共查询到20条相似文献,搜索用时 171 毫秒
1.
The Landau problem on non-commutative quantum mechanics is studied, where
the Heisenberg algebra and the Landau energy levels as well as the
non-commutative angular momentum are constructed in detail in
non-commutative space and non-commutative phase space respectively. 相似文献
2.
3.
In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space.The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity.First,new Poisson brackets have been defined in non-commutative phase space.They contain corrections due to the non-commutativity of coordinates and momenta.On the basis of this new Poisson brackets,a new modified second law of Newton has been obtained.For two cases,the free particle and the harmonic oscillator,the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys.Rev.D,2005,72:025010).The consistency between both methods is demonstrated.It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space.but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. 相似文献
4.
In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. 相似文献
5.
Pulak Ranjan Giri 《Physics letters. A》2008,372(31):5123-5125
We study non-commutative quantum mechanics and exploit the non-commutative parameter as a scale for a scale symmetric system. The Hamiltonian in non-commutative space allows an unusual bound state at the threshold of the energy, E=0. The so(2,1) algebra for the system is also studied in non-commutative space. 相似文献
6.
The topological AC effect on non-commutative phase space 总被引:1,自引:0,他引:1
The Aharonov–Casher (AC) effect in non-commutative (NC) quantum mechanics is studied. Instead of using the star product method,
we use a generalization of Bopp’s shift method. After solving the Dirac equations both on non-commutative space and non-commutative
phase space by the new method, we obtain corrections to the AC phase on NC space and NC phase space, respectively.
PACS 02.40.Gh; 11.10.Nx; 03.65.-w 相似文献
7.
L. R. Ribeiro E. Passos C. Furtado J. R. Nascimento 《The European Physical Journal C - Particles and Fields》2008,56(4):597-606
We investigate the analog of Landau quantization, for a neutral polarized particle in the presence of homogeneous electric
and magnetic external fields, in the context of non-commutative quantum mechanics. This particle, possessing electric and
magnetic dipole moments, interacts with the fields via the Aharonov–Casher and He–McKellar–Wilkens effects. For this model
we obtain the Landau energy spectrum and the radial eigenfunctions of the non-commutative space coordinates and non-commutative
phase space coordinates. Also we show that the case of non-commutative phase space can be treated as a special case of the
usual non-commutative space coordinates. 相似文献
8.
We introduce a master action in non-commutative space, out of which we obtain the action of the non-commutative Maxwell-Chern-Simons theory. Then, we look for the corresponding dual theory at both first and second order in the non-commutative parameter. At the first order, the dual theory happens to be, precisely, the action obtained from the usual commutative self-dual model by generalizing the Chern-Simons term to its non-commutative version, including a cubic term. Since this resulting theory is also equivalent to the non-commutative massive Thirring model in the large fermion mass limit, we remove, as a byproduct, the obstacles arising in the generalization to non-commutative space, and to the first non-trivial order in the non-commutative parameter, of the bosonization in three dimensions. Then, performing calculations at the second order in the non-commutative parameter, we explicitly compute a new dual theory which differs from the non-commutative self-dual model and, further, differs also from other previous results and involves a very simple expression in terms of ordinary fields. In addition, a remarkable feature of our results is that the dual theory is local, unlike what happens in the non-Abelian, but commutative case. We also conclude that the generalization to non-commutative space of bosonization in three dimensions is possible only when considering the first non-trivial corrections over ordinary space.Received: 12 November 2003, Published online: 23 March 2004M. Botta Cantcheff: mbotta_c@ictp.trieste.itP. Minces: Permanent address Centro Brasileiro de Pesquisas Físicas (CBPF), Departamento de Teoria de Campos e Partículas (DCP), Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil 相似文献
9.
Stéphane Attal 《Communications in Mathematical Physics》1996,175(1):43-62
It is known, from a simple algebraic computation, that every Hilbert-Schmidt operator on the Fock space admits a Maassen-Meyer kernel. Maassen-Meyer kernels are a non-commutative extension of the usual notion of chaotic expansion of random variables. Using an extension of the non-commutative stochastic integrals which allows to define these integrals on the whole Fock space, we prove that a Hilbert-Schmidt operator on Fock space is the sum of a series of iterated non-commutative stochastic integrals with respect to the basic theree quantum noises. In this way we recover its Maassen-Meyer kernel which can be completely described from the operator itself. 相似文献
10.
