共查询到20条相似文献,搜索用时 312 毫秒
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论述用L定义光学的哈密顿H,并给出哈密顿公式的基本方程式,利用哈密顿方程式,在旋转对称的光学系统里追迹光线,并利用哈密顿公式得到折射面和透镜的简单结果。最后通过举例说明这个方法是可行的。 相似文献
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Starting from a specific matrix iso-spectral problem, an associated hierarchy of multi-component Hamiltonian equations is constructed, based on zero curvature equations. The key point is to choose appropriate time parts of Lax pairs which can yield evolution equations, and the existence of a Hamiltonian structure for the obtained hierarchy is established by means of the trace identity. An example with five components is computed, along with its Hamiltonian structure. 相似文献
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基于平均场和Bogoliubov近似,将由外界相干抽运场产生并与库耦合的非平衡玻色凝结体系的哈氏量线性化。发现若忽略体系与库的耦合,则线性化后的哈氏量的动力学代数为Heisenberg和SU(1,1)李代数,利用相干态方法计算了它的本征值和本征函数——平移压缩粒子数态与一般SU(1,1)相干态的直积。尔后引进元激发的推迟格林函数计算耦合情形下元激发的能谱,进而给出弱耦合情形下激子体系的态函数。
关键词: 相似文献
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E. A. Gazazyan G. G. Grigoryan D. N. Khachatryan 《Journal of Contemporary Physics (Armenian Academy of Sciences)》2018,53(4):293-300
Propagation of four laser pulses in the five-level ladder system in the case of arbitrary intensities and the different strengths of oscillators is investigated, when one of the eigenstates of the interaction Hamiltonian is formed in the whole volume of the medium. Taking into account the first non-adiabatic correction, the equations of propagation are obtained. An analytical solution of these equations is obtained. The conditions for an effective excitation of the fifth level in the whole volume of medium and the limitations on the interaction parameters are obtained as well. 相似文献
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PARAMETRIC STABILIZATION OF A GYROSCOPIC SYSTEM 总被引:1,自引:0,他引:1
R.J. MCDONALDN. SRI NAMACHCHIVAYA 《Journal of sound and vibration》2002,255(4):635-662
This paper studies the stabilization of a gyroscopic system using parametric stabilization near a combination resonance. The gyroscopic system is near its primary instability, i.e., the bifurcation parameter is such that the system possesses a double zero eigenvalue. The stability of the system is studied for the linear Hamiltonian system, the damped linear system, the forced linear Hamiltonian system, and finally the damped and forced linear system. The addition of the periodic excitation near the critical combination resonance provides the system with an extended stability region when the excitation frequency is slightly above the combination resonance. A non-linear numerical example shows that these results may persist for the non-linear problem. The results of this work, are then discussed in relation to an example gyroscopic problem, a rotating shaft with periodically perturbed rotation rate. 相似文献
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Boris numerical scheme due to its long-time stability, accuracy and conservative properties has been widely applied in many studies of magnetized plasmas. Such algorithms conserve the phase space volume and hence provide accurate charge particle orbits. However, this algorithm does not conserve the energy in some special electromagnetic configurations,particularly for long simulation times. Here, we empirically analyze the energy behavior of Boris algorithm by applying it to a 2 D autonomous Hamiltonian. The energy behavior of the Boris method is found to be strongly related to the integrability of our Hamiltonian system. We find that if the invariant tori is preserved under Boris discretization, the energy error can be bounded for an exponentially long time, otherwise the said error will show a linear growth. On the contrary,for a non-integrable Hamiltonian system, a random walk pattern has been observed in the energy error. 相似文献
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Konstantin E. Starkov 《Physics letters. A》2011,375(36):3184-3187
In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system. 相似文献
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PANG Qian-Jun 《理论物理通讯》2006,45(3):425-428
We present a general discussion on the eigenstate problem of a
bipartite complicated-coupled-oscillator system. By use of a
generalized intermediate entangled state representation, the
eigenvalue and eigenfunction of Hamiltonian are analytically
obtained. As its application, we obtain the energy spectrum for two
special situations of Hamiltonian. 相似文献
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Schrödinger’s equation says that the Hamiltonian is the generator of time translations. This seems to imply that any reasonable definition of time operator must be conjugate to the Hamiltonian. Then both time and energy must have the same spectrum since conjugate operators are unitarily equivalent. Clearly this is not always true: normal Hamiltonians have lower bounded spectrum and often only have discrete eigenvalues, whereas we typically desire that time can take any real value. Pauli concluded that constructing a general a time operator is impossible (although clearly it can be done in specific cases). Here we show how the Pauli argument fails when one uses an external system (a “clock”) to track time, so that time arises as correlations between the system and the clock (conditional probability amplitudes framework). In this case, the time operator is conjugate to the clock Hamiltonian and not to the system Hamiltonian, but its eigenvalues still satisfy the Schrödinger equation for arbitrary system Hamiltonians. 相似文献
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We presented the fractional zero curvature equation and generalized Hamiltonian structure by using of the differential forms
of fractional orders. Example of the fractional AKNS soliton equation hierarchy and its Hamiltonian system are obtained. 相似文献
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A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly, as its application, the multi-component TC equation hierarchy is obtained, then by use of trace identity the Hamiltonian structure of the above system is
presented. Finally, the integrable couplings of the obtained system
is worked out by the expanding matrix Loop algebra. 相似文献
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用Liouville空间投影算符作基,利用虚拟转动对基作用的性质来解决核磁共振中在脉冲和系统哈密顿作用下,高自旋系统弱耦合理论。给出演化公式及脉冲算符的解析分解.
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The Hamiltonian of a radial equation is defined on a half-line,and there is a close relation between its hermitian and the boundary condition of the wave functions at the origin.If the wave functions are nonvanishing and convergent at the origin,the Hamiltonian has a one-parameter family of self-adjoint extensions which are related with the vanishness of the radial probability current at the origin.In this paper the problem on the hermitian of the Hamiltonian of a radial equation is studied systematically.Some methods for determining the parameter for the fermion moving in the magnetic monopole field are discussed. 相似文献
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A discrete integrable system and its Hamiltonian structure are generated by use of Tu model. Then, its Darboux transformation
is obtained, which can get the expression of the new solutions. 相似文献
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In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained. 相似文献
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H. J. Fink J. Maruhn W. Scheid W. Greiner 《Zeitschrift für Physik A Hadrons and Nuclei》1974,268(3):321-331
The fragmentation of a nuclear system is described by a dynamical coordinate, the fragmentation coordinate η=A1?A2/A1+A2 The total Hamiltonian describing a binary heavy ion encounter includes a part H(R, α,η) which describes the fragmentation and its coupling to other degrees of freedom. It is a collective Hamiltonian which is calculated from the microscopic Asymmetric Two-Center Shell Model (ATCSM). The properties of this Hamiltonian are extensively discussed and methods for its solution are described. Formulae for cross sections of specific nuclear fragmentations including fusion are derived. 相似文献
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研究Hamilton系统的形式不变性即Mei对称性,给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系,寻求系统的守恒量.给出一个例子说明本文结果的应用.
关键词:
Hamilton系统
Mei对称性
Noether对称性
Lie对称性
守恒量 相似文献