均匀恒定磁场中带电狄拉克粒子的超对称性和本征能谱

基于狄拉克方程中γ矩阵有结构、可分解的观点, 把γ矩阵分解为自旋空间和正反粒子空间的算子的直积, 确定了均匀恒定磁场中带电狄拉克粒子的哈密顿量的动力学超对称性和可互易的完备的物理量算子集及其量子数集, 求得了用上述量子数完全集标志的该哈密顿量的解析的本征解,讨论了系统的哈密顿H的动力学超对称性中自旋对称性和正反粒子对称性破缺的不同情况,确定了自旋剩余超对称性导致的自旋简并子空间的超对称性变换群算子.     

Dirac Particle Polarization in Uniform Magnetic Field

For Dirac particles in a uniform magnetic field, the polarization operator projections onto three directions remain unchanged. If the orbital angular moment of particles is large with respect to 1, then the spin of moving particles retain the fixed orientation relative to the axes of the cylindrical coordinate system.     

States of a Charged Particle with a Tensor-Like Mass in External Constant Magnetic Field

Abstract

Solutions of the Schrödinger equation for a particle with a tensor-like mass are considered. It is shown that the problem of determination of the coherent states in this case is reduced to integration of the nonlinear system of ordinary differential equations.     

Gravitational Waves Interacting with a Spinning Charged Particle in the Presence of a Uniform Magnetic Field

The equations which determine the response of a spinning charged particle moving in a uniform magnetic field to an incident gravitational wave are derived in the linearized approximation to general relativity. We verify that 1) the components of the 4-momentum, 4-velocity and the components of the spinning tensor, both electric and magnetic moments, exhibit resonances and 2) the co-existence of the uniform magnetic field and the GW are responsible for the resonances appearing in our equations. In the absence of the GW, the magnetic field and the components of the spin tensor decouple and the magnetic resonances disappear.     

Scalar Charged Particle in Weyl–Wigner–Moyal Phase Space. Constant Magnetic Field

A relativistic phase-space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables) is proposed. We take into account the nontrivial charge structure of the position and momentum operators. The evolution equation coincides with its analog in relativistic quantum mechanics with nonlocal Hamiltonian under conditions where particle-pair creation does not take place (free particle and constant magnetic field). The differences in the equations are connected with the peculiarities of the constraints on the initial conditions. An effective increase in coherence between eigenstates of the Hamiltonian is found and possibilities of its experimental observation are discussed.     

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schrödinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schrödinger equation and some special and limiting cases are outlined.     

Thermodynamics of the System of Massive Dirac Fermions in a Uniform Magnetic Field

We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels,through which all thermodynamic quantities can be obtained.Making use of the Abel-Plana formula,these thermodynamic quantities can be expanded as power series with respect to the dimensionless variable b=2eB/T~2.The zero-field magnetic susceptibility is expanded at zero mass,and the leading order term is logarithmic.We also calculate scalar,vector current,axial vector current and energy-momentum tensor of the system through ensemble average approach.Mass correction to chiral separation effect is discussed.For massless chiral fermions,our results recover the chiral magnetic effect for right-and left-handed fermions,as well as chiral separation effect.     

Two Charged Particles in the Plane Under a Constant Perpendicular Magnetic Field

We show that a system with two particles of equal masses and opposite electric charge on a plane subject to a constant magnetic field perpendicular to this plane is a completely integrable system. In the classical case, the separation of variables can be performed in oblate coordinates. In the quantum case, we obtain two independent Hill equations of fourth order. Some approximations lead to Mathieu equations, for which the solutions are well known.     

Two-Point Fermionic Correlators in External Constant Uniform Magnetic Field

The results of calculation of two-point correlation functions of fermionic currents in a constant uniform magnetic field are presented. The off-diagonal correlation functions including the tensor current (namely, the scalar-tensor and pseudoscalar-tensor) are calculated in addition to the correlators of scalar, pseudoscalar, vector, and axial-vector fermionic currents. The tensor fermionic current is a part of the Pauli term in the Lagrangian, which is responsible for the electromagnetic interaction of the fermion through an anomalous magnetic moment. In particular, if we take this interaction into account, we modify the frequency of axion-photon oscillations. In the future, it is planned to investigate this feature in details.     

