B. K. Pal, B. Roy, B. Basu
We have studied a quantum dot with Rashba spin orbit interaction on a plane where the position and momentum coordinates are considered to be noncommutative. The energy spectrum of the system is found to be equivalent to that of a quantum dot with Rashba spin-orbit interaction in a magnetic field under certain conditions.
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Noncommutative oscillator, symmetry and Landau problem
讨论了坐标和动量空间均为非对易的平面上各向同性振子。当非对易参数Θ和\bar Θ满足特定关系时，我们还讨论了三种不同情况下振子的对称性.将Landau问题与非对易空间中的各向同性振子进行了比较，得到了Landau问题中两个非对易参数与磁场之间的关系。
In this paper we discuss a Landau levels problem within the framework of noncommutative configuration space and phase space. We show that the associated energy levels are being shifted in terms of the noncommutative parameter and can be directly obtained from its associated generalized Landau Hamiltonian. A straight forward way of constructing the shifted energy levels is just via a proper defined Bopp shift applied onto the spatial and momenta operators that are used to describe the Landau levels in symmetric gauge potential.
Anyons and the Landau problem in the noncommutative plane
非对易平面中的朗道问题在二重中心扩展平面Galilei群和任意子理论的实现的背景下进行了讨论。
Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
本文在非对易量子力学的背景下，研究了具有非零永久磁矩和电偶极矩的中性粒子在均匀电场和磁场作用下的朗道能量量子化.此外，我们还分析了在外电场和磁场作用下，磁偶极子和电偶极子的非对易量子动力学导致的Landau-Aharonov-Casher和Landau-He-McKellar-Wilkens量子化，得到了能谱和本征函数。此外，我们还分析了非对易相空间中的朗道量子化类似物，得到了它的能谱和本征函数。
The Landau problem and noncommutative quantum mechanics
探讨了非对易量子力学与朗道问题等价的条件。如果选择非对易量子力学中的势为$V= Ω\aleph$，并在文中定义了$\aleph$，那么对于${\tilde θ} = 0.22 \times 10^{-11} cm^2$值（测量空间的非对易效应），朗道问题和非对易量子力学在最低朗道能级上是等价的理论。对于其他系统，可以找到${\tilde θ}$的不同值，因此，应该在物理独立场景中搜索${\tilde θ}$的可能边界。这最后一个事实可以解释在文献中发现的$\tilde θ$的不同界限。
Wigner Functions for the Landau Problem in Noncommutative Spaces
电子在垂直于平面的均匀磁场中在平面上运动称为朗道问题。维格纳函数的朗道问题时，平面是非交换的发现采用解决方案的薛定谔方程以及解决普通 *-genvalue方程的有效哈密顿量。然后，我们假设相空间的动量和坐标是非对易的，并引入了一个广义的 *-根值方程。我们解决这个方程，找到相关的维格纳函数，并表明在适当的选择下的非交换性关系，他们是独立的非交换性参数。
Noncommutative Superspace, Supermatrix and Lowest Landau Level
利用分次（超）李代数，我们可以在曲齐性流形上构造非对易超空间。本文利用一个平坦极限得到平坦的非对易超空间。我们特别考虑了基于分次李代数$osp(1|2)$，$su(2|1)$和$psu(2|2)$的$d=2$和$d=4$超空间.超对称代数的Jacobi恒等式和星积的结合性自动满足。得到了与超对称生成元可交换的协变导数，并可施加手征约束。我们还讨论了这些非对易超空间可以理解为类似于最低朗道能级系统的约束系统。
Classes of f-Deformed Landau Operators: Nonlinear Noncommutative Coordinates from Algebraic Representations
在超空间中，我们考虑了与球谐势阱中的f-变形Landau算子类相关的非线性量子Hall极限的新的算子相关的非对易（NC）几何。利用Fock-Heisenberg张量代数和su（1，1）李代数的Schwinger-Fock实现的酉表示空间确定了不同的NC坐标代数。一个简化的模型，允许一个潜在的N=2超代数进行了讨论。
Physical Observables for Noncommutative Landau Levels
在磁场中的非对易平面上的点粒子的量子力学在本工作中被实现为定义朗道能级的代数的变形。在这种变形的量子力学中，我展示了如何在完全填充的基态能级上定义物理观测量，如密度关联函数和格林函数。此外，它将被证明，变形改变了有效的磁场，它作用在颗粒上的长距离，导致不可压缩流体的分数填充的劳克林型。
Noncommutative mechanics, Landau levels, twistors and Yang-Mills amplitudes
这些讲座分为两个不同的，虽然tenouously相关，部分。第一部分是关于模糊和非对易空间以及此类空间上的粒子力学，换句话说，非对易力学。第二部分是讨论/评论的扭转，以及它们如何可以用于计算杨米尔斯振幅。这两个主题之间的连接点，在最后一节讨论，是在实现全纯映射作为最低的朗道水平波函数，或作为波函数的希尔伯特空间用于模糊版本的两个球。这篇文章是基于在高维量子霍尔效应和非对易几何会议上的演讲，的里雅斯特，2005年3月，冬季学校现代趋势超对称力学，弗拉斯卡蒂，2005年3月和2005年5月，尤蒂卡的卡尔-罗切斯特-锡拉丘兹-多伦多会议。
Starting from the zero modes of the single and bilayer graphene Hamiltonians we develop a mechanism to construct the eigenstates and eigenenergies for Landau levels in noncommutative plane. General formulas for the spectrum of energies are deduced, for both cases, single and bilayer graphene. In both cases we find that the effect to introduce noncommutative coordinates is a shift in the energy spectrum with respect to result obtained in commutative space.
