Andrei A. Kvitsinsky

Adiabatic evolution of an irreversible two level system

The adiabatic dynamics of a two level atom with spontaneous decay is studied. The existence of a complex adiabatic phase shift is established: The real part being the usual Berry’s phase. A closed‐form expression for this phase and the adiabatic transition amplitudes is obtained. Incorporation of a finite preparation time for the initial state yields a new asymptotic form for the adiabatic transition amplitudes which is significantly different from the standard Landau–Zener–Dykhne formula.

Quantum three‐body scattering problem in the adiabatic hyperspherical representation

The adiabatic hyperspherical (AH) approach to the quantum three‐body problem is considered. It is proven that the AH harmonics are complete and differentiable with respect to the hyperradius for a large class of two‐body potentials. For the case of short‐range potentials, the scattering theory is studied in the framework of the AH approach. The asymptotics of the AH potential curves, harmonics, and coupling matrix elements are derived, as well as the structure of the three‐body wave operators and, the S‐matrix in the AH representation is investigated.

Adiabatic dynamics for a class of quantum Hamiltonians

We establish the existence of a special class of unitary transformations that act on the parameter space of a broad class of physical Hamiltonians (including externally imposed electromagnetic fields). For this class, we calculate the quantum amplitudes for adiabatically induced transitions. Processes described include transitions between bound states and transitions from a bound state to the continuum. The leading terms of the adiabatic limit are evaluated in closed form.

S‐matrix and Jost functions of Schrödinger Hamiltonian related to the Stark effect

The scattering theory for the Hamiltonian of the Stark effect is considered. A partial decomposition of the S‐matrix is derived corresponding to separation of variables in the parabolic coordinates, and the analytic structure of the partial Jost functions and S‐matrices are studied.

Hyperfine transitions and fusion in flight via the Faddeev approach

The Faddeev approach, modified for long-range Coulomb forces, is used to study the s-wave scattering states of the muonic atomic systems p+pµ, d+dµ, t+tµ, t+dµ and d+tµ. Elastic and hyperfine-transition cross sections of p+pµ are calculated with and without the hyperfme splitting. Fusion-in-flight reactions are studied. A sharp resonance of the rate of fusion-in-flight is observed for d+tµ atE=76.3 eV. A similar resonance-like behavior of the fusion-in-flight is also obtained in the symmetric mesic atomic collisions.

Three‐body plane wave at zero angular momentum and some addition theorems

A quantum three‐body system with zero angular momentum is considered. The plane wave F related to this problem is studied. It is proved to be a function of two variables that have a meaning of the eikonals on the internal space. A number of explicit formulas for F and its asymptotics are derived. New addition theorems for the scalar hyperspherical harmonics as well as for some special functions are obtained.

Semiclassical quantization for Coulomb systems on a hypersphere

As an approach to the highly excited states of a Coulomb three‐body system, a Schrodinger operator on a hypersphere of radius ρ, the hyperradius of the system, is considered. A corresponding spectral problem is studied in the limit ρ→∞, which is interpreted as semiclassical. For two particular models, the semiclassical quantization rules for eigenvalues along with the WKB‐type approximations for eigenfunctions are obtained. One of the models imitates a heliumlike atom in the Wannier region.