Electromagnetic momentum in frontiers of modern physics

We review the role of the momentum of the electromagnetic (EM) fields P _e in several areas of modern physics. P _e represents the EM interaction in equations for matter and light waves propagation. As an application of wave propagation properties, a first order optical experiment which tests the speed of light in moving rarefied gases is presented. Within a classical context, the momentum P _e appears also in proposed tests of EM interactions involving open currents and angular momentum conservation laws. Moreover, P _e is the link to the unitary vision of the quantum effects of the Aharonov-Bohm (AB) type and, for several of these effects, the strength of P _e is evaluated. These effects provide a quantum approach to evaluate the limit of the photon mass m _ph. A new effect of the AB type, together with the scalar AB effect, provides the basis for table-top experiments which yield the limit m _ph = 9.4 × 10⁻⁵²g, a value that improves the results achieved with recent classical and quantum approaches.      

Quantization of the kicked rotator with dissipation

The effect of dissipation on a quantum system exhibiting chaos in its classical limit is studied by coupling the kicked quantum rotator to a reservoir with angular momentum exchange. A master equation is derived which maps the density matrix from one kick to the subsequent one. Several limiting cases are investigated. The limits of 0 and of vanishing dissipation serve as tests of consistency, in reproducing the maps of the classical kicked damped rotator and of the kicked quantum rotator, respectively. In the limit of strong dissipation the classical map reduces to a circle map. A quantum map corresponding to the circle map is therefore obtained in this limit. In the limit of infinite dissipation the density matrix becomes independent of the initial condition after a single application of the map, allowing for a simple analytical solution for the density matrix. In the semi-classical limit the quantum map reduces to a classical map with quantum mechanically determined classical noise terms, which are evaluated. For sufficiently small dissipation the physical character of the leading quantum corrections changes. Quantum mechanical interference effects then render the Wigner distribution negative in some parts of phase space and prevent its interpretation in classical terms. Numerical results will be presented in a subsequent paper.     

Three-dimensional Wigner-function description of the quantum free-electron laser

A free-electron laser (FEL) operating in the quantum regime can provide a compact and monochromatic x-ray source. Here we present the complete quantum model for a FEL with a laser wiggler in three spatial dimensions, based on a discrete Wigner-function formalism taking into account the longitudinal momentum quantization. The model describes the complete spatial and temporal evolution of the electron and radiation beams, including diffraction, propagation, laser wiggler profile and emittance effects. The transverse motion is described in a suitable classical limit, since the typical beam emittance values are much larger than the Compton wavelength quantum limit. In this approximation we derive an equation for the Wigner function which reduces to the three-dimensional Vlasov equation in the complete classical limit. Preliminary numerical results are presented together with parameters for a possible experiment.     

Pure Bound Field theory and the Decay of Moun in Meso-Atoms

In the present paper we consider the electrically bound quantum particles within the framework of pure bound field theory (PBFT) (Kholmetskii, A.L., et al.: Phys. Scr. 82, 045301 (2010)), which explicitly takes into account the non-radiative nature of electromagnetic (EM) field generated by bound charges in the stationary energy states, and evokes the appropriate modifications of bound EM field, which secure the total momentum conservation law for the isolated system “electron plus nucleus” in the absence of EM radiation. Such a PBFT gives the same gross as well as fine structure of atomic energy levels, as those furnished by the common approach, but implies a scaling transformation of radial coordinates. In this paper we find out that in the classical limit this transformation reflects the dependence of time rate for the orbiting electron on the electric potential of the binding EM field in addition to relativistic dependence on its Lorentz factor. We show that this effect completely eliminates the available up to date discrepancy between calculated and experimental data on the decay rate of bound muon in meso-atoms. We emphasize that the revealed dependence of time rate of quantum electrically bound particles on the electric potential represents the specific effect of PBFT, and, in general, is not extended to the classical world.     

Scaling properties of resonant electron transfer in ion—metal-surface interactions

Scaling properties of resonant electron transfer in the interaction of atoms and positive ions with metal surfaces are revealed by examining the dependence of numerically calculated transition matrix elements and (first-order) transition rates upon the scaled ion-surface distance D = D/D_n, where D_n is the classical threshold distance for electron transfer involving ionic stat principal quantum number n. For zero orbital angular momentum and fixed energy of the ionic states, the n-dependence of the rates at D = 1 is found to approach, in the large-n limit, a simple power law. A scaling law is established that connects, in the range D 1, transition rates for arbitrary (large) principal quantum numbers.     

Field and intensity expectation values of quantum solitons in optical fibers

Expectation values of the field and intensity operators are evaluated for quantum solitons in the normalized fundamental soliton states with a Gaussian momentum superposition and a Poisson distribution for photon numbers. The associate quantum diffusion effects are discussed and the conditions which lead to the classical limit are identified. A numerical estimate is given using experimental data.     

Radiative reaction and quantum mechanics

According to the principles of quantum mechanics, the classical Lorentz-Dirac equations of the electron should follow from quantum electrodynamics in the classical limit. We show this is indeed true for the special case in which the charge does not radiate, provided the momentum operators in the Dirac theory are identified, in the classical limit, with the effective momenta of the Lorentz-Dirac equations.     

