Landau levels of scalar QED in time-dependent magnetic fields

The Landau levels of scalar QED undergo continuous transitions under a homogeneous, time-dependent magnetic field. We analytically formulate the Klein–Gordon equation for a charged spinless scalar as a Cauchy initial value problem in the two-component first order formalism and then put forth a measure that classifies the quantum motions into the adiabatic change, the nonadiabatic change, and the sudden change. We find the exact quantum motion and calculate the pair-production rate when the magnetic field suddenly changes as a step function.     

Fermions in interaction with time-dependent fields

We solve a two-dimensional model describing the interaction of fermions with time-dependent external fields. We work out the second quantized formulation and obtain conditions for equivalence of representations at different times. This implies the existence of sectors which describe charged states. We obtain the time dependence of charges and observe that charge differences become integer for unitary equivalent states. For scattering we require the equivalence of in- and out-representations; nevertheless charged sectors may be reached by suitable interactions and ionization is possible.     

Modulation of electromagnetic waves by time-dependent magnetic fields in a ferrite

The modulation of phase and amplitude of an electromagnetic wave in a ferrite by a longitudinal, time-dependent (sinusoidally modulated) magnetic field has been investigated. In the case of an infinite medium, an analytical expression for the amplitude envelope of the wave is obtained and it is found that the envelope differs appreciably from the sinusoidal form. In the case of a ferrite slab, the amplitude of the transmitted and the reflected components of the magnetic vector have been evaluated by an expansion method. Numerical calculations indicate, as expected, that for a uniform plane wave incident on a ferrite sheet of finite thickness, the transmitted beam is strongly amplitude modulated.     

Matter-wave solutions of Bose—Einstein condensates with three-body interaction in linear magnetic and time-dependent laser fields

We construct, through a further extension of the tanh-function method, the matter-wave solutions of Bose-Einstein condensates (BECs) with a three-body interaction. The BECs are trapped in a potential comprising the linear magnetic and the time-dependent laser fields. The exact solutions obtained include soliton solutions, such as kink and antikink as well as bright, dark, multisolitonic modulated waves. We realize that the motion and the shape of the solitary wave can be manipulated by controlling the strengths of the fields.     

Measuring magnetic fields in plasmas by means of light scattering

The theory of light scattering in plasmas containing a magnetic field yields the special case of modulated scattering spectra. The modulation frequency is governed by the field in the plasma and is equal to the electron cyclotron frequency. In this investigation magnetic fields in a plasma were determined by a laser scattering experiment. The experimental data were: electron densityn _e=10¹⁶cm^?3, electron temperatureT _e=3.2 eV, scattering angle θ=90 °, scattering parameter α=0.6, and a maximum field in the plasma of 125 kG. The spectrum measured at the maximum magnetic field was modulated with 3.6 × 10¹¹ Hz. In scattering experiments with a field reduced by about 20% the observed modulation frequency was 2.8 × 10¹¹ Hz. A thermal spectrum with a smooth profile was found when no field was present in the plasma. Applying the theory of cyclotron modulated spectra one obtains from the scattering experiment magnetic fields of 128, 100, and 0 kG. Within the experimental accuracy these values agree well with the fields determined by means of magnetic probes. Other possible interpretations of the measured deviations from thermal spectra (modulation with the plasma frequency or additional cold electron components in the plasma) are discussed, but they afford no explanation. This experiment has domonstrated that magnetic fields in plasmas can be measured locally and almost without disturbance by means of light scattering.     

Static potential renormalization in time-dependent fields

We consider the scattering of electrons at a static potential under the influence of an additional time-dependent, homogeneous electric field (‘microwave’). Starting from a plane wave basis, we derive a generalization of the Born (first) order approximation in arbitrary strong oscillating fields. As an example, we evaluate the Friedel density oscillations around a static scatterer whose potential is renormalized by the microwave. The microwave leads to a band of inelastic scattering channels with effective potentials, the shape of which can be ‘tuned’ by the microwave polarization and strength.     

Pair production in time-dependent electric fields

The particle production problem in a general time-dependent electric field is formulated by path integrals. The creation of charged scalar particles and electron-positron pairs is studied in detail for an exponentially decaying electric field. Some other exactly solvable cases are also considered.     

有弱偏置磁场及含时激光场中的非线性Gross-Pitaevskii方程新的精确解

利用映射方法和一个适当的变换，得到大量的有弱偏置磁场及含时激光场中的非线性Gross-Pitaevskii方程的新解，这些解包括椭圆函数解，椭圆函数叠加解，三角函数解，亮孤子解，暗孤子解和类孤子解。     

On the possibility of measuring magnetic fields by scattered light

In the following paper we discuss the possibility of measuring magnetic fields by scattered light. In the case of uncorrelated electrons (i.e. α ?1) the electron spectrum is modulated with the electron gyration frequency if a certain condition is fulfilled. The essential parameters are discussed and some spectra are computed numerically.     

Coherent light scattering from ruby dressed with rf photons

We observed a new kind of coherent light scattering from ruby subjected to an rf Stark field and explained it in terms of rf photon dressing. The theory is also applied to explain the sublevel coherence generation by an rf Stark field in the coherent Raman beat spectroscopy.     

