共查询到20条相似文献,搜索用时 15 毫秒
1.
FAN Hong-Yi 《理论物理通讯》2008,50(11):1089-1092
We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions' Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave. 相似文献
2.
FAN Hong-Yi 《理论物理通讯》2004,41(2):205-208
Based on the technique of integral within a Weyl ordered product of
operators, we present applications of the Weyl ordered two-mode Wigner
operator for quantum mechanical entangled system, e.g., we derive the
complex Wigner transform and its relation to the complex fractional Fourier
transform, as well as the entangled Radon transform. 相似文献
3.
4.
By virtue of the technique of integration within an ordered product of operators we present a new formulation of the Weyl quantization scheme in the coherent state representation, which not only brings convenience for calculating the Weyl correspondence of normally ordered operators, but also directly leads us to find both the coherent state representation and the Weyl ordering representation of the Wigner operator. 相似文献
5.
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
6.
Based on the technique of integration within an ordered product ofoperators, the Weyl ordering operator formula is derived and the Fresneloperators' Weyl ordering is also obtained, which together with the Weyltransformation can immediately lead to Fresnel transformation kernel inclassical optics. 相似文献
7.
8.
In the path integral representation, the Hamiltonian in a quantum system is associated with the Hamiltonian in a classical system through the Weyl transformation. From this, it is possible to describe the time evolution in a quantum system by the Hamiltonian in a classical system. In a Bose system, the Weyl transformation is defined by the eigenstates of the canonical operators, since the Hamiltonian is given by a function of the canonical operators. On the other hand, in a Fermi system, the Hamiltonian is usually described by a function of the creation and annihilation operators, and hence the Weyl transformation is defined by the coherent states which are the eigenstate of an annihilation operator. Here, we formulate the Weyl transformation in Fermi systems in terms of the eigenstates of the canonical operators so as to clarify the correspondence between both systems. Using this, we can derive the path integral representation in Fermi systems. 相似文献
9.
FAN Hong-Yi 《理论物理通讯》2008,50(4):935-937
We propose a new two-fold integration transformation in p-q phase space
∫∫-∞∞(dp dq/π)e2i(p-x)(q-y)f(p,q)≡G( x,y),
which possesses some well-behaved transformation properties. We apply this
transformation to the Weyl ordering of operators, especially those Q-P
ordered and P-Q ordered operators. 相似文献
10.
FAN Hong-Yi 《理论物理通讯》2010,54(3):439-442
By virtue of the technique of integration within Weyl ordered of operatorswe derive the formula of Weyl ordering expansion of power product ofcoordinate and momentum operators (21/2Q)m (21/2iP )r=::Hm,r(21/2Q,21/2iP ) ::, the introduction of two-variable Hermite polynomial Hm,r brings much convenience to the study of Weyl correspondence. 相似文献
11.
Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We show that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation. 相似文献
12.
By virtue of the Weyl correspondence and based on the the technique of integration within an ordered product of
operators, we show under what condition the superoperator's Kraus
representation
ρˊ=∑μ
AμρAμ† can be deformed as
ρˊ=(1/π)∫d2αB(α)D(α)ρD†(α),
where D(α) is the displacement operator, B(α) is a probability density related to the classical Weyl correspondence of Aμ. An alternate discussion by using the entangled state representation and through a quantum teleportation process is also presented. 相似文献
13.
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
14.
Three-dimensional type-ⅡWeyl fermions possess overtilted cone-like low-energy band dispersion.Unlike the closed ellipsoidal Fermi surface for type-ⅠWeyl fermions,the Fermi surface is an open hyperboloid for type-ⅡWeyl fermions.We evaluate the spin and density susceptibility of type-ⅡWeyl fermions with repulsive S-wave interaction by means of Green’s functions.We obtain the particle–hole continuum along the tilted momentum direction and perpendicular to the tilted momentum direction respectively.We find the zero sound mode in some repulsive interaction strengths by numerically solving the pole equations of the susceptibility within the random-phase approximation. 相似文献
15.
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
16.
由Wigner算符的完备性和Weyl对应,我们推导出一个能获得纯态密度算符的新等式。借助此公式,可以方便快捷的构造出量子力学中一些有用的新表象。 相似文献
17.
Weak Weyl representations of the canonical commutation relation (CCR) with one degree of freedom are considered in relation
to the theory of time operator in quantum mechanics. It is proven that there exists a general structure through which a weak
Weyl representation can be constructed from a given weak Weyl representation. As a corollary, it is shown that a Weyl representation
of the CCR can be constructed from a weak Weyl representation which satisfies some additional property. Some examples are
given.
The work is supported by the Grant-in-Aid No.17340032 for Scientific Research from Japan Society for the Promotion of Science
(JSPS). 相似文献
18.
We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslov-type indices; these indices intervene in a crucial way in Gutzwiller’s formula of semiclassical mechanics, and are simply related to an index defined by Conley and Zehnder. 相似文献
19.
We present analytic expressions for the gravitational potentials associated with triaxial ellipsoids, spheroids, spheres and disks in Weyl gravity. The gravitational potentials of these configurations in Newtonian gravity, i.e. the potentials derived by integration of the Poisson equation Green's function 1/|r – r| over the volume of the configuration, are well known in the literature. Herein we present the results of the integration of |r – r|, the Green's function associated with the fourth order Laplacian 4 of Weyl gravity, over the volume of the configuration to obtain the resulting gravitational potentials within this specific theory. As an application of our calculations, we solve analytically Euler's equations pertaining to incompressible rotating fluids to show that, as in the case of Newtonian gravity, homogeneous prolate configurations are not allowed within Weyl gravity either. 相似文献
20.
A Weyl ordering product operation (with its representative symbol) is introduced. On the basis of the operation, a technique of integration within a Weyl ordered product is put forward. Application of the technique to the coherent state representation leads us to derive the Weyl ordered forms of some important operators in quantum mechanics, which can be rigorously checked by the relation between our Weyl ordering product operation and the Weyl correspondence rule. 相似文献