Spontaneous photon emission from a non-relativistic free charged particle in collapse models: A case study

We study the photon emission rate of a non-relativistic charged particle interacting with an external classical noise through its position. Both the particle and the electromagnetic field are quantized. Under only the dipole approximation, the equations of motion can be solved exactly for a free particle, or a particle bounded by an harmonic potential. The physical quantity we will be interested in is the spectrum of the radiation emitted by the particle, due to the interaction with the noise. We will highlight several properties of the spectrum and clarify some issues appearing in the literature, regarding the exact mathematical formula of a spectrum for a free particle.     

Radiation of a charge moving over the diffraction grating

The states of a charged particle with a finite free path are determined in the field of a resonant electromagnetic wave. The exact resonance conditions, the modulation and beam instability mechanisms, the charge and current densities (Ohm's law) are obtained for the collisionless beam of resonance particles. Quantum theory of radiation is developed for the resonant adiabatic interaction between a particle and a wave taking into account the interaction with a constant magnetic field induced at the grating surface by the charge and nonresonant waves. The radiation power, the spectrum, and the range of generated frequencies are determined. The results obtained can be used in the plasma and solid-state theories and in electronics.     

Quantum graviton creation in a model universe

Quantization in the spatially inhomogeneous, anisotropic, Gowdy three-torus solution of Einstein's equations leads to the production of gravitons from empty space. The creation of pairs of gravitons occurs only in wave modes with wavelength exceeding the horizon size at an initial time. The final number of created gravitons in any mode is proportional to the number of causally unconnected regions at the initial time over the wavelength of that mode. At large times, graviton number is well defined since the solution is in WKB form. The creation process produces the anisotropic collisionless radiation identical to that discussed by Doroshkevich, Zel'dovich, and Novikov which characterizes the large time classical solution. Near the singularity, the model behaves like an empty Bianchi Type I universe at each point in space (local Kasner). The canonical methods of Arnowitt, Deser, and Misner yield a reduced Hamiltonian from which the classical equations of motion are obtained. The quantization of the rapidly varying gravitational field component resembles the procedures used by Parker or Zel'dovich et al. to study particle creation in curved spacetime.     

Motion and radiation of a charge in a plane wave and a magnetic field

The motion and radiation of an electron moving in the field of a plane wave of elliptical polarization and a magnetic field is considered. By the methods of classical and quantum theory, the effect of the plane-wave polarization on the characteristics of the particle motion and radiation is investigated. Some particular cases are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedeniis Fizika, No. 10, pp. 70–74, October, 1978.     

Effect of the diamagnetic interaction on the intensity of the radiation lines of an atom in a magnetic field

Under the conditions of the total Paschen-Back effect the diamagnetic interaction determines the dependence of the intensity of the Zeeman components of atomic radiation lines on a magnetic field. The change in the matrix elements of the radiative transitions is due to the magnetically induced corrections to the wavefunctions of the initial and final states, whose contributions are of the same order of magnitude for the head lines of the optical series. For the high-frequency lines the positive corrections to the matrix element from the wavefunction of the upper level dominate. A magnetic field also induces dipole radiative transitions with selection rules for the orbital angular momentum | Δl| ≥ 3. The matrix elements of such transitions increase rapidly with the energy of the upper level, making possible efficient single-photon population of the dipole-inaccessible Rydberg states in moderate magnetic fields.     

Synchrotron radiation in curved space—time

Synchrotron emission by ultrarelativistic particles moving in a magnetic field in curved space-time is examined by the method of local coordinates. Generally covariant equations are obtained for the radiation spectrum in the classical and quantum cases. It is shown that the relative magnitude of the quantum corrections to the radiation spectrum increases with particle motion near the event horizon in the Kerr metric. The limit of geodesic synchrotron radiation is examined.     

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.     

Discrete accidental symmetry for a particle in a constant magnetic field on a torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the 1/r and r² potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the θ-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters θ_x and θ_y explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.     

Stochastic electrodynamics. I. On the stochastic zero-point field

This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrödinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrödinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrödinger equation has thea priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned.     

