Constraints in Noncommutative Chern-Simons Mechanics and Hall Effect

We study noncommutative Chern-Simons mechanics and noncommutative Hall effect by Dirac theory in this paper. The magnetic field is introduced by means of minimal coupling. We show that the constraint set will enlarge when a dimensionless parameter takes zero value. In order to illustrate our idea, we study two specific models. One is noncommutative Chern-Simons mechanics which describes a charged particle on a noncommutative plane interacting with a perpendicular uniform magnetic field. The other is a charged particle on a noncommutative plane with a background uniform electromagnetic field. We show that when the dimensionless parameter tends to zero, the particle will live in a lower dimensional space in both models. Noncommutative Chern-Simons mechanics will reduce to a harmonic oscillator and the classical equations of motion of a charged particle in the background of a uniform electromagnetic field are governed by classical Hall law when the dimensionless parameter tends to zero.     

Klein-Gordon Oscillator in Noncommutative Phase Space Under a Uniform Magnetic Field

Using a direct substitution method, Klein-Gordon oscillator in a uniform magnetic field is researched in the noncommutative phase space (NCPS), the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric. It is shown that the Klein-Gordon oscillator in uniform magnetic field in noncommutative phase space has the similar behaviors to the Landau problem in commutative space. In addition, the non-relativistic limit of the energy spectrum is obtained.     

The Schrödinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

We investigate the non-relativistic Schrödinger and Pauli-Dirac oscillators in noncommutative phase space using the five-dimensional Galilean covariant framework. The Schrödinger oscillator presented the correct energy spectrum whose non isotropy is caused by the noncommutativity with an expected similarity between this system and the particle in a magnetic field. A general Hamiltonian for the 3-dimensional Galilean covariant Pauli-Dirac oscillator was obtained and it presents the usual terms that appears in commutative space, like Zeeman effect and spin-orbit terms. We find that the Hamiltonian also possesses terms involving the noncommutative parameters that are related to a type of magnetic moment and an electric dipole moment.     

A new limit for the noncommutative space–time parameter

The spectrum of the hydrogen atom in the framework of noncommutative quantum mechanics is studied and the related phenomenology is presented. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in the atom. To the first order in the noncommutative parameter, it is equivalent to an electron in the fields of a Coulomb potential and an electric dipole and this allows us to get a bound for this parameter. In a second step, we compute noncommutative corrections of the energy levels and find that they are at the second order in the parameter of noncommutativity. By comparing our results to those obtained from experimental spectroscopy, we get another limit for this parameter.     

Noncommutativity effects in FRW scalar field cosmology

We study effects of noncommutativity on the phase space generated by a non-minimal scalar field which is conformally coupled to the background curvature in an isotropic and homogeneous FRW cosmology. These effects are considered in two cases, when the potential of scalar field has zero and nonzero constant values. The investigation is carried out by means of a comparative detailed analysis of mathematical features of the evolution of universe and the most probable universe wave functions in classically commutative and noncommutative frames and quantum counterparts. The influence of noncommutativity is explored by the two noncommutative parameters of space and momentum sectors with a relative focus on the role of the noncommutative parameter of momentum sector. The solutions are presented with some of their numerical diagrams, in the commutative and noncommutative scenarios, and their properties are compared. We find that impose of noncommutativity in the momentum sector causes more ability in tuning time solutions of variables in classical level, and has more probable states of universe in quantum level. We also demonstrate that special solutions in classical and allowed wave functions in quantum models impose bounds on the values of noncommutative parameters.     

Anisotropy and Magnetic Field Effects on Entanglement of a Two-Spin (1/2,1) Mixed-Spin Heisenberg XY Chain

We study the entanglement in anisotropic (1/2,1) mixed-spin Heisenberg XY model under the presence of an external magnetic field at thermal equilibrium. By adjusting the anisotropic parameter and the magnetic field, one is able to obtain entanglement at higher temperature. We find the evidence of the quantum phase transition in the model and observe that the quantum phase transition point at low temperature moves toward weak magnetic field with the increase of the anisotropic parameter.     

Quantum speed limit for a three-qubit system in spin-chain environment with multisite interaction

We study the relationship between the quantum speed limit (QSL) time of a three-qubit system, and the quantum phase transitions (QPTs) of a spin-chain environment with the three-spin interaction. We find that the three-spin interaction can effectively manipulate the critical value of the QSL time. It makes the QSL time mark more clearly the quantum phase transition of the one-dimensional spin-chain models, especially the XX model. The dynamical evolution of the QSL time presents a periodic behavior in quantum-critical environment, whereas the three-spin interaction and external magnetic field can destroy this periodicity.     

Induced modification of the geometric phase of a qubit coupled to an XY spin chain by Dzyaloshinsky-Moriya interaction

We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya(DM) interaction in the presence of a transverse magnetic field.An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit.We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.     