Quantum mechanics on the noncommutative plane and sphere
考虑非对易平面上粒子的量子力学。解决了带电粒子在具有谐振子势的磁场中的朗道问题。当磁场的值等于非对易性参数的倒数时，存在一个临界点，在该临界点处态密度变为无穷大。非对易双球面上的朗道问题也得到了解决，并与平面问题进行了比较。
Quaternion Landau-Ginsburg models and noncommutative Frobenius manifolds
我们将经典的Landau-Ginsburg模型推广到满足开闭拓扑场论公理的四元数Landau-Ginsburg模型。然后利用[J. Geom. Phys.，51（2003），387-403]证明了四元数Landau-Ginsburg模型的模空间是非交换的Frobenius流形.
Landau Problem in Noncommutative Quantum Mechanics
研究了非对易量子力学中的朗道问题。首先通过求解非对易（NC）空间上的Schr $\ddot{o}$ dinger方程，得到了朗道能级和由空-空非对易性引起的能量修正。然后讨论了非对易相空间情形，即空间-空间和动量-动量非对易情形，得到了哈密顿量的显式表达式以及相应的本征函数和本征值。
A (p,q)-deformed Landau problem in a spherical harmonic well: spectrum and noncommuting coordinates
本文考虑球对称调和势中Landau问题的（p，q）-变形。量子谱以及空间非对易性的建立，无论是完整的朗道问题或其量子霍尔投影。在适当的极限p，q=1下，恢复了每个朗道能级上的非对易几何。然而，在（p，q）-变形的情况下，得到了一个新的空间坐标的非交换代数，这也可能是感兴趣的凝聚态系统中的集体现象。
Landau Levels in the noncommutative $AdS_2$
我们制定的朗道问题的背景下的非交换模拟的表面的恒定负曲率，即$AdS_2$表面，并获得的频谱和对比相同的朗道水平的情况下，发现交换$AdS_2$空间。
Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
本文在锥形Gödel型时空中求解具有反常磁矩的非对易Dirac方程，得到费米子相对论与非相对论朗道能谱，并推广了文献中的若干特例。
Landau Diamagnetism in Noncommutative Space and the Nonextensive Thermodynamics of Tsallis
本文考虑电子在外部均匀磁场B中的行为，其中垂直于B的空间坐标取为非对易。这导致了标准热力学的一般化。计算磁化率，我们发现通常的朗道抗磁性被修改。我们还根据Tsallis的非广延统计量（1-q）<<1，在因式分解的方法计算的易感性。两种方法在一定条件下是一致的。
We consider a charged particle moving in a two dimensional plane in the presence of a background magnetic field perpendicular to the plane, i.e. the Landau system in a phase-space where the coordinates and momenta both follow canonical noncommutative algebra. A set of generalized transformations is derived in this paper which maps the NC problem to an equivalent commutative problem. In this set up, we study the Aharonov-Bohm effect and the Landau levels. For the Aharonov-Bohm effect, the phase-shift is found to contain corrections due to phase-space noncommutativity and also depends on the sca…
Renormalization Group Equations and the Lifshitz Point In Noncommutative Landau-Ginsburg Theory
对任意维非对易Landau-Ginsburg理论进行了单圈重整化群（RG）分析.我们采用了现代版本的威尔逊RG方法，其中壳积分在动量空间绕过潜在的红外奇异性，由于紫外-红外混合。在RG变换下，相互作用顶点中的动量相关三角因子是边缘的，并且它们的边缘性在一个循环中保持不变，这是非交换几何的特征。一个负的$Θ$依赖的反常尺寸被发现作为一个新的效应的紫外-红外混合。我们还发现了一个非交换的Wilson-Fisher（NCWF）不动点在小于四维。在大的非对易性，量子涨落引起的动量空间不稳定性，并确定了相应的一阶相变连同在相图中的Lifshitz点。在Lifshitz点附近，我们引入了两个临界指数$ν_m$和$β_k$，它们的值在平均场水平上分别被确定为1/4和1/2。
We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in $ν=1/m$(m odd) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in two-dimensional guiding center space emerges from these internal geometric modes. Using the Dirac bracket method, we find that this quantum geometric field theory is a topological non-commutative Chern-Simons theory.Topological indices, such as the guiding center angular momentum (also called the shift) and the guiding center spin, which characterize the fractional qua…
