Transport and dissipation in low-dimensional systems
Abstract
We study the onset of dissipation in low dimensional quantum-mechanical systems and it's relation to transport phenomena. In one dimension we study the problem of spin diffusion. We discuss the example of the 1D spin-1/2 Heisenberg chain. We show that there are no diffusive excitations in perturbation theory. This result is supported by exact numerical diagonalisation of the Heisenberg Hamiltonian, which shows finite stiffness at low temperatures so that the transport is ballistic. However, the addition of an arbitrarily small spin-phonon interaction term leads to diffusive behavior in the long time limit. In this case we estimate the spin-diffusion coefficient. In two dimensions we study motion of vortices in arrays of Josephson junctions at zero temperature where it is controlled by quantum tunneling from one plaquette to another. The tunneling process is characterized by a finite time and can be slow compared to the superconducting gap (so that tauDelta≫ 1). The dissipation which accompanies this process arises from rare processes when a vorter excites a quasiparticle above the gap while tunneling through a single junction. We find that the dissipation is significant even in the case tauDelta≫ 1, in particular it is not exponentially small in this parameter. We use the calculated energy dissipation for the single vortex jump to estimate the physical resistance of the whole array.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1998
- Bibcode:
- 1998PhDT........84N