非对易空间中耦合谐振子的能级分裂 总被引:1,自引:1,他引:0
非对易空间效应的出现引起了物理学界的广泛兴趣。 介绍了非对易空间中量子力学的代数关系,在所考虑的空间变量的对易关系中包含了坐标 坐标的非对易性, 并且把 Moyal-Weyl 乘法在非对易空间中通过一个Bopp变换转变成普通的乘法。 然后给出了非对易空间中耦合谐振子的能级分裂情况。 The effect of noncommutativity of space have caused the physical academic circles widespread interest. In this paper, the non commutative (NC) is introduced, which contain non commutative of coordinate coordinate, and find that the Moyal Weyl product in NC space can be replaced with a Bopp shift. Then, the energy splitting of the coupling harmonic oscillator in non commutative spaces are discussed. 相似文献
11.
In order to find a non-commutative analog of Schwarzschild or Schwarzschild–de Sitter black hole we investigate spherically
symmetric spaces generated by four non-commutative coordinates in the frame formalism. We present two solutions which, however,
do not possess the prescribed commutative limit. Our analysis indicates that the appropriate non-commutative space might be
found as a subspace of a higher-dimensional space. 相似文献
12.
13.
Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space 总被引:1,自引:0,他引:1
In this paper, the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space; the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric function. It is shown that in the non-commutative space,the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem. 相似文献
14.
15.
By using a generalized Bopp’s shift formulation, instead of the star product method, we investigate the Aharonov–Casher (AC)
effect for a spin-1 neutral particle in non-commutative (NC) quantum mechanics. After solving the Kemmer equations both on
a non-commutative space and a non-commutative phase space, we obtain the corrections to the topological phase of the AC effect
for a spin-1 neutral particle both on a NC space and a NC phase space.
PACS 02.40.Gh, 11.10.Nx, 03.65.-w 相似文献
16.
Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space 总被引:1,自引:0,他引:1
In this paper,the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space;the corresponding exact energy is obtained,and the analytic eigenfunction is presented in terms of the confluent hypergeometric function.It is shown that in the non-commutative space,the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem. 相似文献
17.
非对易几何、弦论和圈量子引力理论的发展,使非对易空间受到越来越多的关注.非对易量子理论不同于平常的量子理论,它是弦尺度下的特殊的物理效应,处理非对易量子力学问题需要特殊方法.本文首先介绍了Moyal方程与Wigner函数,利用Moyal-Weyl乘法与Bopp变换将H(x,p)变换成^H(^x,^p),考虑坐标—坐标、动量—动量的非对易性,实现对非对易相空间中星乘本征方程的求解.并利用非对易相空间量子力学的代数关系,讨论了非对易相空间中狄拉克振子的Wigner函数和能级,研究结果发现非对易相空间中狄拉克振子的能级明显依赖于非对易参数. 相似文献
18.
We study general relativity in the framework of non-commutative differential geometry. As a prerequisite we develop the basic notions of non-commutative Riemannian geometry, including analogues of Riemannian metric, curvature and scalar curvature. This enables us to introduce a generalized Einstein-Hilbert action for non-commutative Riemannian spaces. As an example we study a space-time which is the product of a four dimensional manifold by a two-point space, using the tools of non-commutative Riemannian geometry, and derive its generalized Einstein-Hilbert action. In the simplest situation, where the Riemannian metric is taken to be the same on the two copies of the manifold, one obtains a model of a scalar field coupled to Einstein gravity. This field is geometrically interpreted as describing the distance between the two points in the internal space.Dedicated to H. ArakiSupported in part by the Swiss National Foundation (SNF) 相似文献
19.
The isotropic oscillator on a plane is discussed where the coordinate and momentum space are both considered to be non-commutative.
We also discuss the symmetry properties of the oscillator for three separate cases when the non-commutative parameters Θ and
for x and p-space, respectively, satisfy specific relations. We compare the Landau problem with the isotropic oscillator on non-commutative
space and obtain a relation between the two non-commutative parameters and the magnetic field of the Landau problem. 相似文献
20.
The Landau problem in non-commutative quantum mechanics (NCQM) is studied.First by solving the Schr(o)dinger equations on noncommutative (NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity.Then we discuss the noncommutative phase space case,namely,space-space and momentum-momentum non-commutative case,and we get the explicit expression of the Hamfltonian as well as the corresponding eigenfunctions and eigenvalues. 相似文献