We show that (2+1) dimensional noncommutative Dirac oscillator in an external magnetic field is mapped onto the same but with reduced angular frequency in absence of magnetic field. We construct the relativistic Landau levels by solving corresponding Dirac equation in (2+1) dimensional noncommutative phase space. We observe that lowest Landau levels are exactly same as in commutative space and independent of non-commutative parameter. All the Landau levels become independent of noncommutative parameter for a critical value of the magnetic field. Several other interesting features along with th…
A study of a riveting connection between noncommutativity and the anomalous dilatation (scale) symmetry is presented for a generalized quantum Hall system due to time dilatation transformations. On using the "Peierls substitution" scheme, it is shown that noncommutativity between spatial coordinates emerges naturally at a large magnetic field limit. Thereafter, we derive a path-integral action for the corresponding noncommutative quantum system and discuss the equivalence between the considered noncommutative system and the generalized Landau problem thus rendering an effective commmutative de…
Canonical Group Quantization of Noncommutative Graphene with Symmetric and Landau Dual Magnetic Fields
本文利用正则群量子化方法研究了双重磁场下的非对易石墨烯，证明其相空间正则群等价于$\mathtt{H}^2\rtimes \mathbb{R}$，并发现对称与Landau双重规范对能谱具有相同的修正结果。
The N=1 supersymmetric invariant Landau problem is constructed and solved. By considering Landau level projections remaining non trivial under N=1 supersymmetry transformations, the algebraic structures of the N=1 supersymmetric covariant non(anti)commutative superplane analogue of the ordinary N=0 noncommutative Moyal-Voros plane are identified.
In this paper, we apply recent methods of localized GLSMs to make predictions for Gromov-Witten invariants of noncommutative resolutions, as defined by e.g. Kontsevich, and use those predictions to examine the connectivity of the SCFT moduli space. Noncommutative spaces, in the present sense, are defined by their sheaves, their B-branes. Examples of abstract CFT's whose B-branes correspond with those defining noncommutative spaces arose in examples of abelian GLSMs describing branched double covers, in which the double cover structure arises nonperturbatively. This note will examine the GLSM f…
Quantum Hall Liquid on a Noncommutative Superplane
在非对易超平面上构造了超对称量子霍尔液体。我们探讨了朗道问题的超对称形式。在最低的朗道能级上，出现了无自旋的玻色子态和自旋为1/2的下费米子态，表现出超手征性质。结果表明，Laughlin波函数和拓扑激发都有其超伙伴。讨论了超对称量子霍尔系统与双层量子霍尔系统的相似性。
Noncommutative Solitons and the W_{1+\infty} Algebras in Quantum Hall Theory
我们证明了Moyal空间中非对易场论的U（\infty）对称变换是由Landau问题中的两个W_{1+\infty}代数的组合产生的.这种无限对称性的几何意义是通过研究非对易孤子上的不变子群的变换来说明的，这些变换会产生孤子的变形和增强。特别地，我们发现在文献[22]中首次引入的孤子的提升仅在无限“theta”极限下有效。
