共查询到20条相似文献,搜索用时 15 毫秒
1.
The relationship between Jacobi’s last multiplier and the Lagrangian of a second-order ordinary differential equation is quite
well known. In this article we demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing
the Hamiltonians of certain well known first-order systems of differential equations arising in biology. 相似文献
2.
Toyoki Matsuyama 《The European Physical Journal C - Particles and Fields》1999,8(1):163-169
We investigate the canonical structure of the (2+1)-dimensional non-linear model in a polynomial formulation. A current density defined in the non-linear model is a vector field, which satisfies a formal flatness (or pure gauge) condition. It is the polynomial formulation in which the vector field is regarded as a dynamic variable
on which the flatness condition is imposed as a constraint condition by introducing a Lagrange multiplier field. The model
so formulated has gauge symmetry under a transformation of the Lagrange multiplier field. We construct the generalized Hamiltonian formalism of the model
explicitly by using the Dirac method for constrained systems. We derive three types of the pre-gauge-fixing Hamiltonian systems:
In the first system the current algebra is realized as the fundamental Dirac Brackets. The second one manifests the similar
canonical structure as the Chern-Simons or BF theories. In the last one there appears an interesting interaction as the dynamic
variables are coupled to their conjugate momenta via the covariant derivative.
Received: 29 September 1998 / Published online: 14 January 1999 相似文献
3.
We study an application of the Jacobi last multiplier to a generalized Hamilton system. A partial differential equation on the last multiplier of the system is established. The last multiplier can be found by the equation. If the quantity of integrals of the system is sufficient, the solution of the system can be found by the last multiplier. 相似文献
4.
Sumit Kumar Rai Bhabani Prasad Mandal 《International Journal of Theoretical Physics》2013,52(10):3512-3521
We consider the finite field dependent BRST (FFBRST) transformations in the context of Hamiltonian formulation using Batalin-Fradkin-Vilkovisky method. The non-trivial Jacobian of such transformations is calculated in extended phase space. The contribution from Jacobian can be written as exponential of some local functional of fields which can be added to the effective Hamiltonian of the system. Thus, FFBRST in Hamiltonian formulation with extended phase space also connects different effective theories. We establish this result with the help of two explicit examples. We also show that the FFBRST transformations is similar to the canonical transformations in the sector of Lagrange multiplier and its corresponding momenta. 相似文献
5.
J. Klusoň 《The European Physical Journal C - Particles and Fields》2011,71(12):1820
We consider RFDiff invariant Hořava–Lifshitz gravity action with additional Lagrange multiplier term that is a function of
scalar curvature. We find its Hamiltonian formulation and we show that the constraint structure implies the same number of
physical degrees of freedom as in General Relativity. 相似文献
6.
《Journal of Nonlinear Mathematical Physics》2013,20(2):284-304
Abstract After giving a brief account of the Jacobi last multiplier for ordinary differential equations and its known relationship with Lie symmetries, we present a novel application which exploits the Jacobi last multiplier to the purpose of finding Lie symmetries of first-order systems. Several illustrative examples are given. 相似文献
7.
J. van der Rest 《Journal of magnetism and magnetic materials》1983,30(3):359-364
It is not well established that the ground state of the Hubbard Hamiltonian is not always paramagnetic. It is also well established that the ground state of the alloy analogy approximation of the non-degenerate Hubbard Hamiltonian is always paramagnetic. It has been claimed on the other hand that the ground state of the alloy analogy approximation of the doubly degenerate Hubbard Hamiltonian is not always paramagnetic. We show in this article that this last statement is not fully proved. Contradictory results are in fact obtained, depending upon the physical quantity one computes: total energy calculations have indeed been reported showing a magnetic instability while we prove here that magnetic susceptibility calculations do not. We conclude therefore that the ground state of the alloy analogy approximation of the doubly degenerate Hubbard Hamiltonian is not known at the present time. 相似文献
8.
