Energy and time as conjugate dynamical variables

The energy and time variables of the elementary classical dynamical systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group on this space is canonical, but not Hamiltonian equivariant. Although it has no effect at classical level, the lack of equivariance makes the Galilei action inconsistent with the canonical quantization. A Hamiltonian equivariant action can be obtained by assuming that the inertial parameter in the extended phase-space is quasi-isotropic. This condition leads naturally to the Lorentz transformations between moving frames as a particular case of symplectic transformations. The limit speed appears as a constant factor relating the two additional canonical coordinates to the energy and time. Its value is identified with the speed of light by using the relationship between the electromagnetic potentials and the symplectic form of the extended phase-space.Comment: Replaced to write Eqs. (34), (35) in the general for

Heating-Assisted Atom Transfer in the Scanning Tunneling Microscope

The effects of a voltage pulse on the localization probability for a Xe atom prepared in a pure state localized on the STM surface at 0 temperature is investigated by numerically integrating the time-dependent Schroedinger equation. In these calculations the environmental interactions are neglected, and voltage pulses of 20 and 7 ns with symmetric triangular and trapezoidal shapes are considered. The atom dynamics at an environmental temperature of 4 K is studied in the frame of a stochastic, non-linear Liouville equation for the density operator. It is shown that the irreversible transfer from surface to tip may be explained by thermal decoherence rather than by the driving force acting during the application of the voltage pulse.Comment: 14 pages, Latex, 4 postscript figure