In this thesis some systems with exotic symmetries, which are a peculiarity in 2+1 space-time dimensions, are studied. Coded in the exotic structure, there appear noncommutative coordinates and a phases structure. This kind of systems has attracted attention from different areas of physics independently. Among them, we can mention: theory of ray representations of Lie groups, anyon physics, some condensed matter systems, for instance the quantum Hall effect, planar gauge and gravitation theories, noncommutative field theory, noncommutative geometry, and noncommutative quantum mechanics. We foc…
The $\star$-value Equation and Wigner Distributions in Noncommutative Heisenberg algebras
在Weyl-Wigner-Groenewold-Moyal相空间形式下，考虑Seiberg-Witten映射的量子力学等价性，从而在非对易Heisenberg代数上建立一个量子力学.然后将该方法应用于2维非对易相空间平面上的精确可解朗道和谐振子问题，以导出它们正确的能谱和相应的维格纳分布。我们将我们的结果与以前出现在文献中的其他结果进行比较。
Super-extended noncommutative Landau problem and conformal symmetry
本文研究了非对易平面上自旋为1/2的超对称粒子在任意磁场作用下的运动，特别注意了均匀情况。根据磁场的不同，系统有三个不同的相位。由于超对称性，分离亚临界和超临界情况的边界临界相可以被看作是对零能量本征子空间的约化。在亚临界相，系统由奇异Newton-Hooke对称性的超扩展和共形的so（2，1）~ su（1，1）对称性描述，在超临界相，共形的so（2，1）~ su（1，1）对称性变为so（3）~ su（2）对称性。在临界阶段，自旋自由度被冻结，超对称性消失。
Noncommutative Landau problem in graphene: a gauge-invariant analysis with the Seiberg-Witten map
本文结合 SW 映射与 Moyal 星积建立规范不变的无质量 NC Dirac Hamiltonian，计算石墨烯 NC Landau 能谱并揭示低温自发磁化。
Quantum Mechanics on the Noncommutative Torus
分析了在恒定磁场中非对易环面上带电粒子的可观量代数。我们提出了一套发电机的代数，这符合发电机的交换环面，但在不同的值的磁场，并证明存在一个临界值的磁场的代数减少。然后，我们得到了代数的不可约表示，并将它们与非交换丛联系起来。最后对朗道能级、态密度和临界情况作了评述。
Noncommutative Quantum Mechanics: The Two-Dimensional Central Field
考虑非对易平面上的量子力学。对于一般的二维中心场，我们发现当非对易参数（$θ$）取较大值时，该理论可以微扰求解，并给出了本征态和本征值的显式表达式.格林函数是明确获得，我们表明，它可以表示为一个无穷级数。对于多项式型势，我们发现了一个光滑的极限为小值的$θ$和非多项式的这个极限必然是突然的。朗道问题，作为一个非交换系统的极限情况下，也被认为是。
Landau system in noncommutative space has been considered. To take into account the issue of gauge invariance in noncommutative space, we incorporate the Seiberg-Witten map in our analysis. Generalised Bopp-shift transformation is then used to map the noncommutative system to its commutative equivalent system. In particular we have computed the partition function of the system and from this we obtained the susceptibility of the Landau system and found that the result gets modified by the spatial noncommutative parameter $θ$. We also investigate the de Hass--van Alphen effect in noncommutative …
We consider an interacting scalar quantum field theory on noncommutative Euclidean space. We implement a family of noncommutative deformations, which -- in contrast to the well known Moyal-Weyl deformation -- lead to a theory with modified kinetic term, while all local potentials are unaffected by the deformation. We show that our models, in particular, include propagators with anisotropic scaling z=2 in the ultraviolet (UV). For a Φ^4-theory on our noncommutative space we obtain an improved UV behaviour at the one-loop level and the absence of UV/IR-mixing and of the Landau pole.