Decoherence of quantum Brownian motion in noncommutative space

The decoherence of a harmonic oscillator under two-dimensional quantum Brownian motion on a noncommutative plane is investigated. The interaction with the environment is considered by two separate models so-called coupled and uncoupled. The two-dimensional master equation and its noncommutative counterpart are derived for both employed models. The rate of the linear entropy (predictability sieve) is chosen as a criterion to investigate the purity in the presence of the space noncommutativity. Besides, a two-dimensional charged harmonic oscillator on a plane which is imposed by a perpendicular magnetic field is introduced as a realization of our model. Therefore, our approach provides a formalism to investigate the influence of the magnetic field on the decoherence of the pure states. We show that in the high magnetic field limit the rate of the decoherence will be decreased.     

Spectroscopy of nanoscopic semiconductor rings

Making use of self-assembly techniques, we realize nanoscopic semiconductor quantum rings in which the electronic states are in the true quantum limit. We employ two complementary spectroscopic techniques to investigate both the ground states and the excitations of these rings. Applying a magnetic field perpendicular to the plane of the rings, we find that, when approximately one flux quantum threads the interior of each ring, a change in the ground state from angular momentum l = 0 to l = -1 takes place. This ground state transition is revealed both by a drastic modification of the excitation spectrum and by a change in the magnetic-field dispersion of the single-electron charging energy.     

Exact master equation for a noncommutative Brownian particle

We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.     

Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels

We have studied a quantum dot with Rashba spin-orbit interaction in noncommutative phase space. The energy eigenvalues are analogous to Landau energy levels. It is shown that this system is related with a physically realizable model of a quantum dot with Rashba spin-orbit interaction in a magnetic field whereby a relation is derived among the noncommutative parameters, spin-orbit coupling strength and magnetic field.     

Induced modification of geometric phase of a qubit coupled to an XY spin chain by the Dzyaloshinsky–Moriya interaction

We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya (DM) interaction in the presence of a transverse magnetic field. An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit. We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by the DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.     

On the Chirality Quantum Phase Transition of the Dirac Oscillator

Dirac oscillator subjects to an external magnetic field is re-examined. We show that this model can be mapped onto different quantum optics models if one insists to introduce two kinds of phonons which associate with the excitations of Dirac oscillator and magnetic field respectively. The conclusion about chirality quantum phase transition in the paper “Chirality quantum phase transition in the Dirac oscillator” (Bermudez et al. Phys. Rev. A, 77, 063815 2008) is only valid for a specific mapped quantum optics models rather than the Dirac oscillator itself. Thus, the conclusions about chirality quantum phase transitions in this paper are not universal.     

非对易相空间中谐振子体系热力学性质的探讨

2000年以来, 有关非对易空间的各种物理问题一直是研究的热点, 并在量子力学、场论、凝聚态物理、天体物理等各领域中已被广泛地探讨. 采用统计物理方法讨论非对易效应对谐振子体系热力学性质的影响. 先以对易相空间中确定二维和三维谐振子的配分函数求出谐振子体系的热力学函数; 非对易相空间中的坐标和动量通过坐标-坐标和动量-动量之间的线性变换而以对易相空间中的坐标和动量来表示; 最终以非对易相空间中求出配分函数来讨论非对易效应对谐振子体系热力学性质的影响. 结果显示, 在非对易相空间中谐振子体系的配分函数和熵表达式均包含因非对易引起的修正项. 从分析结果得出如下结论: 非对易效应对谐振子的配分函数和熵函数等微观状态函数有一定的影响, 但对谐振子体系的内能、热容量等宏观热力学函数没有影响. 研究结果只是对应于满足玻尔兹曼统计的经典体系, 对于满足费米-狄拉克和玻色-爱因斯坦统计的量子体系需进一步推广研究.     

Non-commutative harmonic oscillator in magnetic field and continuous limit

The spectra of a charged harmonic oscillator minimally coupled to a perpendicular magnetic field in the non-commutative plane are studied by using the path integral formulation. We get the spectra in a mapping-independent way. Interestingly, we find that the spectra have no continuous limit when the dimensionless parameter tends to zero. In order to get a finite result, a truncation is inevitable. Finally, we give a reasonable explanation of truncation from the constrained theory point of view.     

Quantum Phase for an Electric Multipole Moment in Noncommutative Quantum Mechanics

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric multipole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations, we obtain quantum phases of the electric multipole moment both on a noncommutative space and a noncommutative phase space. We demonstrate that these phase are geometric and dispersive.     

Stability of the spontaneous quantum Hall state in the triangular Kondo-lattice model

We study the behavior of the quarter-filled Kondo-lattice model on a triangular lattice by combining a zero-temperature variational approach and finite-temperature Monte Carlo simulations. For intermediate coupling between itinerant electrons and classical moments S(j), we find a thermodynamic phase transition into an exotic spin ordering with uniform scalar spin chirality and (S(j))=0. The state exhibits a spontaneous quantum Hall effect. We also study how its properties are affected by the application of an external magnetic field.     

Quantum phase for an electric quadrupole moment in noncommutative quantum mechanics

We study the noncoInmutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by intro ducing a shift for the magnetic field, we give the Schrodinger equations in the presence of an external magnetic field both on a noncommutative space and a noncomlnutative phase space, respectively. Then by solving the SchrSdinger equations both on a noneommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. Wc demonstrate that these phases are geometric and dispersive.