Energy–momentum tensor for the electromagnetic field in a dielectric

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy–momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Rather than construct a total momentum from the Abraham momentum or the Minkowski momentum, we define a thermodynamically closed system consisting of a propagating electromagnetic field and a negligibly reflecting dielectric and we identify the Gordon momentum as the conserved total momentum by the fact that it is invariant in time. In the formalism of classical continuum electrodynamics, the Gordon momentum is therefore the unique representation of the total momentum in terms of the macroscopic electromagnetic fields and the macroscopic refractive index that characterizes the material. We also construct continuity equations for the energy and the Gordon momentum, noting that a time variable transformation is necessary to write the continuity equations in terms of the densities of conserved quantities. Finally, we use the continuity equations and the time–coordinate transformation to construct an array that has the properties of a traceless, symmetric energy–momentum tensor.     

On the conservation of momentum for a sound pulse reflecting from a pressure-release boundary

When a "massless" one-dimensional sound pulse (mass of a sound pulse is defined as an integral of the perturbation of density over the pulse length) reflects from a pressure-release boundary, its momentum changes sign. This obviously violates momentum conservation. However, in contrast to the case of an unbounded medium, calculation of the momentum in a bounded region includes a second-order term as well. Apparently, the second-order correction to the linear solution ensures momentum conservation in this case. The purpose of this Letter is to find a concrete form of this second-order correction. It appears that, as a result of the nonlinear interaction of the pulse with a pressure-release boundary, the latter experiences second-order net shift. This leads to the generation of a massive second-order rarefaction pulse whose momentum is directed opposite to the direction of propagation of the pulse itself. Appearance of this pulse ensures total momentum conservation.     

Photon momentum in a surface plasmon

It is shown that the photon momentum in a surface plasmon is ? k, where k is the plasmon wave vector. In a significantly delayed plasmon on a thin metal film or filament, the photon momentum is several hundred times larger than the momentum of a photon of the same frequency in a plane wave in free space. The plasmon-plasmon and free-space plane wave-plasmon scattering by a free electron is considered. It is shown that, in contrast to the plane wave-plane wave scattering, the electron acquires a significant momentum, while the scattered plasmon frequency significantly changes. The former process is similar to the Compton effect: scattering of X-ray and γ quanta (having a significant momentum) by an electron. In the latter process, the system composed on an incident photon and an electron at rest, which has a small total momentum, generates a photon and an electron, each having a large momentum. A device for detecting electrons from plasmons excited in nearby metal nanofilms and nanowires can be developed on the basis of this principle.     

Symmetric Surface Momentum and Centripetal Force for a Particle on a Curved Surface

The Hermitian surface momentum operator for a particle confined to a 2D curved surface spanned by orthogonal coordinates and embedded in 3D space is expressed as a symmetric expression in derivatives with respect to the surface coordinates and so is manifestly along the surface. This is an alternative form to the one reported in the literature and usually named geometric momentum, which has a term proportional to the mean curvature along the direction normal to the surface, and so"apparently"not along the surface. The symmetric form of the momentum is the sum of two symmetric Hermitian operators along the two orthogonal directions defined by the surface coordinates.The centripetal force operator for a particle on the surface of a cylinder and a sphere is calculated by taking the time derivative of the momentum and is seen to be a symmetrization of the well-known classical expressions.     

Symmetric Surface Momentum and Centripetal Force for a Particle on a Curved Surface

The Hermitian surface momentum operator for a particle confined to a 2D curved surface spanned by orthogonal coordinates and embedded in 3D space is expressed as a symmetric expression in derivatives with respect to the surface coordinates and so is manifestly along the surface. This is an alternative form to the one reported in the literature and usually named geometric momentum, which has a term proportional to the mean curvature along the direction normal to the surface, and so "apparently" not along the surface. The symmetric form of the momentum is the sum of two symmetric Hermitian operators along the two orthogonal directions defined by the surface coordinates. The centripetal force operator for a particle on the surface of a cylinder and a sphere is calculated by taking the time derivative of the momentum and is seen to be a symmetrization of the well-known classical expressions.     

