When we calculate gravitational waveforms from extreme-mass-ratio inspirals by metric perturbation, it is a common strategy to use the adiabatic approximation. Under that approximation, we first calculate the linear metric perturbation induced by geodesics orbiting a black hole, then we calculate the adiabatic evolution of the parameters of geodesics due to the radiation reaction effect through...

Adiabatic vacua are known to be Hadamard states. We show, however that the energy-momentum tensor of a linear Klein-Gordon field on Robertson-Walker spaces developes a generic singularity on the initial hypersurface if the adiabatic vacuum is of order less than four. Therefore, adiabatic vacua are physically reasonable only if their order is at least four. A certain non-local large momentum exp...

Adiabatic vacua are known to be Hadamard states. We show, however that the energy-momentum tensor of a linear Klein-Gordon eld on Robertson-Walker spaces developes a generic singularity on the initial hypersurface if the adiabatic vacuum is of order less than four. Therefore, adiabatic vacua are physically reasonable only if their order is at least four. A certain non-local large momentum expan...

We study adiabatic charge transport in a two dimensional lattice model of electron gas at zero temperature. It is proved that if the Fermi level falls in the localization regime then, for a slowly varied weak electric field, in the adiabatic limit the accumulated excess Hall transport is correctly described by the linear response Kubo-Štreda formula. Corrections to the leading term are given in...

Numerical integrators for second-order differential equations with time-dependent high frequencies are proposed and analysed. We derive two such methods, called the adiabatic midpoint rule and the adiabatic Magnus method. The integrators are based on a transformation of the problem to adiabatic variables and an expansion technique for the oscillatory integrals. They can be used with far larger ...

We study the adiabatic charge transport in a two dimensional Landau model perturbed by a bounded potential at zero temperature. It is proved that if the Fermi level falls in a spectral gap then in the adiabatic limit the accumulated excess Hall transport is correctly described by the linear response Kubo-Štreda formula. Corrections to the leading term are given in an asymptotic series for the H...

The conventional generic model is deemed to explain the dynamics of γ-ray burst remnants very well, no matter whether they are adiabatic or highly radiative. However, we find that for adiabatic expansion, the model could not reproduce the Sedov solution in the non-relativistic phase, thus the model needs to be revised. In the present paper, a new differential equation is derived. The generic mo...

A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ) = ∑ l U (l)(τ) with U (l)(τ) being at least of the order ν. In particular U (0)(τ) corresponds to the adiabatic approximation and yields Berry’s adiabatic phase. It is sh...