The control is the potential well absolute position. For two kinds of potential shape (periodic and box), we propose approximated solutions to the stead-state motion planing problem: steering in finite time the particle from an initial well position to a final well position, the initial and final particle energies being identical. This problem is a quantum analogue of the water tank problem, wh...

The effect of inter-dot many body interactions on the transport properties of coupled dots connected to leads is studied. Results are obtained by exactly diagonalizing a cluster composed by the double-dot and its vicinity, which is then connected to the leads. We analyse two configurations: coupled dots aligned and perpendicular to the leads. We show that in the weak coupling limit they present...

A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs states in terms of path measures (Euclidean Gibbs measures). It covers the case of crystals without translation invariance, as well as the case of asymmetric...

A time-dependent wave packet method has been developed to study atom–triatom ABC1D→AB1CD reactions in full six dimensions ~6D!. The approach employs a body-fixed coupled angular momentum basis for three angular coordinates, and three 1D bases for three radial coordinates. It permits the calculation of diatom AB vibrational state resolved total reaction probability for an initial rovibrational s...

Some situations are discussed where subquantum oscillations in momentum arise in connection with Fisher information and the quantum potential.

A time-dependent wave packet method has been employed to calculate the state-to-state reaction probability for the H1H2O~0,0,0!→H2~v1 , j1!1OH~v2 , j2! reaction for J50 and initial nonrotating H2O on the modified Schatz–Elgersman potential energy surface in full six dimensions ~6D!. Starting from a wave packet for an atom–triatom asymptotic state in atom–triatom Jacobi coordinates, we transfer ...

We consider a non-interacting gas under the inverted harmonic potential and present infinitely degenerate non-stationary orthogonal states. discuss that it has an infinite entropy at absolute zero temperature. show uncertainty in position of particle can be as there exists solution which asymptotes to Dirac delta function. obtain new free wave packet using eigenstates for potential. It unique s...

A theory of the competition between fusion and quasi-fission in a heavy fusing system is proposed, which is based on a master equation and the two-center shell model. Fusion and quasi-fission arise from a diffusion process in an ensemble of nuclear shapes evolving towards the thermal equilibrium. The master equation describes the diffusion of the nuclear shapes due to quantum and thermal fluctu...