We consider the most general class of teleparallel gravitational theories quadratic in the torsion tensor, in three space-time dimensions, and carry out a detailed investigation of its Hamiltonian formulation in Schwinger's time gauge. This general class is given by a family of three-parameter theories. A consistent implementation of the Legendre transform reduces the original theory to a one-parameter family of theories. By calculating the Poisson brackets, we show explicitly that the constraints of the theory constitute a first-class set. Therefore, the resulting theory is well defined with regard to time evolution. The structure of the Hamiltonian theory rules out the existence of the Newtonian

We apply the Hamiltonian formulation of teleparallel theories of gravity in 2+1 dimensions to a circularly symmetric geometry. We find a family of one-parameter black hole solutions. The BTZ solution fixes the unique free parameter of the theory. The resulting field equations coincide with the teleparallel equivalent of Einstein's three-dimensional equations. We calculate the gravitational energy of the black holes by means of the simple expression that arises in the Hamiltonian formulation and conclude that the resulting value is identical to that calculated by means of the Brown-York method.Comment: 20 pages, Latex file, no figure

We theoretically demonstrate that the transport inefficiency recently found experimentally for branched-out mesoscopic networks can also be observed in a quantum ring of finite width with an attached central horizontal branch. This is done by investigating the time evolution of an electron wave packet in such a system. Our numerical results show that the conductivity of the ring does not necessary improves if one adds an extra channel. This ensures that there exists a quantum analogue of the Braess Paradox, originating from quantum scattering and interference.

We study the gravitomagnetic effect in the context of absolute parallelism with the use of a modified geodesic equation via a free parameter b. We calculate the time difference in two atomic clocks orbiting the Earth in opposite directions and find a small correction due the coupling between the torsion of space time and the internal structure of atomic clocks measured by the free parameter.