One-magnon states and electron spin resonance in spin-ladders with singlet-rung ground statein a staggered magnetic field

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One-magnon problem for spin-ladders with exact singlet-rung ground state in arbitrary oriented constant and staggered magnetic fields is studied. For two special configurations when the both fields are parallel or perpendicular to each other the exact formulas for eigenstates and eigenvectors are presented. In the parallel case the one-magnon contribution to the ESR absorption line shape is obtained. The latter is non-Lorentzian, has finite range and a gap around resonance. For low fields both the range of the spectrum and the width of the gap are controlled by the width of the one-magnon zone in zero magnetic field. Some other interactions usually contributing to the ESR line shape are also briefly discussed.