Lagrangian and Hamiltonian formalisms for relativistic dynamics of a charged particle with dipole moment

The Lagrangian and Hamiltonian formulations for the relativistic classical dynamics of a charged particle with dipole moment in the presence of an electromagnetic field are given. The differential conservation laws for the energy-momentum and angular momentum tensors of a field and particle are discussed. The Poisson brackets for basic dynamic variables, which form a closed algebra, are found. These Poisson brackets enable us to perform the canonical quantization of the Hamiltonian equations that leads to the Dirac wave equation in the case of spin 1/2. It is also shown that the classical limit of the squared Dirac equation results in equations of motion for a charged particle with dipole moment obtained from the Lagrangian formulation. The inclusion of gravitational field and non-Abelian gauge fields into the proposed formalism is discussed.Received: 4 June 2005, Published online: 27 July 2005     

正电子面沟道辐射的非线性特征

经典物理学指出,在电磁场中作加速运动的带电粒子将不断向外辐射能量.在晶体沟道中运动的带电粒子也不例外,晶格场可以使带电粒子的辐射能量达到很高.对于10MeV的正电子,辐射能量可达keV量级.粒子在沟道中的运动行为决定于粒子晶体的相互作用势,常用的相互作用势有Lindhard势、Moliere势和正弦平方势.由于粒子在沟道中的运动行为十分类似于震荡器中运动的自由电子,可望把沟道辐射改造为Χ射线激光或γ射线激光.从Lindhard势出发,将其展开到四次项,在经典力学框架内,粒子的运动方程可以化为含立方项的二阶非线性微分方程,并利用Jacobian椭圆函数和第一类全椭圆积分解析地表示了系统的解和粒子运动周期,导出了正电子面沟道辐射的瞬时辐射强度、平均辐射强度和最大辐射频率,指出了利用沟道辐射作为γ激光的可能性.     

The texture problem in Mössbauer spectroscopy

The theory of preferred orientation determination (crystallographic- or spintexture) by Mössbauer effect is presented for the case of unpolarized and polarized source radiation. The maximum information one can get out from Mössbauer measurements for the case of dipole radiation (M1) are nine expansion coefficients of the texture distribution expanded in a series of spherical harmonics. These coefficients can be obtained by a fitting procedure of the experimentally determined line intensity ratios in an absorption spectrum with rotated source and absorber. The general theory is applied for M1 radiation (Fe⁵⁷) and the cases of pure Zeeman or quadrupole splitting of source and absorber. Extension to higher multipole radiation can be easily done. Some graphs of possible textures are shown.     

Collisionless Plasma Expansion in the Presence of a Dipole Magnetic Field

The collisionless interaction of an expanding high–energy plasma cloud with a magnetized background plasma in the presence of a dipole magnetic field is examined in the framework of a 2D3V hybrid (kinetic ions and massless fluid electrons) model. The retardation of the plasma cloud and the dynamics of the perturbed electromagnetic fields and the background plasma are studied for high Alfvén–Mach numbers using the particle–in–cellmethod. It is shown that the plasma cloud expands excluding the ambient magnetic field and the background plasma to form a diamagnetic cavity which is accompanied by the generation of a collisionless shock wave. The energy exchange between the plasma cloud and the background plasma is also studied and qualitative agreement with the analytical model suggested previously is obtained (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental determination of dust-particle charge in a discharge plasma at elevated pressures

The charge of dust particles is determined experimentally in a bulk dc discharge plasma in the pressure range 20-100 Pa. The charge is obtained by two independent methods: one based on an analysis of the particle motion in a stable particle flow and another on an analysis of the transition of the flow to an unstable regime. Molecular-dynamics simulations of the particle charging for conditions similar to those of the experiment are also performed. The results of both experimental methods and the simulations demonstrate good agreement. The charge obtained is several times smaller than predicted by the collisionless orbital motion theory, and thus the results serve as an experimental indication that ion-neutral collisions significantly affect particle charging.     

Phase memory effects in probe-field spectroscopy of two-level systems at low collision frequencies

The absorption (amplification) spectrum of a weak probe field by two-level atoms located in a strong resonant laser field and colliding with buffer-gas atoms is analyzed theoretically. The analysis is performed for low collision frequencies compared to the Doppler absorption linewidth (low gas pressure) and with allowance made for an arbitrary change in the phase of the radiation-induced dipole moment at elastic collisions between gas particles. The phase memory effects have been found to lead to a strong qualitative and quantitative transformation of the probe-field spectrum even at rare collisions, when the well-known Dicke manifestation mechanism of the phase memory effects (the removal of Doppler broadening due to the restriction of the spatial particle motion by collisions) is inoperative. The strong influence of the phase memory effects on the spectral resonances at low gas pressures stems from the fact that the phase-conserving collisions change the velocity dependence of the partial refractive index n(v) (the refractive index for particles moving with velocity v).     

