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1.
We find that the coherent state projection operator representation of
symplectic transformation constitutes a loyal group representation of
symplectic group. The result of successively applying squeezing operators on
number state can be easily
derived. 相似文献
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3.
We study the symplectic Radon transform from the point of view of the metaplectic representation of the symplectic group and its action on the Lagrangian Grassmannian. We give rigorous proofs in the general setting of multi-dimensional quantum systems. We interpret the Radon transform of a quantum state as a generalized marginal distribution for its Wigner transform; the inverse Radon transform thus appears as a “demarginalization process” for the Wigner distribution. 相似文献
4.
FANHong-Yi CHENJun-Hua 《理论物理通讯》2003,40(5):589-594
We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed. 相似文献
5.
We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed. 相似文献
6.
Probability representation of classical states described by symplectic tomograms is discussed. Tomographic symbols of classical
observables which are functions on phase-space are studied. Explicit form of kernel of commutative star-product of the tomographic
symbols is obtained. 相似文献
7.
We study symplectic unitary representations for the Galilei group and derive the Schrödinger equation in phase space. Our formalism is based on the noncommutative structure of the star product. Guided by group theoretical concepts, we construct a physically consistent phase-space theory in which each state is described by a quasi-probability amplitude associated with the Wigner function. As applications, we derive the Wigner functions for the 3D harmonic oscillator and the noncommutative oscillator in phase space. 相似文献
8.
FANHong-Yi HEHai-Yan 《理论物理通讯》2005,44(1):137-142
Using the nonlinear coherent state representation we derive nonlinear squeezed states and the multiplication rule of nonlinear squeezing operators. We find that the symplectic matrices multiplication rule in nonlinear coherent state projection operator representation maps into the multiplication rule of successive nonlinear squeezing operators.The technique of integral within an ordered product of operators plays an essential role in deriving the multiplication rule. 相似文献
9.
FAN Hong-Yi HE Hai-Yan 《理论物理通讯》2005,44(7)
Using the nonlinear coherent state representation we derive nonlinear squeezed states and the multiplication rule of nonlinear squeezing operators. We find that the symplectic matrices multiplication rule in nonlinear coherent state projection operator representation maps into the multiplication rule of successive nonlinear squeezing operators.The technique of integral within an ordered product of operators plays an essential role in deriving the multiplication rule. 相似文献
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11.
Simone Gutt 《Letters in Mathematical Physics》2006,78(3):307-328
This note contains a short survey on some recent work on symplectic connections: properties and models for symplectic connections whose curvature is determined by the Ricci tensor, and a procedure to build examples of Ricci-flat connections. For a more extensive survey, see Bieliavsky et al. [Int. J. Geom. Methods Mod. Phys. 3, 375–420 2006]. This note also includes a moment map for the action of the group of symplectomorphisms on the space of symplectic connections, an algebraic construction of a large class of Ricci-flat symmetric symplectic spaces, and an example of global reduction in a non-symmetric case. 相似文献
12.
Pavol Severa 《Letters in Mathematical Physics》2004,68(1):31-39
There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for all functions f and g. We notice that this noncommutative differential algebra has a geometrical realization as a convolution algebra of the symplectic groupoid integrating the Poisson manifold. This quantization is just a part of a quantization of the odd symplectic category (where objects are odd symplectic supermanifolds and morphisms are Lagrangian relations) in terms of 2-graded chain complexes. It is a straightforward consequence of the theory of BV operator acting on semidensities, due to H. Khudaverdian. 相似文献
13.
辛时域有限差分算法研究等离子体光子晶体透射系数 总被引:1,自引:0,他引:1
相较于传统的时域有限差分算法,辛时域有限差分算法具有高准确度性和低色散性.传统的时域有限差分算法的计算准确度较低,数值色散误差较大,并且破坏了麦克斯韦方程的辛结构,从而导致其稳定性较差.然而辛时域有限差分算法可以克服这些缺点,从而保证了整个仿真计算的准确性和稳定性.本文基于辛时域有限差分算法,对等离子体光子晶体的带隙特性,透射系数等进行了研究,并与传统的时域有限差分算法进行了对比,验证了辛时域有限差分算法的优势和可行性. 相似文献
14.
Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory 下载免费PDF全文
This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates. 相似文献
15.
The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified, and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups.Supported in part by a Soros Foundation Grant awarded by the American Physical SocietyUnité Associée au C.N.R.S., URA 280 相似文献
16.
以二维自对偶场为研究对象,给出二维自对偶场方程解流形上的辛结构,并证明该辛结构是Poincare不变的.二维自对偶场的拉氏量L是一分量共形群不变的.上述辛结构在该共形群下亦保持不变.并给出二维自对偶场守恒流的几何表述. 相似文献
17.
A. I. Molev 《Communications in Mathematical Physics》1999,201(3):591-618
A basis for each finite-dimensional irreducible representation of the symplectic Lie algebra ¤(2n) is constructed. The basis vectors are expressed in terms of the Mickelsson lowering operators. Explicit formulas for the matrix elements of generators of ¤(2n) in this basis are given. The basis is natural from the viewpoint of the representation theory of the Yangians. The key role in the construction is played by the fact that the subspace of ¤(2nm 2) highest vectors in any finite-dimensional irreducible representation of ¤(2n) admits a natural structure of a representation of the Yangian Y((2)). 相似文献
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19.
We derive a kind of operator disentangling formulae and their coherent state represen tation by virtue of the correspondence be tween symplectic transformations and their quantum mechanical images. The application of the formulae in calculating Feynman transformation matrix elements is discussed. 相似文献
20.
Andreas Floer 《Communications in Mathematical Physics》1989,120(4):575-611
LetP be a symplectic manifold whose symplectic form, integrated over the spheres inP, is proportional to its first Chern class. On the loop space ofP, we consider the variational theory of the symplectic action function perturbed by a Hamiltonian term. In particular, we associate to each isolated invariant set of its gradient flow an Abelian group with a cyclic grading. It is shown to have properties similar to the homology of the Conley index in locally compact spaces. As an application, we show that if the fixed point set of an exact diffeomorphism onP is nondegenerate, then it satisfies the Morse inequalities onP. We also discuss fixed point estimates for general exact diffeomorphisms. 相似文献