Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach

We investigate variations of the Zitterbewegung frequency of electron due to an external static and uniform magnetic field employing the expectation value quantum approach, and compare our results with the classical model of spinning particles. We demonstrate that these two so far compatible approaches are not in agreement in the presence of an external uniform static magnetic field, in which the classical approach breaks the usual symmetry of free particles and antiparticles states, i.e. it leads to CP violation. Hence, regarding the Zitterbewegung frequency of electron, the classical approach in the presence of an external magnetic field is unlikely to correctly describe the spin of electron, while the quantum approach does, as expected. We also show that the results obtained via the expectation value are in close agreement with the quantum approach of the Heisenberg picture derived in the literature. However, the method we use is capable of being compared with the classical approach regarding the spin aspects. The classical interpretation of spin produced by the altered Zitterbewegung frequency, in the presence of an external magnetic field, are discussed.     

Magnetization and diamagnetism of a longitudinal autosoliton in <Emphasis Type="Italic">p</Emphasis>-InSb in an external longitudinal magnetic field

It has been experimentally shown that a longitudinal thermal-diffusion autosoliton, which is generated in a nonequilibrium electron–hole plasma in p-InSb, in an external longitudinal magnetic field acquires diamagnetic properties. The results of the calculation and numerical estimates of the diamagnetism have been presented.     

Effects of confinement on a magnetized ideal gas: I. The electron gas

Using the framework of the grand canonical ensemble the effects of a two (or three) dimensional confinement (harmonic) potential on the magnetic properties of an ideal electron gas are investigated. The high temperature results for the magnetic moment obtained by Felderhof and Raval are generalized to take into account the spin. At low temperature the confinement potential introduces a new oscillatory phenomena besides a modification or even a destruction of the de Haas-van Alphen effect. The changes in Landau diamagnetism are also analysed.     

Periodicity and chaos in strongly perturbed classical orbitals for Coulomb interactions

Within the framework of classical mechanics two prototypes of strongly perturbed orbitals, the diamagnetism in hydrogen and electronic double excitation, are analyzed near critical phase space points (fixed points). The motion of the hydrogen electron under the joint influence of the Coulomb field and the magnetic field is periodic for any field strengths. For a two-electron atom however we find a chaotic time evolution of the electron pair correlation, causing presumably irregular spectral patterns.     

Landau Diamagnetism,Pauli Paramagnetism,and Determination of Longitudinal and Transverse Kinetic Energy Components of a Degenerate Nonrelativistic Electron Gas

The Fermi energy, density of average kinetic energy, and average density of kinetic energy of the transverse finite motion of an electron gas of a specified concentration are calculated taking into account Landau diamagnetism and Pauli paramagnetism. The kinetic energy of a longitudinal continuous electron motion along the direction of the external magnetic field H is estimated. It is shown that the kinetic energy of the longitudinal continuous motion vanishes with increase in the external magnetic field strength in the quantum limit where the maximum Landau quantum number N _m = 0. For N _m > 0, the longitudinal kinetic energy component of a degenerate electron gas somewhat increases with magnetic field strength. The cause of the erroneous result is discussed.     

Magnetic properties of charged spin-1 Bose gases with ferromagnetic coupling

The magnetic properties of a charged spin-1 Bose gas with ferromagnetic interactions are investigated within mean-field theory. It is shown that a competition between paramagnetism, diamagnetism and ferromagnetism exists in this system. It is shown that diamagnetism, being concerned with spontaneous magnetization, cannot exceed ferromagnetism in a very weak magnetic field. The critical value of reduced ferromagnetic coupling of the paramagnetic phase to ferromagnetic phase transition [Formula: see text] increases with increasing temperature. The Landé-factor g is introduced to describe the strength of the paramagnetic effect which comes from the spin degree of freedom. The magnetization density [Formula: see text] increases monotonically with g for fixed reduced ferromagnetic coupling [Formula: see text] as [Formula: see text]. In a weak magnetic field, ferromagnetism makes an immense contribution to the magnetization density. On the other hand, at a high magnetic field, the diamagnetism tends to saturate. Evidence for condensation can be seen in the magnetization density at a weak magnetic field.     

A generalized Schrödinger formalism as a Hilbert space representation of a generalized Liouville equation

A generalized Schrödinger formalism has been presented which is obtained as a Hilbert space representation of a Liouville equation generalized to include the action as a dynamical variable, in addition to the positions and the momenta. This formalism applied to a classical mechanical system had been shown to yield a similar set of Schrödinger like equations for the classical dynamical system of charged particles in a magnetic field. The novel quantum-like predictions for this classical mechanical system have been experimentally demonstrated and the results are presented.     

An analytically solvable model of confined electrons in a magnetic field and its relation to Landau diamagnetism

Here we present analytic results for the Slater sum and the magnetic moment for arbitrary magnetic field strengths for an assembly of harmonically confined, but initially free, electrons. The relevance of the results to the generalized Landau diamagnetism of such confined electrons is emphasized.     

Korteweg-de Vries方程的准孤立子解及其在离子声波中的应用

应用推广的tanh函数展开法,给出了Korteweg-de Vries方程具有准孤立子行为的两组孤子-椭圆周期波解,其中一组为新解.推导了均匀磁化等离子体中描述离子声波动力学行为的Korteweg-de Vries方程,发现电子分布、离子电子温度比、磁场大小、磁场方向对离子声准孤立子的波形具有显著影响.     