Noncommutative QED and Muon Anomalous Magnetic Moment
在非对易QED中，计算了μ子反常$g$值$a_μ=(g-2)/2$，直到单圈水平。我们认为E821实验中的相对论μ介子几乎总是处于最低朗道能级。所以μ介子的空间坐标不会相互交换。利用E821实验的参数，$B=14.5$ KG和μ子能量3.09GeV/c，我们得到了对$a_μ$的非对易性修正约为$1.57\times 10^{-9}$，这使得标准模型的预测与实验结果非常接近。
We introduce ABJM quantum field theory in the noncommutative spacetime by using the component formalism and show that it is N=6 supersymmetric. For the U(1)_κ x U(1)_{-κ} case, we compute all one-loop 1PI two and three point functions in the Landau gauge and show that they are UV finite and have well-defined commutative limits theta^{μν} -> 0, corresponding exactly to the 1PI functions of the ordinary ABJM field theory. This result also holds for all one-loop functions which are UV finite by power counting. It seems that the quantum noncommutative ABJM field theory is free from the noncommutat…
Representations of noncommutative quantum mechanics and symmetries
本文给出了用相空间变量的一般常数算符表示非对易空间上量子力学的统一方法。我们发现在任意维中存在两个相以及它们之间的对偶关系。分析了给定系统的不同表示的物理等价条件。讨论了相空间的对称性和分类。特别地，研究了物理系统的动力学对称性。最后，我们将我们的分析应用到二维谐振子和朗道问题。
Noncommutative space-time models
FRT量子欧氏空间$O_q^N$用笛卡尔生成元表示.通过压缩和解析延拓得到了N维Cayley-Klein空间的量子类似。在量子Cayley-Klein空间中引入非对易常曲率空间作为球面。当N=5时，其中的一部分被解释为（1+3）时空模型的非对易类比。结果提出了具有基本长度和基本时间的量子（反）德西特、牛顿、伽利略运动学。
In this paper, we investigated the Pauli equation in a two-dimensional noncommutative phase-space by considering a constant magnetic field perpendicular to the plane. We mapped the noncommutative problem to the equivalent commutative one through a set of two-dimensional Bopp-shift transformation. The energy spectrum and the wave function of the two-dimensional noncommutative Pauli equation are found, where the problem in question has been mapped to the Landau problem. Further, within the classical limit, we have derived the noncommutative semi-classical partition function of the two-dimensiona…
Noncommutative Geometry and Anyonic Field Theory in the Magnetic Field
考虑了一种在Minkowski空间中得到非对易时空的简单方法。这对应于在平面中引入磁场${\rm\bf B} = B \hat {\rm\bf k}$。我们在坐标空间中构造了一个包含Moyal相位因子的格林函数。简单的计算需要向最低朗道能级（LLL）投影。利用这个格林函数和第二量子化形式，我们研究了非对易几何中任意子的热力学性质。事实证明，Moyal相因子有助于热力学势$Ω$，而不是自由粒子的性质。
On Critical Phenomena in a Noncommutative Space
在本文中，我们证明了在短距离的坐标非交换性可以通过紫外-红外混合的临界现象。在对称阶段的Landau-Ginsburg模型，noncommutativity被证明会产生一个非零的异常尺寸在一个循环，并导致不稳定的一个新的阶段在大noncommutativity。特别地，在小于四维的情况下，单圈临界指数$η$在Wilson-Fisher不动点处是非零的。
Noncommutative gravity: fuzzy sphere and others
紧空间的非对易类似物上的引力可以给出普通对易引力的有限模截断。我们用有限维$(N\times N)$ -矩阵的形式得到了引力在非对易双球面和非对易${\bf CP}^2$上的作用量。讨论了交换大$N$极限。
Spherically Symmetric Noncommutative Space: d = 4
为了找到Schwarzschild或Schwarzschild-de Sitter黑洞的非对易类似物，我们在标架形式下研究了由四个非对易坐标生成的球对称空间。我们提出了两个解决方案，但不posess规定的交换限制。我们的分析表明，适当的非交换空间可能被发现作为一个高维空间的子空间。
We study the noncommutative ϕ^4_4-quantum field theory at the self-duality point. This model is renormalisable to all orders as shown in earlier work of us and does not have a Landau ghost problem. Using the Ward identity of Disertori, Gurau, Magnen and Rivasseau, we obtain from the Schwinger-Dyson equation a non-linear integral equation for the renormalised two-point function alone. The non-trivial renormalised four-point function fulfils a linear integral equation with the inhomogeneity determined by the two-point function. These integral equations are the starting point for a perturbative s…
Quantum mechanics on noncommutative Riemann surfaces
研究了在恒定磁场作用下，常曲率非对易黎曼曲面上带电粒子的量子力学。我们制定的问题，考虑量子力学上的非对易AdS_2覆盖空间和衡量一个离散的对称群，定义了一个genus-g表面。虽然覆盖空间上没有磁场量子化，但为了在黎曼曲面上具有单值态，需要量子化条件。对于非对易的AdS_2和亚临界值的磁场的频谱有一个离散的朗道水平的一部分，以及一个连续的，而超临界值，我们得到一个纯粹的非对易阶段完全由朗道水平。
We propose a bicosmology model which is the classical analog of noncommutative quantum mechanics. From this point of view the sources of the modified FRW equations are dark energy ones governed by a Chapligyn's equation state. The parameters of noncommutativity $θ$ and $B$ are interpreted in terms of the Planck area and a like-magnetic field, presumably the magnetic seed of magnetogenesis.