超晶格量子阱的沟道辐射及其谱分布

在经典物理框架内和偶极近似下, 导出了超晶格量子阱沟道辐射频率和辐射谱分布。指出了对于自发辐射谱分布, 存在一个普适的线型因子, 而粒子的最大辐射能量与相对论因子γ 有关, 且与γ3/2成正比。以正弦平方势为例进行了具体讨论。结果表明, 由于势阱深度和噪音的影响, 谐波数l只取少数几个值。超晶格量子阱沟道辐射只存在不多的几条谱线, 为进一步应用提供了可能。最后, 还给出了一种可能的实验方案, 讨论了如何利用弯晶把超晶格量子阱的沟道辐射改造为相干辐射。 In the frame of classical physics and the dipole approximation the radiation frequency and the spectral distribution are derived for the channeling radiation of a charged particle in a superlattice quantum well. It indicated that there is a line type factor f(ξ) suited to various cases in the spontaneous radiations spectrum. Results also show that the maximum radiation energy is proportional to γ3/2 , but the relativistic effects have double effects in the spontaneous radiation of a charged particle. The case for the sine squared potential is discussed specifically. The harmonic number can be defined as a few variable values by the effects of the potential well depth and noise. In general there is a few spectral lines in the channeling radiation spectrum for the superlattice quantum well, and possibilities are provided for further application. Finally, a possible experimental scheme is proposed, and it is discussed that how to transform the channeling radiation in the quantum well into the cohenent radiation by the bent crystal.     

On classical and quantum relativistic dynamics

A canonical formalism for the relativistic classical mechanics of many particles is proposed. The evolution equations for a charged particle in an electromagnetic field are obtained and the relativistic two-body problem with an invariant interaction is treated. Along the same line a quantum formalism for the spinless relativistic particle is obtained by means of imprimitivity systems according to Mackey theory. A quantum formalism for the spin-1/2 particle is constructed and a new definition of spin1/2 in relativity is proposed. An evolution equation for the spin-1/2 particle in an external electromagnetic field is given. The Bargmann Michel, and Telegdi equation follows from this formalism as a quasiclassical approximation. Finally, a new relativistic model for hydrogenlike atoms is proposed. The spectrum predicted is in agreement with Dirac's when radiative corrections have been added.     

理想腔中具有正交偶极矩的级联型三能级原子发射谱

假设原子具有两正交跃迁电偶极矩，运用全量子论研究了与单模电磁场共振相互作用的等距三能级原子的发射谱. 对不依赖于场强耦合和依赖强度耦合两种情况分别进行了发射谱的计算，并比较了原子偶极矩正交和平行条件下发射谱的异同. 结果表明，一般情况下，具有平行偶极矩的原子的发射谱谱线少于具有正交偶极矩的原子的谱线，一些谱线由于干涉而消失. 关键词： 量子光学 发射谱 电偶极矩 级联型三能级原子     

Nonlinear gain of a dipole antenna immersed in a collisionless plasma

This paper presents an investigation of the effect of collisionless plasma on the equatorial gain of a high power dipole antenna. The plasma experiences a ponderomotive force in the non-uniform radiation field and the electron density gets redistributed; the plasma gets depleted in the centre and the near equatorial zone of the antenna. This nonuniformity in the electron density (hence in the dielectric constant) tends to converge the electromagnetic power to the equatorial zone. For typical parameters a 20% (i.e., ∼1 dB) enhancement in the gain of the antenna has been predicted within the limits of the perturbation theory. Work partially supported by NSF (USA)     

Classical theory of radiation from a charge moving in a spiral

The radiation emission of a particle spiraling in a medium is investigated. The electric and magnetic field intensities are calculated, and an equation is obtained in integral form for the radiation spectrum. Two limiting cases are thoroughly analyzed: those of circular and rectilinear motion of the charge.Translated from Izvestiya VUZ. Fizika, No. 5, pp. 29–34, May, 1971.The authors wish to thank Professor A. F. Lubchenko for useful advice and discussions during the completion of this work.