Electronic properties of a Weyl semimetal in crossed magnetic and electric fields

The study of Weyl semimetals is one of the most challenging problems of condensed matter physics. These materials exhibit interesting properties in a magnetic field. In this work, we investigate the Landau bands and the density of states (DOS) oscillations in a Weyl semimetal in crossed magnetic and electric fields. An expression is obtained for the energy spectrum of the system using the following three different methods: an algebraic approach, a Lorentz shift-based approach, and a quasi-classical approach. It is interesting that the energy spectrum calculated in terms of the quasi-classical approach coincides with the spectrum obtained using the microscopic approaches. An electric field is shown to change the Landau bands radically. In addition, the classical motion of a three-dimensional Dirac fermion in crossed fields is studied. In the case of a Dirac spectrum, the longitudinal (with respect to magnetic field) component of momentum (p _z ∥ H) is shown to be an oscillating function of the magnetic field. When the electric field is v⊥H/c, the Landau levels collapse and the motion becomes fully linear in an unusual manner. In this case, the wavefunction of bulk states vanishes and only states with p _z = 0 are retained. An electric field affects the character of DOS oscillations. An analytical expression is obtained for the quantum capacitance in crossed fields in the cases of strong and weak electric fields. Thus, an electric field is an additional parameter for adjusting the diamagnetic properties of Weyl semimetals.     

Characteristics of electrons moving in a magnetic field at low energy levels

The motion and radiation of electrons moving in a magnetic field at low energy levels are investigated using quantum theory. An important difference between the results obtained and the equations of classical theory is established. It is shown that the radiation essentially depends on the orientation of the particle spins. The existence of a metastable excited state of the electron is revealed. Radiation in super-high fields is demonstrated.     

Motion and radiation of an electron exhibiting a vacuum magnetic moment in the field of a plane electromagnetic wave

A study is made of the motion of an electron exhibiting an anomalous magnetic moment and moving in the field of a plane circularly polarized electromagnetic wave. An exact solution is found to the generalized Dirac equation and is utilized to study the emission of electromagnetic radiation from the electron (the Compton effect). It is shown that allowance for the anomalous magnetic moment of the electron leads to: a frequency shift, a change in the total radiated power, polarization of the radiation, and to spin effects.     

Third-Order Magnetic Susceptibility of an Ideal Fermi Gas

At low temperature and under weak magnetic field, non-interacting Fermi gases reveal both Pauli paramagnetism and Landau diamagnetism, and the magnitude of the diamagnetic susceptibility is 1/3 of that of the paramagnetic one. When the temperature is finite and the magnetic field is also finite, we demonstrate that the paramagnetism and diamagnetism start to deviate from the ratio 1/3. For understanding the magnetic properties of an ideal Fermi gas at quite low temperature and under quite weak magnetic field, we work out explicitly the third-order magnetic susceptibility in three cases, from intrinsic spin, orbital motion and in total. An interesting property is in third-order magnetic susceptibilities:when viewing individually, they are both diamagnetic, but in total it is paramagnetic.     

Force law in material media,hidden momentum and quantum phases

We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The latter expression implies two novel quantum effects with non-topological phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field. These phases, in general, are not related to dynamical effects, because they are not equal to zero, when the classical force on a dipole is vanishing. The implications of the obtained results are discussed.     

Radiative damping of a relativistic electron in classical electrodynamics

An exact solution of the problem of the reaction of the field generated by a relativistic classical electron is derived. It is found that the solution differs dramatically from the known formulas by the presence of a component that is even under time reversal. It is also shown that the component of the generalized radiative damping force that is odd under time reversal coincides with the well-known relativistic damping force obtained from the approximate nonrelativistic formula via a Lorentz transformation. Zh. éksp. Teor. Fiz. 114, 1661–1671 (November 1998)     

Magnetic properties of electrons in metal-ammonia solutions

A theoretical approach is proposed to describe the concentration and temperature dependence of the static magnetic susceptibility of a metal-ammonia solution. A mechanism is also suggested to explain the transition of the system from the paramagnetic to the diamagnetic state. The theory is based on the assumption that both single-particle and two-electron bound singlet formations of the bipolar type exist in the solution. It is shown that diamagnetism is due to the electron orbital motion and to the relative motion of the quasiparticles. Zh. Tekh. Fiz. 67, 1–13 (August 1997)     

Classical origins of the Aharonov-Bohm effect

It is shown, in a large variety of manifestations, that the Aharonov—Bohm effect has classical counterparts in aspects concerning energy and momentum balance. No counterexamples are found in the cases considered, although whenever image charges shield the magnetic field region from the electric field of the passing electron the classical momentum effects, while present, would not be observable. Similarly, if the magnetic flux is maintained by superconductors, magnetic shielding will also render the classical energy effect unobservable. Partial shieldings of either type will reduce but not totally eliminate the corresponding observable classical manifestations of these effects.     

匀强磁场与简谐势阱中的低维荷电自旋-1玻色气体

采用截断求和法和半经典近似,以二维理想玻色气体为例,研究了磁场和简谐势阱中低维荷电自旋-1玻色子的相变及磁性质．结果表明,电荷-磁场和自旋-磁场作用的竞争导致玻色-爱因斯坦凝聚临界温度随磁场的增大先略微上升后缓慢下降．截断求和法能够有效的改进半经典近似的不足．最后,讨论了磁化强度由抗磁性到顺磁性的转变及自旋因子临界值随磁场和温度的变化．     

Analysis of the diamagnetic effect in multipole Galatea traps

The toroidal current emerging after the injection of a plasmoid through the magnetic shell of the Trimyx-3M (microwave) multipole trap is measured using the Rogowski loop. This current is due to diamagnetism of the plasma. The relation between the diamagnetic current and the maximal plasma pressure produced at the magnetic field separatrix is obtained. It is shown hence that magnetic measurements in a multi-pole trap for a known concentration make it possible to determine the plasma temperature in the trap and the energy confinement time.