We study quantization of a gauge analogon of the Grosse-Wulkenhaar model: we find divergent one-loop contributions to the 1-point and 2-point Green functions. We obtain that five counterterms are necessary for renormalization and that all divergences are logarithmic.
Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
非交换Feynman图是一个带状图，它可以画在亏格$g$ 2-曲面上.本文给出了非交换Feynman图在拓扑意义下的一般收敛定理，并对标量场中的几类图给出了证明。我们提出了Bogoliubov-Parasiuk的递归减法公式的一个非交换模拟，并证明了从一类$Ω_d$减去图满足收敛定理的条件。对于$\re^d$上的一般标量非对易量子场论，类$Ω_d$小于理论中所有图的类。这就留下了非对易场论的微扰重整化问题。我们评论了超对称性如何改善这种情况，并建议Wess-Zumino模型的非对易模拟是可重整化的。
Nondecoupling phenomena in QED in a magnetic field and noncommutative QED
研究了强恒定磁场中QED的动力学性质及其与非对易QED的联系。结果表明，在最低朗道能级（LLL）占优区，费米子行列式中的U（1）规范对称性转化为非对易的$U(1)_{nc}$规范对称性.在这个区域中，有效作用量与非对易QED中的作用量密切相关，原来的U（1）规范沃德恒等式被打破（LLL反常）。另一方面，它示出，虽然在红外区域中的无限数量的更高的朗道水平的每一个的贡献被抑制，它们的累积贡献不是（非去耦现象）。这导致了红外动力学中原始U（1）规范对称性的恢复。这一现象背后的物理学反映了在这个问题中，在空间无限大的边界动力学的重要作用。
Motivated by the precision attained by SQUID devices in measuring magnetic fields, we study in this article the thermodynamic behaviour of a fermion gas in two and three dimen\-sional spatial space with noncommutative coordinates and momenta. An explicit expression, both for Landau's diamagnetism and Pauli's paramagnetism, is obtained for the magnetization and magnetic susceptibility of the gas in two and three spatial dimensions. These results show that an upper bound for the noncommutative parameter $θ\lesssim (10 \,\text{Gev})^{-2}$ could be obtained.
Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane
采用不依赖表象的方法研究非对易平面上的量子霍尔与简谐振子系统，修正了非对易空间对称规范的错误形式，得到霍尔系统谱、电导率等静态性质及非平衡动力学，还发现非对易简谐振子动力学呈准周期行为。
Noncommutative gauge symmetry in the fractional quantum Hall effect
本研究证明最低朗道能级粒子系统可耦合探测U(1)规范场实现非交换U(1)规范对称不变性，构建Seiberg-Witten型映射解决相关理论矛盾，并给出满足该对称性的有效场论构建步骤。
Noncommutative Geometry, Extended W(infty) Algebra and Grassmannian Solitons in Multicomponent Quantum Hall Systems
非对易几何支配量子霍尔（QH）效应的物理。我们引入第二量子化密度算符的Weyl序来研究最低朗道能级的电子动力学。我们分析了由整数填充因子$ν=k\leq N$的$N$组分电子组成的QH系统.基本代数是SU（N）-扩展的W $_{\infty}$。一个特殊的特征是非对易几何通过产生交换库仑相互作用导致SU（N）量子相干性的自发发展。有效哈密顿量为格拉斯曼$G_{N,k}$西格玛模型，动力学场为格拉斯曼$G_{N,k}$场，描述了$k(N-k)$复Goldstone模和一类拓扑孤子（格拉斯曼孤子）.
Landau Levels Analog to Electric Dipole
本文研究了中性粒子在外加磁场中的量子动力学。我们证明了在一个特定的场偶极子配置，我们有一个类似的朗道能级的量子化。我们研究这种量化的动机最近的分析Landau-Aharonov-Casher（LAC）量化的Ericsson和Sjöqvist[物理修订版A { \bf 65} 013607（2001）]。得到了系统的能量本征函数和本征值。
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras $sl(2,\mathbb{R})$ or $su(2)$ according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some…
A generalized algebra of noncommutative coordinates and momenta embracing non-Abelian gauge fields is proposed. Through a two-dimensional realization of this algebra for a gauge field including electromagnetic vector potential and two spin-orbit-like coupling terms, a Dirac-like Hamiltonian in noncommutative coordinates is introduced. We established the corresponding energy spectrum and from that we derived the relation between the energy level quantum number and the magnetic field at the maxima of Shubnikov-de Haas oscillations. By tuning the non-commutativity parameter θin terms of the value…
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