We present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Appling this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, c...

We study shot noise for entangled electrons in a 4-lead beam-splitter with one incoming lead driven by adiabatically rotating magnetic fields. We propose a setup of an adiabatically rotating magnetic field which is appropriate for an electron beam to transport through. Using the scattering matrix approach, we find that shot noise for the singlet and that for the entangled triplet oscillates bet...

I review the mapping from the partition function of a d-dimensional quantum system to that of a d+ 1-dimensional classical system and I apply it to several models, in particular the classical 1d Ising, 2d XY, and 3d Ising models. These examples respectively illustrate the general features of the classical/quantum correspondence, a Berry phase term, and the role of gauge constraints. The limitat...

We study numerically the Berry phase in semiconductor quantum dots (QDs) that is induced by letting the dots to move adiabatically in a closed loop in the 2D plane along the circular trajectory. We show that the Berry phase is highly sensitive to the Rashba and Dresselhaus spin-orbit lengths. Based on the Finite Element Method, we solve the Schrödinger equation and investigate the evolution of ...

Quantum mechanical phases arising from a periodically varying Hamiltonian are considered. These phases are derived from the eigenvalues of a stationary, “dressed” Hamiltonian that is able to treat internal atomic or molecular structure in addition to the time variation. In the limit of an adiabatic time variation, the usual Berry phase is recovered. For more rapid variation, nonadiabatic correc...