<正>This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space.The Birkhoff's equations in the event space are given.The Poisson theory of the Birkhoffian system in the event space is established.The definition of the Jacobi last multiplier of the system is given,and the relation between the Jacobi last multiplier and the first integrals of the system is discussed.The researches show that for a Birkhoffian system in the event space,whose configuration is determined by(2n + 1) Birkhoff's variables,the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known.An example is given to illustrate the application of the results. 相似文献
9.
This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion.Equations of a dynamical system of relative motion in phase space are given.Poisson theory of the system is established.The Jacobi last multiplier of the system is defined,and the relation between the Jacobi last multiplier and the first integrals of the system is studied.Our research shows that for a dynamical system of relative motion,whose configuration is determined by n generalized coordinates,the solution of the system can be found by using the Jacobi last multiplier if (2n 1) first integrals of the system are known.At the end of the paper,an example is given to illustrate the application of the results. 相似文献
10.
11.
We employ Jacobi’s last multiplier (JLM) to study planar differential systems. In particular, we examine its role in the transformation
of the temporal variable for a system of ODEs originally analysed by Calogero–Leyvraz in course of their identification of
isochronous systems. We also show that JLM simplifies to a great extent the proofs of isochronicity for the Liénard-type equations. 相似文献
12.
We show that the Suslov nonholonomic rigid body problem studied in by Fedorov and Kozlov (Am. Math. Soc. Transl. Ser. 2 168:141–171, 1995), Jovanović (Reg. Chaot. Dyn. 8(1):125–132, 2005), and Zenkov and Bloch (J. Geom. Phys. 34(2):121–136, 2000) can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifolds of the integrable examples are not necessary tori 相似文献
13.
In this paper, we attempt to reconstruct one of the last and incomplete projects of Volodya Geyler. We study the motion of a quantum particle in the plane to which a halfline lead is attached, assuming that the particle has spin ½ and the plane component of the Hamiltonian contains a spin-orbit interaction, of Rashba or Dresselhaus type. We construct a class of admissible Hamiltonians and derive an explicit expression for the Green function, which is applied to scattering in a system of this kind. 相似文献
14.
有不少的极性半导休,电子与表面声学声子和体纵光学声子的耦合弱,但与表面光学声手的耦台强.本文同时考虑体纵光学声子、表面光学声子以及表面声学声予的影响,研究这类半导体的表面电予的性质,采用线性组合算符和拉格朗日乘子法,导出其有效哈密顿量和重正化质量。 相似文献
15.
The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy's principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations. 相似文献
16.
We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a Hamiltonian system (a Fermi-Pasta-Ulam chain of oscillators); (ii) a general model for spatiotemporal chaos (the complex Ginzburg-Landau equation); (iii) experimental data taken from a CO2 laser with delayed feedback. In the last case, the convective Lyapunov exponent is determined directly from the experimental data. 相似文献
17.
18.
We derive a non-hermitian boson-fermion Hamiltonian, that is equivalent to the entirely fermionic Richardson Hamiltonian which describes the dynamics of conduction electrons in a superconductor. This is done using a generalized Dyson mapping, that replaces Cooper pairs with bosons. We show that the calculation of some physical quantities is simpler when one uses the boson-fermion Hamiltonian rather than the original Richardson Hamiltonian. 相似文献
19.
本文研究多原子极性晶体中表面激子的性质.采用线性组合算符和拉格朗日乘子法,导出强耦合多原子极性晶体中表面激子的有效哈密顿量,得到了强耦合表面激子的重正化质量. 相似文献
20.
We study the interaction of many fields. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to neglect some terms in the rotated Hamiltonian. We show that coherent states remain coherent under the action of a quadratic Hamiltonian and by solving the eigenvalue and eigenvector problem for tridiagonal matrices we also show that a system of n interacting harmonic oscillators, initially in coherent states, remain coherent during the interaction. 相似文献