Effect of periodically time-dependent magnetic fields on a population of spin states of radical pairs

The time dependences for a population of radical pair spin states and the amplitudes of the transitions between them are calculated for magnetic fields of complex configuration. The abovementioned values are derived directly from the solution to the Liouville equation for the components of a spin density matrix for a radical pair. The oscillating mechanism of the relaxation of partial populations of spin levels upon the monotonous reduction of the full population was established in the course of our calculations.     

Tuning the flow of light in semiconductor-based photonic crystals by magnetic fields

Tuning the flow of light by external fields is a challenging task for scientific studies and optical applications, but it is important in many applications such as switches, modulators, and slow wave structures. Here, new results are presented which demonstrate that this effectively can be achieved by external magnetic fields in one-dimensional photonic crystals made from semiconducting material. The advantage of using semiconducting material is the magnetic-field dependent dielectric function of the free charge carriers particularly where the magnetic field causes large and strongly varying contributions – near the plasma frequency and the cyclotron resonance frequency. The results of simulations on the basis of a multiple scattering method at infrared and microwave frequencies and of experiments on Indium Antimonide in the latter frequency regime confirm the tunability up to the extreme case from full transparency to opaqueness and vice versa.     

Impact of spin-zero particle-photon interactions on light polarization in external magnetic fields

If the recent PVLAS results on polarization changes of a linearly polarized laser beam passing through a magnetic field are interpreted by an axion-like particle, it is almost certain that it is not a standard QCD axion. Considering this, we study the general effective interactions of photons with spin-zero particles without restricting the latter to be a pseudo-scalar or a scalar, i.e., a parity eigenstate. At the lowest order in effective field theory, there are two dimension-5 interactions, each of which has previously been treated separately for a pseudo-scalar or a scalar particle. By following the evolution in an external magnetic field of the system of spin-zero particles and photons, we compute the changes in light polarization and the transition probability for two experimental set-ups: one-way propagation and round-trip propagation. While the first may be relevant for astrophysical sources of spin-zero particles, the second applies to laboratory optical experiments like PVLAS. In the one-way propagation, interesting phenomena can occur for special configurations of polarization where, for instance, transition occurs but light polarization does not change. For the round-trip propagation, however, the standard results of polarization changes for a pseudoscalar or a scalar are only modified by a factor that depends on the relative strength of the two interactions.     

The influence of time-dependent electric and magnetic fields on the dynamic localization of lattice electrons

In this paper we deal with the derivation of dynamic localization conditions for electrons on the one-dimensional (1D) lattice under the influence of ac electric and magnetic fields of the same frequency. We resort, for convenience, to a tight-binding single-band Hamiltonian. Our emphasis is on a more fundamental theoretical understanding by investigating interplays between such fields and the nearest-neighbor hopping interactions characterizing the Hamiltonian. In general, such conditions get expressed in terms of infinite sums of binary products of Bessel functions of the first kind. These sums are hardly tractable, but we found that selecting in a suitable manner the phases of time-dependent modulations leads to controllable frequency-mixing effects providing appreciable simplifications. Such mixings concern competitions between the number of flux quanta and the quotients of field amplitudes and field frequencies. More exactly, tuning one of the mixed frequencies to zero opens the way to establishing the simplified dynamic localization conditions. By resorting again to the zeros of the Bessel function of zeroth order. This results in quickly tractable relationships between the amplitudes of electric and magnetic fields, the field frequency, and the zeros referred to just above. Pure field limits and superpositions between uniform electric and time-dependent magnetic fields are also discussed. Comments concerning the role of disorder and of the Coulomb interaction are also made.     

First passage time problems in time-dependent fields

This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency * for which the mean residence time on the line segment is a minimum. It is shown that for a random walk on a line segment of lengthL the mean residence time goes likeL ² for largeL when *, but when =* the dependence is proportional toL. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation.     

Multiphonon absorption of light in quantum-well systems in uniform electric and magnetic fields

The effect of a transverse electric field on the multiphonon absorption of light in quantum-well systems in a uniform magnetic field aligned parallel to the spatial quantization axis is investigated. It is shown that, when the interaction of an electron with long-wavelength vibrations is taken into account, the half-width of the absorption line does not depend on the electric-field vector E. As the electric field strength increases, the maximum of the light absorption shifts toward the long-wavelength range and decreases. The effect of the electric field on the shape of the zero-phonon line and first vibrational satellites is analyzed with due regard for the interaction of charge carriers with optical phonons. It is demonstrated in particular that the half-width of the zero-phonon line substantially depends on the electric-field vector E and can reach several millielectron-volts at the electric field strength E = 2 × 10⁴ V/cm.     

Electron-positron pair production by photons in nonuniform strong fields

A probability of electron-positron pair production by photons in strong nonuniform fields is derived by applying a model trajectory method in the frame of a semiclassical approach. In addition to the well known invariant field parameter chi, a new invariant parameter nu is introduced to characterize the nonuniformity of the field. For nu>1, the obtained expression is reduced to the uniform-field approximation while it approaches the Bethe-Heitler formula for nu<1. The pair production is predicted for relatively weak external fields where the uniform-field approximation gives no effect. The theory agrees well with the experimental results of crystal-assisted pair production.