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 共查询到19条相似文献,搜索用时 109 毫秒
1.
王顺金 《物理学进展》2011,19(4):331-370
从控制与利用微观系统的量子工程的观点,讨论了人造量子系统的基本物理问题。针对人造量子系统中的一大类———非自治量子系统的求解问题,提出了代数动力学理论方法。运用代数动力学,对人造量子系统进行了理论研究;对可积的非自治系统,详细介绍了线性系统和非线性可积系统的求解问题;对不可积系统,用代数动力学观点研究了量子规则运动和无规运动的特征,它们之间的过渡,以及它们对时间有关外场的不同响应。  相似文献   

2.
量子系统的动力学对称性研究与代数动力学   总被引:2,自引:0,他引:2  
文章介绍了量子系统的动力学对称性理论和代数动力学在人造了系统和量子光学系统中的应用。  相似文献   

3.
左维  王顺金 《物理学报》1995,44(9):1363-1372
利用代数动力学方法,分别在两种不同的规范条件下,得到了描述量子辐射场与经典流相互作用的hw(4)线性非自治量子系统在谐振子表象和相干态表象中的精确解及其Cartan不变算子,建立和澄清了量子解与经典解之间存在的直接对应的规则。结果表明代数动力学方法对于具有非半单李代数结构的线性动力系统仍然适用。  相似文献   

4.
左维  王顺金 《物理学报》1995,44(9):1353-1362
利用代数动力学方法得到了SU(1,1)+h(3)线性非自治量子系统的精确解及其Cartan不变算子,并发现了量子解与经典解之间的新的间接对应关系。结果还表明代数动力学方法对于这种具有非半单李代数结构的线性动力系统仍然适用。  相似文献   

5.
SU(3)线性非自治量子系统的代数动力学求解   总被引:1,自引:0,他引:1       下载免费PDF全文
张文忠  王顺金 《物理学报》1997,46(2):209-226
利用代数动力学方法,得到了量子物理中十分重要的SU(3)线性非自治量子系统的严格解及其不变Cartan算子,并建立起量子解与经典解之间的对应关系.同时计算了周期系统的非绝热Berry相因子 关键词:  相似文献   

6.
SU(1,1)线性非自治量子系统的代数动力学求解   总被引:2,自引:0,他引:2       下载免费PDF全文
左维  王顺金  A.Weiguny  李福利 《物理学报》1995,44(8):1184-1191
利用代数动力学方法得到了SU(1,1)线性非自治量子系统的精确解及其Cartan不变算子,并建立和澄清了量子解与经典解之间的对应关系.另外还讨论了周期系统的非绝热和绝热Berry相因子. 关键词:  相似文献   

7.
代数动力学与SU(2)线性非自治量子系统   总被引:3,自引:0,他引:3       下载免费PDF全文
左维  王顺金 《物理学报》1995,44(8):1177-1183
利用代数动力学方法得到了SU(2)线性非自治量子系统的精确及其Cartan不变算子,并应用得到的解计算了时间有关的磁场中中微子的反转概率以及束流动力学中的粒子自旋极化问题,另外还讨论了周期系统的非绝热Berry相因子. 关键词:  相似文献   

8.
基于代数动力学,精确求解了旋转磁场中的朗道系统,讨论了它的一般几何相位,给出了一般量子几何相位中对应于规范势的那部分相位的经典对应. 数值计算结果显示出非绝热演化和绝热演化的重大区别:非绝热演化诱导的非绝热量子激发引起系统物理量的非周期性和复杂性,体现了环境对系统的影响.  相似文献   

9.
严晓波  王顺金 《物理学报》2006,55(4):1591-1595
研究了各向异性耦合的三粒子海森伯自旋环链团簇在随时间变化的磁场中的运动.该系统的哈密顿量具有SU(2)代数结构.用代数动力学方法对此系统进行求解,得到了严格的解析解.基于严格解, 可以构造一位量子逻辑门.通过调节磁场强度和频率, 就可以控制该量子逻辑门, 实现一位量子逻辑门的任何操作. 关键词: 代数动力学 自旋环链团簇 一位量子逻辑门  相似文献   

10.
我们研究了含时旋转磁场中海森堡XXX模型下的双量子比特的动力学演化情况.基于此非自治系统的代数结构,我们用代数动力学方法求得了系统的精确解析解.在此基础上,进一步研究了在不同初态下系统的纠缠测度随时间的演化,发现纠缠测度由系统的初态的系数和耦合强度决定.  相似文献   

11.
We define and discuss the notion of quantum integrability of a classically integrable system within the framework of deformation quantization, i.e. the question whether the classical conserved quantities (which are already in involution with respect to the Poisson bracket) commute with respect to some star product on the phase space after possible quantum corrections. As an example of this method, we show by means of suitable 2 by 2 quantum R-matrices that a list of Toda-like classical integrable systems given by Y. B. Suris is quantum integrable with respect to the usual star product of the Weyl type in flat 2n-dimensional space.  相似文献   

