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The effect of currents of mass on bending of light rays is considered in the weak field regime. Following Fermat's principle and the standard theory of gravitational lensing, we derive the gravitomagnetic correction to time delay function and deflection angle caused by a geometrically-thin lens. The cases of both rotating and shifting deflectors are discussed.

The instability of plane surface of a liquid metal in an electric field is shown to arise in arbitrarily weak field, as distinct from the well-known Tonks–Frenkel instability which takes place only in sufficiently high field. Only an account for the atomic structure of the metal leads to finite strength of the critical field which provokes the instability; however, even in this case the critical field occurs essentially less than the Tonks–Frenkel field.

It is shown that in the weak field approximation solutions of Brans-Dicke equations are simply related to the solutions of General Relativity equations for the same matter distribution. A simple method is developed which permits to obtain Brans-Dicke solutions from Einstein solutions when both theories are considered in their linearized forms. To illustrate the method some examples found in the literature are discussed., Comment: 12 pages, latex, no figures

The mean displacement moments for the strong field trapping model are calculated. Their asymptotic behaviour is 〈Xn(t)〉 ∼ (Vefft)n, where Veff is an effective drift velocity. This is in sharp contrast with the weak field case, for which 〈X n (t)〉 ∼ t n 3 . The mean survival (first passage) time and the upstream and downstream trapping probabilities are also obtained.

The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a numerical experiment up to the fiftieth order of the perturbation expansion. A simple mapping suggested by the analytic structure and the strong field behavior gives an excellent agreement with the exact value for an intermediate range of the electric field, $0.03\leq E\leq0.25$. The imaginary part of the energy (the decay width) as well as the real part of the energy is reproduced from the standard perturbation series., Comment: 14 pages, 8 figures

A general form of the gain formula for the Compton-type free-electron laser with electromagnetic fields of any polarization and field strength is presented. In the case of circularly polarized fields, the result is reduced to the Chan-Tsui formula and can also be further reduced to the Colson formula by means of the first order “weak field” approximation.

The gain formula for the free-electron laser obtained from the simple pendulum equation by means of the weak field approximation is shown to be incompatible with the experimental condition of the Stanford first free-electron laser amplifier.

Using exact formulae we prove that the weak field expansions of the thermodynamic properties of an electron gas in a uniform magnetic field at T = 0 K do not exist. This holds in both Schrodinger and Dirac theories and further for both non-interacting and interacting electron gases. We also derive a formula for the mean value of the total susceptibility 〈ξ t 〉 in the interval betweem two consecutive Landau levels.

We discuss the excitation of a two-level atom by a field of arbitrary amplitude and detuning which turns on suddenly and then decays exponentially, a scheme of current interest in subnatural linewidth spectroscopy. The strong and weak field cases are compared.

Taking the effect of a weak field on a pinned charge-density-wave as an effective pinning energy, we obtained the field-dependent excitation energy of a phase-kink soliton.

The temperature dependence of the weak field paramagnetic susceptibility in the low temperature quasi-bound state is calculated self-consistently in a model proposed by Takano and Ogawa.