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Here we want to correct the wrong impression that no previous work on perturbation theory with two or more perturbations [1, 2] exists. Our intention was to express that the derivation of an energy splitting formula for a system with two perturbations (B x and K ) is missing. Chapter 5: Transversal magnetic field influence on integer spinsWrong expression: 1Here we want to clarify that the ratio 1has the following property: . B K Kx D = D  Equations (8) and (9) are not correct. We accidentally assumed that the ratio 1But this is not the case. Corrected version:For certain values which satisfy equation (6) and for spin quantum numbers, for which AbstractWe present a perturbative approach for the resonant tunnel splittings of an arbitrary effective single spin system. The Hamiltonian of such a system contains a uniaxial anisotropy, a transversal magnetic field and a second-order transversal anisotropy. Further, we investigate the influence of the transversal magnetic field on the energy splittings for higher integer quantum spins and we introduce an exact formula, which defines values of the transversal magnetic field, the transversal anisotropy and the uniaxial anisotropy where the contribution of the transversal magnetic field to the energy splitting is at least equal to the contribution of the transversal anisotropy.

Hereby we want to give a reply to the comment by Garg on our manuscript 'Perturbative calculations of quantum spin tunneling in effective spin systems with a transversal magnetic field and transversal anisotropy'. Within our work [1] we presented a perturbative solution for the resonant tunnel splitting energy E

Quantum mechanical objects or nano-objects have been proposed as bits for information storage. While time-averaged properties of magnetic, quantum-mechanical particles have been extensively studied experimentally and theoretically, experimental investigations of the real time evolution of magnetization in the quantum regime were not possible until recent developments in pump-probe techniques. Here we investigate the quantum dynamics of effective spin systems by means of analytical and numerical treatments. Particular attention is paid to the quantum revival time and its relation to the magnetization tunneling. The quantum revival time has been initially defined as the recurrence time of a total wave-function. Here we show that the quantum revivals of wave-functions and expectation values in spin systems may be quite different which gives rise to a more sophisticated definition of the quantum revival within the realm of experimental research. Particularly, the revival times for integer spins coincide which is not the case for half-integer spins. Furthermore, the quantum revival is found to be shortest for integer ratios between the on-site anisotropy and an external magnetic field paving the way to novel methods of anisotropy measurements. We show that the quantum tunneling of magnetization at avoided level crossing is coherent to the quantum revival time of expectation values, leading to a connection between these two fundamental properties of quantum mechanical spins.

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