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Quantum speed limit and entanglement of a two-spin Heisenberg XYZ system in an inhomogeneous external magnetic field are investigated. The physical system studied is the excess electron spin in two adjacent quantum dots. The influences of magnetic field inhomogeneity as well as spin–orbit coupling are studied. Moreover, the spin interaction with surrounding magnetic environment is investigated as a non-Markovian process. The spin–orbit interaction provides two important features: the formation of entanglement when two qubits are initially in a separated state and the degradation and rebirth of the entanglement.

Quantum speed limit time and entanglement in a system composed of coupled quantum dots are investigated. The excess electron spin in each quantum dot constitutes the physical system (qubit). Also the spin interaction is modeled through the Heisenberg model and the spins are imposed by an external magnetic field. Taking into account the spin relaxation as a non-Markovian process, the quantum speed limit and entanglement evolution are discussed. Our findings reveal that increasing the magnetic field leads to the faster quantum evolution. In addition, the temperature increment causes the longer quantum speed limit time as well as the entanglement degradation.

Thermal and electron transport through organic molecules attached to three-dimensional gold electrodes in two different configurations, namely para and meta with thiol-terminated junctions is studied theoretically in the linear response regime using Green's function formalism. We used thiol-terminated (–SH bond) benzene units and found a positive thermopower because the highest occupied molecular orbital (HOMO) is near the Fermi energy level. We investigated the influence of molecular length and molecular junction geometry on the thermoelectric properties. Our results show that the thermoelectric properties are highly sensitive to the coupling geometry and the molecular length. In addition, we observed that the interference effects and increasing molecular length can increase the thermoelectric efficiency of device in a specific configuration.

The charge and spin-dependent thermoelectric properties of different lengths of polythiophene in a molecular junction are investigated using the B ¨uttiker probe method within Green function formalism in linear response regime. The coupling of the molecular chain to three-dimensional ferromagnetic electrodes is described by a tight-binding model for both parallel and antiparallel spin configurations. The decrease of height of transmission probability peaks and thermoelectric coefficients are observed in the presence of the B ¨uttiker probes. The reduction is more intensive in the strong dephased chains.Results show that the spin magnetothermopower is bigger than the charge magnetothermopower due to the larger difference between the spin thermopowers with respect to the charge ones. In addition, we observed that the kind of carriers participating in the thermoelectric transport depends on the number of the thiophene rings.

Using Keldysh nonequilibrium Green function formalism and mapping a many-body electron—phonon interaction onto a one body problem, the electron transport through a serially coupled double quantum dot system is analyzed. The influence of the electron—phonon interaction, temperature, detuning, and interdot tunneling on the transmission coefficient and current is studied. Our results show that the electron—phonon interaction results in the appearance of the side peaks in the transmission coefficient, whose height is strongly dependent on the phonon temperature. We have also found that the inequality of the electron—phonon interaction strength in two dots gives rise to an asymmetry in the current—voltage characteristic. In addition, the temperature difference between the phonon and electron subsystems results in the reduction of the saturated current and the destruction of the step-like behavior of the current. It is also observed that the detuning can improve the magnitude of the current by compensating the mismatch of the quantum dots energy levels induced by the electron—phonon interaction.