Yu. B. Melnikov

Two‐body scattering on a graph and application to simple nanoelectronic devices

The two‐body system on a graph with one junction is considered. The effective three‐body scattering problem turns out to be exactly solvable for pointwise interactions. Additional degrees of freedom corresponding to a dynamics of some structure (e.g., an atomic cluster) located in the junction (point of common contact) of three thin electrodes are considered. These degrees of freedom bring effective energy‐dependent interaction into the effective Schrodinger equation in the scattering channel. The wave function of the system is constructed in the explicit form using the extension theory methods. The obtained results are applied to the qualitative description of a simple three‐electrode nanoelectronic device. The perturbation theory approach based on the analysis of the Liouville equation is suggested for calculation of the conductivity for such a device in terms of the obtained wave function.

Coulomb two-body problem with internal structure

Методами теории расширений с выходом из основного гильбертова пространства построена модель взаимодействия внешнего (кулоновского) и внутреннего (кваркового) каналов в задаче двух тел. Изучено взаимное влияние спектров соответствующих канальных гамильтонианов, приводящее, в частности, к перестройке спектров адронных атомов. Получено явное представление для ^-матрицы и изучены ее особенности на энергетической поверхности

Two‐body resonance scattering and annihilation of composite charged particles

A model of two‐body scattering including interaction between the external (Coulomb) and internal (e.g., quark) channels is constructed and investigated. A mathematically strict description is based on extensions theory for symmetric operators. Extra (internal) channel simulates complicated structure of charged particles and generates energy‐dependent effective interaction in the external channel. The main effects of this short‐range energy‐dependent interaction in the system of charged particles (Zel’dovich effect, appearance of resonances, relative shift formula, and so on) are studied. Both for models of zero–range and nonzero–range energy‐dependent interaction stationary scattering theory is constructed. In the frames of the same method a model of a system with extra (annihilation) scattering channel is considered.

Three-body deuteron-nucleus scattering with extra resonance channels

SummaryBy methods of dimensional reduction of 6-body problem in triangle representation, the 3-body differential dynamical equations with energy-dependent interactions describing elastic scattering and break-up in (np)4He system are constructed. The energy dependence of interactions is generated by internal structure of nucleus4He. The simple models for these energy-dependent interactions are constructed by the extended Hilbert space approach. In the frames of these models the contributions of 5-body resonances5Heg.s.,5Lig.s. and 6-body resonance6Li* (1+) into elastic scattering and deuteron break-up amplitudes for αd-reaction are investigated on the basis of modified Faddeev equations.

Generalized string‐flip model for quantum cluster scattering

The generalized string‐flip model for quantum scattering in a system of two N‐body clusters is under consideration. The extra channel interpreted as the quark compound bag is considered which generates energy‐dependent integral boundary conditions in the effective boundary problem. It is shown that the standard string‐flip model can be generalized for N identical particles in a cluster. The effective Hamiltonian and effective integral equations for the partial s‐wave S matrix are proven to be form invariant with respect to N. The effective configuration space is shown to be two‐dimensional for every N and its geometry for different N is discussed. Results of the numerical calculations of s‐wave scattering phases, inelasticity parameters, and scattering lengths for N=2 (meson–meson scattering) and N=3 (baryon–baryon scattering) are presented. The resonance influence of the extra channel is investigated. Generalizations including spin–spin interaction and quark color group SU(n) are also presented.

\bar{p}N Scattering with Annihilation Channel in an Extended Hilbert Space Model

The expressions for scattering length and partial total cross-section for \(\bar{p}n\) and \(\bar{p}p\) systems are obtained in the frame of an extended Hilbert space model with annihilation channel. A numerical algorithm for scattering data calculation is suggested. The numerical calculations for \(\bar{p}n\) and \(\bar{p}p\) scattering data at orbital momentum L = 0, 1, 2, 3 are performed on this base. The interaction parameters are fitted via two-body scattering data. A satisfactory agreement between experimental and theoretical data is obtained.

Total S-matrix and adiabatic amplitudes for the three-body problem

The three-body quantum scattering problem reduced by the expansion of the wavefunction over the specially constructed basis to a two-body problem is considered. The asymptotics of this basis, as well as the solutions of the effective two-body equations are derived. A total S-matrix for 2 → (2, 3) processes is expressed in terms of adiabatic amplitudes and vice versa.

Representation of the Three-Body S-Matrix in Terms of Effective Amplitudes

In tie triangle representation of three-body scattering problem in ℝ3, a relation between effective amplitudes and the three-body S-matrix for 2 → (2 , 3) processes is obtained.