For the Hamiltonian integrable systems governed by SL(2)-invariant r-matrix (such as Heisenberg magnet, Toda lattice, nonlinear Schrödinger equation) a general procedure for constructing Bäcklund transformation is proposed. The corresponding BT is shown to preserve the Poisson bracket. The proof is given by a direct calculation using the r-matrix expression for the Poisson bracket.

In this paper, we study a class of Schrödinger-Poisson (SP) systems with general nonlinearity where the does not require Ambrosetti-Rabinowitz and Nehari monotonic conditions. We establish new estimates explore associated energy functional which is coercive bounded below on Sobolev space. Together Ekeland variational principle, prove existence ground state solutions. Furthermore, when ‘charge’ ...

Interaction and correlation effects in quantum dots play a fundamental role in defining both their equilibrium and transport properties. Numerical methods are commonly employed to study such systems. In this paper we investigate the numerical calculation of quantum transport of electrons in spherical centered defect InGaAs/AlGaAs quantum dot (SCDQD). The simulation is based on the imaginary time...

It is shown that, for a large class of statistical mixtures, the Wigner-Poisson (or Hartree) system can be reduced to an effective Schrödinger-Poisson system, in which the Schrödinger equation contains a new nonlinearity. For the case of a zero-temperature one-dimensional electron gas, this additional nonlinearity is of the form Ψ 4. In the long wavelength limit, the results obtained from the e...

In quantum mechanics, the space-fractional Schrödinger equation provides a natural extension of the standard Schrödinger equation when the Brownian trajectories in Feynman path integrals are replaced by Levy flights. Here an optical realization of the fractional Schrödinger equation, based on transverse light dynamics in aspherical optical cavities, is proposed. As an example, a laser implement...

We describe some elements of the theory of semigroups generated by second order differential operators needed to study the Hardy-type space H1 L related to the time independent Schrödinger operator L = −∆+ V , with V ≥ 0 a potential satisfying a reverse Hölder inequality. Its dual space is a BMO-type space BMOL, that turns out to be the suitable one for the versions of some classical operators ...

Abstract A previous study by Mantas and Vecil (Int J High Perform Comput Appl 34(1): 81–102, 2019) describes an efficient accurate solver for nanoscale DG MOSFETs through a deterministic Boltzmann-Schrödinger-Poisson model with seven electron–phonon scattering mechanisms on hybrid parallel CPU/GPU platform. The transport computational phase, i.e. the time integration of Boltzmann equations, was...

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two mai...