We construct a generally applicable short-time perturbative expansion for coherence loss. Successive terms of this expansion yield characteristic times for decorrelation processes involving successive powers of the Hamiltonian. The second order results are sufficient to precisely reproduce expressions for "decoherence times" obtained in the literature by much more involved and indirect methods. Examples illustrating the influence of initial conditions and the need to evaluate higher order terms are given in the context of the Jaynes-Cummings model. It is shown that, in this case, the short-time decoherence behavior can probe the importance of antiresonant contributions. [S0031-9007(96)00590-X] PACS numbers: 03.65.Db, 05.45.+bThe study of open quantum systems and/or subsystems has recently attracted the attention of physicists from very different areas: cosmology [1], condensed matter [2], quantum optics [3], particle physics [4], as well as of theorists working on the fundamentals of the quantum measurement process [5]. The problem can be stated very generally by considering several interacting subsystems and asking for the looks of the effective dynamics of one such subsystem. Generic, exact answers within the standard framework of quantum mechanics have been given before [6]. Recent experimental developments [7] as well as the analysis of models related to them [8] now indicate, however, that the specific knowledge of the (often very short) time scale for the onset of decoherence processes may be of considerable value. In order to meet such demand we develop here a short-time perturbative scheme to extract decorrelation time scales from the in general highly nonlinear effective dynamics of open quantum subsystems. Our results are generally applicable to situations in which the subsystem of interest appears as part of a larger, closed Hamiltonian system. They are based on a hierarchical analysis of the short-time dynamics of intersubsystem correlation processes which bears a strong resemblance in spirit to ordinary timedependent perturbation expansions.We consider the general case of a dynamically closed (i.e., autonomous) quantum system which is described as being composed of two interacting subsystems, so that the full Hamiltonian is written as a sum of three termsthe last of which represents the interaction between the subsystems, while H 0 describes their bare dynamics. Note that no a priori limitation is being imposed on the nature or complexity of the subsystems. In particular, all current models involving quantum systems coupled to dynamically implemented reservoirs (e.g., [9]) fit into the above characterization, the same being true all the way to 0031-9007͞96͞77(2)͞207(4)$10.00

We demonstrate that scattering of particles strongly interacting in three dimensions (3D) can be suppressed at low energies in a quasi-one dimensional (1D) confinement. The underlying mechanism is the interference of the s-and p-wave scattering contributions with large s-and p-wave 3D scattering lengths being a necessary prerequisite. This low-dimensional quantum scattering effect might be useful in "interacting" quasi-1D ultracold atomic gases, guided atom interferometry and impurity scattering in strongly confined quantum wire-based electronic devices.

A wave-packet propagation method is developed and applied to investigate the quantum dynamics of scattering processes of identical and distinguishable atoms in harmonic waveguides. The quantum dynamics of the confinement-induced resonances ͑CIRs͒ for ultracold collisions of identical particles, s-wave CIRs for bosons and p-wave CIRs for fermions, is explored in detail. Our multigrid approach allows us to fully take into account the coupling between the center-of-mass ͑c.m.͒ and relative motions in the case of distinguishable atoms. The latter includes, in particular, s-and p-partial-wave mixing, caused by the confining trap, which acts differently on the different atomic species. Specifically, we explore in detail the recently discovered ͓J. I. Kim, V. S. Melezhik, and P. Schmelcher, Phys. Rev. Lett. 97, 193203 ͑2006͔͒ dual CIR, which is based on a destructive interference mechanism leading to complete transmission in the waveguide, although the corresponding scattering in free space exhibits strong s-and p-wave scattering.

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Finite size effects alter not only the energy levels of small systems, but can also lead to new effective interactions within these systems. Here the problem of low energy quantum scattering by a spherically symmetric short range potential in the presence of a general cylindrical confinement is investigated. A Green's function formalism is developed which accounts for the full 3D nature of the scattering potential by incorporating all phase-shifts and their couplings. This quasi-1D geometry gives rise to scattering resonances and weakly localized states, whose binding energies and wavefunctions can be systematically calculated. Possible applications include e.g. impurity scattering in ballistic quasi-1D quantum wires in mesoscopic systems and in atomic matter wave guides. In the particular case of parabolic confinement, the present formalism can also be applied to pair collision processes such as two-body interactions. Weakly bound pairs and quasi-molecules induced by the confinement and having zero or higher orbital angular momentum can be predicted, such as p-and d-wave pairings.