Intrinsic and extrinsic nature of the orbital angular momentum of a light beam

We explain that, unlike the spin angular momentum of a light beam which is always intrinsic, the orbital angular momentum may be either extrinsic or intrinsic. Numerical calculations of both spin and orbital angular momentum are confirmed by means of experiments with particles trapped off axis in optical tweezers, where the size of the particle means it interacts with only a fraction of the beam profile. Orbital angular momentum is intrinsic only when the interaction with matter is about an axis where there is no net transverse momentum.     

Optical and sound helical structures in a Mandelstam-Brillouin mirror

It is shown theoretically that the phase conjugation of a speckle optical field in a Mandelstam-Brillouin mirror is accompanied by the excitation of helical hypersonic waves with a step equal to one-half of the optical wavelength. The excitation of these waves violates the initial isotropy of the dielectric medium. The predicted effect admits clear physical interpretation based on the angular momentum conservation. The angular momentum transfer from the light to the medium occurs in the vicinity of an optical singularity (optical vortex line) due to reversal of the light orbital angular momentum by the phase-conjugation mirror. The excitation of hypersonic waves transferring the angular momentum is the necessary condition for the reversal of the angular momentum of the reflected light.     

Dynamics of momentum distribution and structure factor in a weakly interacting Bose gas with a periodical modulation

The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated. The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated. An exact relation between the time derivatives of momentum distribution and dynamical structure factor is derived, which indicates that the single-particle property is strongly related to the two-body property in the evolutions of Bose-Einstein condensates. It is found that the momentum distribution and dynamical structure factor cannot display periodical behavior. For stable dynamics, some particular peaks in the curves of momentum distribution and dynamical structure factor appear synchronously, which is consistent with the derivative relation.     

运动三能级原子与驻波激光场斜交相互作用的理论分析

分析了一个运动的三能级原子与一个驻波激光场地斜交相互作用时的动量传递行为。结果表明，当原子和光场由于多普勒效应满足一定条件时，将产生受激拉曼跃迁。如果作用光相对于原子而言为一个“π／２脉冲”光时，那么经过作用后，原子将处于一个相干迭加态，其中一个态与加始相同。     

Energy and angular momentum transfers from an electromagnetic wave to a copper ring in the UHF band

Electromagnetic waves could carry orbital angular momentum. Such momentum can be transferred to macroscopic objects and can make them rotate under a constant torque. Based on experimental observations, we investigate the origin of orbital angular momentum and energy transfer. Due to angular momentum and energy conservation, we show that angular momentum transfer is due to the change in the sign of angular momentum upon reflection. This leads to a rotational Doppler shift of the electromagnetic wave frequency, ensuring energy conservation.     

Nucleon internal structure: a new set of quark, gluon momentum, angular momentum operators and parton distribution functions

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.     

Electromagnetic angular momentum flux tensor in a medium

Electromagnetic angular momentum describes the ability of electromagnetic field to impose torque on matter. We show that for an electromagnetic field ?C such as an optical beam field ?C in a medium, the torque density is determined by two fundamental quantities: the angular momentum flux tensor and the angular momentum density of the field. It is remarkable that the tensor alone gives the full picture of the angular momentum transfer between the field and the medium in all stationary electromagnetic phenomena. We derive a general expression for this tensor and apply the theory to several important examples without resorting to the classical paraxial approximation.     

Nonlinear momentum relaxation of an impurity in a harmonic chain

A microscopic derivation of the generalized Langevin equation for arbitrary powers of the momentum of an impurity in a harmonic chain is presented. As a direct consequence of the Gaussian character of the conditional momentum distribution function, nonlinear momentum coupling effects are absent for this system and the Langevin equation takes on a particularly simple form. The kernels which characterize the decay of higher powers of the impurity momentum depend on the ratio of the masses of the impurity and bath particles, in contrast to the situation for the momentum Langevin equation for this system. The simplicity of the harmonic chain dynamics is exploited in order to investigate several features of the relaxation, such as the factorization approximation for time-dependent correlation functions and the decay of the kinetic energy autocorrelation function.     

谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的巨涡旋态

研究谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的基态。发现凝聚体形成巨涡旋时,其涡旋个数等于平均角动量,且凝聚体密度分布和角动量密度分布相同,进而得到凝聚体形成巨涡旋时所处基态是角动量的本征态。发现势阱从各向同性的环形势阱逐渐变为各向异性的环形势阱的过程中,凝聚体的平均角动量与涡旋个数之比先由1平缓下降,然后迅速下降,最后保持在0.5附近。同时给出凝聚体密度分布和角动量分布的特征,并作出相应解释。     

Quark mixings in a subquark model

Quark mixings and theor momentum dependences are discussed in a subquark model in which the weak current is made of the iso-doublet spinor subquarks. The Cabibbo angle is predicted to become larger as momentum transfer between quarks grows up.     

电子在均匀磁场中的状态--对自旋的讨论之二

求得了在均匀磁场中的电子沿着磁场方向的动量、角动量分量和能量的共同本征态。计算了电子产生的磁矩,由此继续论证所谓的总磁矩和总角动量其实质是相对论性的轨道磁矩和轨道角动量的看法。     

The propagation of a polarized gaussian beam in a smoothly inhomogeneous isotropic medium

In the frame of the eikonal-based complex geometrical optics, which describes the phase front and cross section of a light beam using the quadratic expansion of a complex-valued eikonal, we investigate the transverse deflections of a polarized Gaussian beam (GB) in a smoothly inhomogeneous isotropic medium, which is called the spin Hall effect of the beam. The linear complex-valued eikonal terms are introduced firstly to describe the polarization-dependent transverse shifts of the beam in the inhomogeneous medium. We find that the polarization-dependent transverse shifts of the beams include two parts: one originates from the coupling between the spin angular momentum and the extrinsic orbital angular momentum due to the curve trajectory of the center of gravity of the polarized GB, and the other from the coupling between the spin angular momentum and the intrinsic orbital angular momentum due to the rotation of the beam with respect to the central ray.     

Suppressed Dispersion for a Randomly Kicked Quantum Particle in a Dirac Comb

I study a model for a massive one-dimensional particle in a singular periodic potential that is receiving kicks from a gas. The model is described by a Lindblad equation in which the Hamiltonian is a Schrödinger operator with a periodic δ-potential and the noise has a frictionless form arising in a Brownian limit. I prove that an emergent Markov process in an adiabatic limit governs the momentum distribution in the extended-zone scheme. The main result is a central limit theorem for a time integral of the momentum process, which is closely related to the particle’s position. When normalized by $t^{\frac{5}{4}}$ the integral process converges to a time-changed Brownian motion whose diffusion rate depends on the momentum process. The scaling $t^{\frac{5}{4}}$ contrasts with $t^{\frac{3}{2}}$ , which would be expected for the case of a smooth periodic potential or for a comparable classical process. The difference is a wave effect driven by momentum reflections that occur when the particle’s momentum is kicked near the half-spaced reciprocal lattice of the potential.     

Electromechanical noise in a diffusive conductor

Electrons moving in a conductor can transfer momentum to the lattice via collisions with impurities and boundaries, giving rise to a fluctuating mechanical stress tensor. The root-mean-squared momentum transfer per scattering event in a disordered metal (of dimension L greater than the mean-free path l and screening length xi) is found to be reduced below the Fermi momentum by a factor of order l/L for shear fluctuations and (xi/L)(2) for pressure fluctuations. The excitation of an elastic bending mode by the shear fluctuations is estimated to fall within current experimental sensitivity for a nanomechanical oscillator.     

Controlled generation of momentum states in a high-finesse ring cavity

A Bose-Einstein condensate in a high-finesse ring cavity scatters the photons of a pump beam into counterpropagating cavity modes, populating a bi-dimensional momentum lattice. A high-finesse ring cavity with a sub-recoil linewidth allows to control the quantized atomic motion, selecting particular discrete momentum states and generating atom-photon entanglement. The semiclassical and quantum model for the 2D collective atomic recoil lasing (CARL) are derived and the superradiant and good-cavity regimes discussed. For pump incidence perpendicular to the cavity axis, the momentum lattice is symmetrically populated. Conversely, for oblique pump incidence the motion along the two recoil directions is unbalanced and different momentum states can be populated on demand by tuning the pump frequency.