Limitations of the strong field approximation in ionization of the hydrogen atom by ultrashort pulses

We present a theoretical study of the ionization of hydrogen atoms as a result of the interaction with an ultrashort external electric field. Doubly-differential momentum distributions and angular momentum distributions of ejected electrons calculated in the framework of the Coulomb-Volkov and strong field approximations, as well as classical calculations are compared with the exact solution of the time dependent Schr ödinger equation. We show that in the impulsive limit, the Coulomb-Volkov distorted wave theory reproduces the exact solution. The validity of the strong field approximation is probed both classically and quantum mechanically. We found that classical mechanics describes the proper quantum momentum distributions of the ejected electrons right after a sudden momentum transfer, however pronounced the differences at latter stages that arise during the subsequent electron-nucleus interaction. Although the classical calculations reproduce the quantum momentum distributions, it fails to describe properly the angular momentum distributions, even in the limit of strong fields. The origin of this failure can be attributed to the difference between quantum and classical initial spatial distributions.     

Quantum description of free electrons in the laser

The fully quantum mechanical theory of the free electron laser is formulated in the moving frame introduced by the authors. The laser and wiggler fields are taken to be at their classical limit and quantum effects of the electron motion are considered. The Schrodinger equation is written down and solved for the unsaturated gain and momentum distribution. The results are found to be closely related to the corresponding expressions from a fully classical theory.     

Relativistic quantum correlations in bipartite fermionic states

The influences of relative motion, the size of the wave packet and the average momentum of the particles on different types of correlations present in bipartite quantum states are investigated. In particular, the dynamics of the quantum mutual information, the classical correlation and the quantum discord on the spin correlations of entangled fermions are studied. In the limit of small average momentum, regardless of the size of the wave packet and the rapidity, the classical and the quantum correlations are equally weighted. On the other hand, in the limit of large average momentum, the only correlations that exist in the system are the quantum correlations. For every value of the average momentum, the quantum correlations maximize at an optimal size of the wave packet. It is shown that after reaching a minimum value, the revival of quantum discord occurs with increasing rapidity.     

Quantum-classical correspondence of the Dirac equation with a scalar-like potential

Quantum matrix elements of the coordinate, momentum and the velocity operator for a spin-1/2 particle moving in a scalar-like potential are calculated. In the large quantum number limit, these matrix elements give classical quantities for a relativistic system with a position-dependent mass. Meanwhile, the Klein-Gordon equation for the spin-0 particle is discussed too. Though the Heisenberg equations for both the spin-0 and spin-1/2 particles are unlike the classical equations of motion, they go to the classical equations in the classical limit.      

Thomson and Compton scattering with an intense laser pulse

Our paper concerns the scattering of intense laser radiation on free electrons and it is focused on the relation between nonlinear Compton and nonlinear Thomson scattering. The analysis is performed for a laser field modeled by an ideal pulse with a finite duration, a fixed direction of propagation and indefinitely extended in the plane perpendicular to it. We derive the classical limit of the quantum spectral and angular distribution of the emitted radiation, for an arbitrary polarization of the laser pulse. We also rederive our result directly, in the framework of classical electrodynamics, obtaining, at the same time, the distribution for the emitted radiation with a well defined polarization. The results reduce to those established by Krafft et al. [Phys. Rev. E 72, 056502 (2005)] in the particular case of linear polarization of the pulse, orthogonal to the initial electron momentum. Conditions in which the differences between classical and quantum results are visible are discussed and illustrated by graphs.     

Fluctuation-induced attraction of vortices in anisotropic superconductors

We study the fluctuation-induced attraction of vortices for continuous anisotropic superconductors by using quantum statistical physics. In the low temperature or quantum limit, only the low-lying modes are relevant, the induced short-range attractive potential is proportional to (k_BT)³K₁(ΓR/λ), while in high temperature or classical limit, the induced attractive potential reduced to long-range van der Waals type k_BT/R⁴ for two vortices separated by a distance R.     

Gauge Transformation and Constraint Induced Operator Ordering for Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion of a particle is constrained, excess terms exist using hermitian form of Cartesian momentum pi （i=1, 2,3） in usual kinetic energy （1/2/μ）∑ pi^2 , and the correct kinetic energy turns out to be （1/2μ） ∑1/ fipi f ipi, where 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 with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.     

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.     

Electromagnetic momentum, magnetic model of light and effects of the Aharonov-Bohm type

The wave equation for light propagation in slowly moving media, which is analogous to that of quantum effects of the Aharonov-Bohm type, is characterized by the interaction momentum , related to the flow . In effects of the Aharonov-Bohm type the interaction momentum is related to the momentum of the electromagnetic (em) fields, that characterizes an em flow . It is shown that in both cases has the same physical origin. Calculation of the interaction em momentum for the light wave dragged by the flow yields exactly the Fresnel-Fizeau momentum. These results corroborate the validity of the magnetic model for light and highlight the role and relevance of the em momentum in new effects of classical and quantum physics. A tentative test of an astrophysical Fizeau-Aharonov-Bohm effect is discussed.     

Proposal for a chaotic ratchet using cold atoms in optical lattices

We investigate a new type of quantum ratchet which may be realized by cold atoms in a double-well optical lattice, pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate D is asymmetric in momentum up to a finite time t(r). The quantum behavior produces a corresponding asymmetry in the momentum distribution which is "frozen-in" by dynamical localization provided the break time t(*)>or=t(r). We conclude that the cold atom ratchets require Db/ variant Planck's over 2pi approximately 1, where b is a small deviation from period-one pulses.