Perturbations of the Motion of a Charged Particle in a Noisy Magnetic Field

We consider deterministic and stochastic perturbations of the motion of a charged particle in a noisy magnetic field. The noise in the magnetic field leads to the mixing on the energy surfaces and allows to apply averaging principle. We describe long-time energy evolution and its metastable states for a given initial energy and a time scale.     

Thermodynamics of a Charged Particle in a Noncommutative Plane in a Background Magnetic Field

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 space and observe that the oscillation of the magnetization and the susceptibility gets noncommutative corrections. Interestingly, the susceptibility in the noncommutative scenario is non-zero in the range of the magnetic field greater than the threshold value which is in contrast to its commutative counterpart. The results obtained are valid upto all orders in the noncommutative parameter θ.     

About the Gravitational Field and the Gravitational Energy of a Charged Particle with Field Mass

Russian Physics Journal -     

A Secondary Operator Ordering Problem for a Charged Rigid PlanarRotator in Uniform Magnetic Field

When the motion of a particle is constrained, an excess term exists using hermitian form of Cartesian momentum pi(i= 1, 2, 3) in usual kinetic energy (1/2μ)∑Pi^2, and the correct kinetic energy turns out to be (1/2μ)∑(1/fi)pifipi, where the fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions f i is given for a charged rigid planar rotator in the uniform magnetic fieM.     

电磁场中带电粒子在非对易相空间的能级

非对易空间效应是出现在弦的尺度下的一种物理效应。 首先扼要介绍了非对易相空间中的量子力学代数、 Moyal Weyl乘法和广义Bopp变换, 然后讨论了电磁场中带电粒子的Hamiltonian算符, 最后给出了其在非对易相空间中的能级情况。     

带电粒子在匀强磁场中做匀速圆周运动的单元教学思路与框架

立足于大概念教学理念,以培养学生的核心素养为目标,通过分析带电粒子在匀强磁场中做匀速圆周运动的规律,结合高考对这部分内容的考查特点,总结了带电粒子在匀强磁场中做匀速圆周运动的模型构建思路,绘制了以"弦"为分析问题核心和以"半径"为解决问题核心的框架,解决了带电粒子在匀强磁场中运动教学结构分散问题.用几道典型的题例证了用...     

Squeezing of Relative and Center-of-Orbit Coordinates of a Charged Particle by Step-Wise Variations of a Uniform Magnetic Field with an Arbitrary Linear Vector Potential

We consider a quantum charged particle moving in the xy plane under the action of a time-dependent magnetic field described by means of the linear vector potential A = H(t) [?y(1 + β), x(1 ? β)] /2 with a fixed parameter β. The systems with different values of β are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are ellipses for |β| < 1 and hyperbolas for |β| > 1. Using the approximation of the stepwise variation of the magnetic field H(t), we obtain explicit formulas describing the evolution of the principal squeezing in two pairs of noncommuting observables: the coordinates of the center of orbit and relative coordinates with respect to this center. Analysis of these formulas shows that no squeezing can arise for the circular gauge (β = 0). On the other hand, for any nonzero value of β, one can find the regimes of excitations resulting in some degree of squeezing in the both pairs. The maximum degree of squeezing can be obtained for the Landau gauge (|β| = 1) if the magnetic field is switched off and returns to the initial value after some time T, in the limit T → ∞.     

A Secondary Operator Ordering Problem for a Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion of a particle is constrained, an excess term exists using hermitian form of Cartesian momentum pi (i = 1, 2, 3) in usual kinetic energy (1/2μ)∑p2i, and the correct kinetic energy turns out to be (1/2μ) ∑(1/ fi)pifipi, where the fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field.