuum states (TDESVS) are constructed and their normalization and completeness are investigated. Using the entangled state representation and Weyl ordering form of the Wigner operator, the Wigner functions of TDESVS are obtained and the variations of Wigner functions with the parameters m, n and r are investigated. Besides, two marginal distributions of Wigner functions of TDESVS are obtained, which exhibit some entangled properties of the two-particle's system in TDESVS. 相似文献
12.
FAN Hong-Yi 《理论物理通讯》2006,45(2):245-248
The Moyal bracket is an exemplification of Weyl's correspondence to
formulate quantum mechancis in terms of Wigner function. Here we present a
formalism of Weyl-ordered operator Moyal bracket by virtue of the method of
integral within a Weyl ordered product of operators and the Weyl
ordering operator formula. 相似文献
13.
FANHong-Yi 《理论物理通讯》2002,38(6):729-732
In the context of the nonlinear coherent state(NLCS)theory we introduce the generalized weyl ordering operator formulation.The corresponding generalzied wigner operator turns out to be the Weyl ordered diracδ-operator functions.The completeness relation of NLCS is recast into generalized Weyl ordering form,The relationship between normal ordering,antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistent theory for NLCS. 相似文献
14.
FAN Hong-Yi 《理论物理通讯》2002,38(12)
In the context of the nonlinear coherent state (NLCS) theory we introduce the generalized Weyl orderingoperator formulation. The corresponding generalized Wigner operator turns out to be the Weyl ordered Dirac δ-operatorfunctions. The completeness relation of NLCS is recast into generalized Weyl ordering form. The relationship betweennormal ordering, antinormal ordering and the generalized Weyl ordering is established which constitute a self-consistenttheory for NLCS. 相似文献
15.
Xiang-Guo Meng Ji-Suo Wang Bao-Long Liang 《International Journal of Theoretical Physics》2009,48(8):2390-2400
Using the entangled state representation of Wigner operator and some formulae related to the two-variable Hermite polynomials,
the Wigner function of the squeezed pair coherent state (SPCS) and its two marginal distributions are derived. Based on the
entangled Husimi operator introduced by Fan et al. (Phys. Lett. A 358:203, 2006) and the Weyl ordering invariance under similar transformations, we also obtain the Husimi function of the SPCS and its marginal
distribution functions. The comparison between the two quasibability functions shows that, for the same amount of information
included in two functions, the solving process of the Husimi function is simpler than that of the Wigner function.
Work supported by the Natural Science Foundation of Shandong Province of China under Grant Y2008A23 and the Natural Science
Foundation of Liaocheng University under Grant X071049. 相似文献
16.
17.
18.
In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon transform of a phase space distribution of the covariant phase space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables. 相似文献
19.
《中国物理 B》2019,(8)
Based on the Weyl expansion representation of Wigner operator and its invariant property under similar transformation, we derived the relationship between input state and output state after a unitary transformation including Wigner function and density operator. It is shown that they can be related by a transformation matrix corresponding to the unitary evolution. In addition, for any density operator going through a dissipative channel, the evolution formula of the Wigner function is also derived. As applications, we considered further the two-mode squeezed vacuum as inputs, and obtained the resulted Wigner function and density operator within normal ordering form. Our method is clear and concise, and can be easily extended to deal with other problems involved in quantum metrology, steering, and quantum information with continuous variable. 相似文献
20.
New two-fold integration transformation for the Wigner operator in phase space quantum mechanics and its relation to operator ordering
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Using the Weyl ordering of operators expansion formula (Hong-Yi
Fan, \emph{ J. Phys.} A {\bf 25} (1992) 3443) this paper finds a
kind of two-fold integration transformation about the Wigner
operator $\varDelta \left( q',p'\right) $
($\mathrm{q}$-number transform) in phase space quantum mechanics,
$\iint_{-\infty}^{\infty}\frac{{\rm d}p'{\rm d}q'}{\pi
}\varDelta \left( q',p'\right) \e^{-2\i\left(
p-p'\right) \left( q-q'\right) }=\delta \left(
p-P\right) \delta \left( q-Q\right),$
and its inverse%
$
\iint_{-\infty}^{\infty}{\rm d}q{\rm d}p\delta \left( p-P\right)
\delta \left( q-Q\right) \e^{2\i\left( p-p'\right) \left(
q-q'\right) }=\varDelta \left(
q',p'\right),$ where $Q,$ $P$ are the coordinate
and momentum operators, respectively. We apply it to study mutual
converting formulae among $Q$--$P$ ordering, $P$--$Q$ ordering and Weyl
ordering of operators. In this way, the contents of phase space
quantum mechanics can be enriched. The formula of the Weyl
ordering of operators expansion and the technique of integration within the Weyl
ordered product of operators are used in this discussion. 相似文献