Electron self-trapping on a nano-circle

We study the self-trapping of quasiparticles (electrons, holes, excitons, etc) in a molecular chain with the structure of a ring, taking into account the electron-phonon interaction and the radial and tangential deformations of the chain. A discrete system of equations is obtained and solved numerically. The analytical solutions for the wave function of a quasiparticle and for the molecule displacements that determine the distortion of the ring, are also obtained and solved in the continuum approximation. The numerical solutions of the system of discrete nonlinear equations reveals several regimes of quasiparticle localisation in the chain which depend on the values of the parameters of the system. It is shown that the transversal deformation of the chain favours the formation of a soliton.Comment: 43 pages 9 figure

On the theory of the Schrödinger equation with the full set of relativistic corrections

All relativistic corrections to the Scrödinger equation which determine the interlink between spin and orbit of moving particles, are directly calculated from the Dirac equation using the spin invariant operators. It is shown that among the second order corrections there are not only the well-known Darwin and Thomas terms, but also the new ones. Only with the account of the latter corrections the energies found with the obtained spin-orbit interaction operator, coincide with the energies of the Dirac equation exact solution. The problem of electron spectrum in the quantum well type structures is studied in details and the physical reasons for the appearance of spin-orbit interaction operators in the Dresselhaus or Rashba form, are analyzed

Ratchet behaviour of polarons in molecular chains

We study the ratchet behaviour of polarons in diatomic molecular chains under the influence of an external electromagnetic field which is periodic in time. We show that in asymmetric chains a harmonic unbiased field causes a drift of polarons. This phenomenon has a threshold with respect to the intensity and the frequency of the field. In spatially symmetric chains a harmonic periodic electric field generates oscillations of polarons but does not result in their movement. The polaron drift current can be induced in symmetric chains by a time periodic asymmetric external field. This complex dynamics of polarons is generated by the interplay between the Peierls–Nabarro barrier and dissipative effects in the chains

Thermal enhancement and stochastic resonance of polaron ratchet

We study the ratchet drift of large polarons (solitons) in molecular diatomic chains induced by unbiased time periodic electric fields at nonzero temperature below its critical value. We show that, at a nonzero temperature, the critical value of the intensity of the electric field above which the ratchet phenomenon takes place is lower than at zero temperature for the same frequency of the field. We show that there is a range of temperatures for which the polaron drift is larger than that at zero temperature. We also show that temperature decreases the value of the lowest critical period of the field. And, finally, we demonstrate that there is a stochastic resonance in a polaron ratchet, namely that there is an optimal temperature at which the polaron drift is a maximum. The values of the stochastic resonance temperature, the lowest critical values of the field intensity, and its period depend on various parameters of the system and, in particular, on the anisotropy of the chain parameters. This temperature induced decrease of the critical value of the field intensity and its period, as well as the stochastic resonance itself, may be important for practical applications of the ratchet phenomenon in systems involving conducting polymers and other low-dimensional materials. They may also be important in some biological macromolecules where the ratchet phenomenon could take place in biomotors and energy and/or charge transport