12.
We present an approach to higher-dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the algebro-geometric definition of quantum integrability, we utilize the bispectral duality of quantum Hamiltonian systems to construct nontrivial Darboux transformations between completely integrable quantum systems. As an application, we are able to construct new quantum integrable systems as the Darboux transforms of trivial examples (such as symmetric products of one dimensional systems) or by Darboux transformation of well-known bispectral systems such as quantum Calogero–Moser.  相似文献   

13.
During the last few decades, algebraic geometry has become a tool for solving differential equations and spectral questions of mechanics and mathematical physics. This paper deals with the study of the integrable systems from the point of view of algebraic geometry, inverse spectral problems and mechanics from the point of view of Lie groups. Section 1 is preliminary giving a little background. In Section 2, we study a Lie algebra theoretical method leading to completely integrable systems, based on the Kostant-Kirillov coadjoint action. Section 3 is devoted to illustrate how to decide about the algebraic complete integrability (a.c.i.) of Hamiltonian systems. Algebraic integrability means that the system is completely integrable in the sense of the phase space being foliated by tori, which in addition are real parts of a complex algebraic tori (abelian varieties). Adler-van Moerbeke's method is a very useful tool not only to discover among families of Hamiltonian systems those which are a.c.i., but also to characterize and describe the algebraic nature of the invariant tori (periods, etc.) for the a.c.i. systems. Some integrable systems, such as Kortewege—de Vries equation, Toda lattice, Euler rigid body motion, Kowalewski's top, Manakov's geodesic flow on S O (4), etc. are treated.  相似文献   

14.
Nonlinear nonautonomous discrete dynamical systems (DDS) whose continuum limits are the well-known Painlevé equations, have recently arisen in models of quantum gravity. The Painlevé equations are believed integrable because each is the isomonodromy condition for an associated linear differential equation. However, not every DDS with an integrable continuum limit is necessarily integrable. Which of the many discrete versions of the Painlevé equations inherit their integrability is not known. How to derive all their integrable discrete versions is also not known. We provide a systematic method of attacking these questions by giving a general discrete isomonodromy problem. Discrete versions of the first and second Painlevé equations are deduced from this general problem.  相似文献   

15.
Denghui Li 《中国物理 B》2022,31(8):80202-080202
This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters. The boson-fermion correspondence for these symmetric functions have been presented. In virtue of quantum fields, we derive a series of infinite order nonlinear integrable equations, namely, universal character hierarchy, symplectic KP hierarchy and symplectic universal character hierarchy, respectively. In addition, the solutions of these integrable systems have been discussed.  相似文献   

16.
There has been some substantial research about the connections between quantum chaos and quantum correlations in many-body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin-1/2 chains are compared. The CC and QD between nearest-neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite-size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis.  相似文献   

17.
We propose a method to construct new quantum integrable models. As an example, we construct an integrable anisotropic quantum spin chain which includes the nearest-neighbor, next-nearestneighbor and chiral three-spin couplings. It is shown that the boundary fields can enhance the anisotropy of the first and last bonds, and can induce the Dzyloshinsky–Moriya interactions along the z-direction at the boundaries. By using the algebraic Bethe ansatz, we obtain the exact solution of the system. The energy spectrum of the system and the associated Bethe ansatz equations are given explicitly. The method provided in this paper is universal and can be applied to constructing other exactly solvable models with certain interesting interactions.  相似文献   

18.
Previous studies show that, in quantum chaotic and integrable systems, the so-called out-of-time-ordered correlator(OTOC) generically behaves differently at long times, while, it may show similar early growth in one-body systems. In this paper, by means of numerical simulations, it is shown that OTOC has similar early growth in two quantum many-body systems, one integrable and one chaotic.  相似文献   

19.
The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed matter physics. Classical integrable systems are considered and a new approach is reported to obtain the classical analogs of the quantum metric tensor and the Berry curvature. An advantage of this approach is that it can be applied to a wide variety of classical systems corresponding to quantum systems with bosonic and fermionic degrees of freedom. The approach used arises from the semiclassical approximation of the Berry curvature and the quantum metric tensor in the Lagrangian formalism. This semiclassical approximation is exploited to establish, for the first time, the relation between the quantum metric tensor and its classical counterpart. The approach described is illustrated and validated by applying it to five systems: the generalized harmonic oscillator, the symmetric and linearly coupled harmonic oscillators, the singular Euclidean oscillator, and a spin-half particle in a magnetic field. Finally, some potential applications of this approach and possible generalizations that can be of interest in the field of condensed matter physics are mentioned.  相似文献   

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