We demonstrate that decoherence of many-spin systems can drastically differ from decoherence of single-spin systems. The difference originates at the most basic level, being determined by parity of the central system, i.e. by whether the system comprises even or odd number of spin-1/2 entities. Therefore, it is very likely that similar distinction between the central spin systems of even and odd parity is important in many other situations. Our consideration clarifies the physical origin of the unusual two-step decoherence found previously in the two-spin systems.

During the reconstruction of the edge of a quantum Hall liquid, Coulomb interaction energy is lowered through the change in the structure of the edge. We use theory developed earlier by one of the authors [K. Yang, Phys. Rev. Lett. 91, 036802 (2003)] to calculate the electron spectral functions of a reconstructed edge, and study the consequences of the edge reconstruction for the momentum-resolved tunneling into the edge. It is found that additional excitation modes that appear after the reconstruction produce distinct features in the energy and momentum dependence of the spectral function, which can be used to detect the presence of edge reconstruction.The paradigm of the Quantum Hall effect (QHE) edge physics is based on an argument due to Wen, 1 according to which the low-energy edge excitations are described by a chiral Luttinger liquid (CLL) theory. One attractive feature of this theory is that due to the chirality, the interaction parameter of the CLL is often tied to the robust topological properties of the bulk and is independent of the details of electron interaction and edge confining potential; studying the physics at the edge thus offers an important probe of the bulk physics. It turns out, however, that the CLL ground state may not always be stable. 2,3 On the microscopic level, the instability is driven by Coulomb interactions and leads to the change of the structure of the edge. This effect has been termed "edge reconstruction". One of its manifestations is the appearance of new low-energy excitations of the edge not present in the original CLL theory.Based on the insight from numerical studies of the edge reconstruction, 4,5 a field-theoretic description of the effect has been proposed by one of us. 6 Remarkably, it provides an explicit expression for the electron operator in terms of the fields that describe the low-energy edge excitations after the reconstruction. This allows one to calculate many observable quantities. In this paper, we describe the calculation of the spectral function of the electron in the reconstructed edge. This function can be probed in tunneling experiments where the electron's momentum parallel to the edge is conserved (the so-called momentum-resolved tunneling). Experiments of this kind are currently being performed. 7,8 It has also been proposed that momentum-resolved tunneling may be used to detect the multiple branches of edge excitations of hierarchy states. 9 Our results show that the appearance of the new edge excitations after the reconstruction modifies the electron spectral function qualitatively. It leads to the redistribution of the spectral weight away from the peak corresponding to the original edge mode, and produces singularities corresponding to the new edge modes. For simplicity we have focused on the principal Laughlin sequence, although generalization to the hierarchy states should be straightforward. We also propose a particular experimental setup that involves momentum-resolved 0 k E k Condensation k FIG. 1: The spectrum of the edge excitations afte...

During the reconstruction of the edge of a quantum Hall liquid, Coulomb interaction energy is lowered through the change in the structure of the edge. We use theory developed earlier by one of the authors [K. Yang, Phys. Rev. Lett. 91, 036802 (2003)] to calculate the electron spectral functions of a reconstructed edge, and study the consequences of the edge reconstruction for the momentum-resolved tunneling into the edge. It is found that additional excitation modes that appear after the reconstruction produce distinct features in the energy and momentum dependence of the spectral function, which can be used to detect the presence of edge reconstruction.

I consider the problem of vortex tunneling in a two-dimensional superconductor. The vortex dynamics is governed by the Magnus force and the Ohmic friction force. Under-barrier motion in the vicinity of the saddle point of the pinning potential leads to a model with quadratic Hamiltonian which can be analytically diagonalized. I find the dependence of the tunneling probability on the normal state quasiparticle relaxation time $\tau$ with a minimum at $\omega_0\tau\sim 1$, where $\omega_0$ is the level spacing of the quasiparticle bound states inside the vortex core. The results agree qualitatively with the available experimental data.Comment: RevTeX, 6 pages, 2 figures. Published versio

Received DAY MONTH YEAR Revised DAY MONTH YEARDuring the reconstruction of the edge of a quantum Hall liquid, Coulomb interaction energy is lowered through the change in the structure of the edge. We use theory developed earlier by one of the authors [K. Yang, Phys. Rev. Lett. 91, 036802 (2003)] to calculate the electron spectral functions of a reconstructed edge, and study the consequences of the edge reconstruction for the momentum-resolved tunneling into the edge. It is found that additional excitation modes that appear after the reconstruction produce distinct features in the energy and momentum dependence of the spectral function, which can be used to detect the presence of edge reconstruction. Keywords: Quantum Hall Effect; Edge Reconstruction; TunnelingThe paradigm of the Quantum Hall effect (QHE) edge physics is based on an argument due to Wen, 1 according to which the low-energy edge excitations are described by a chiral Luttinger liquid (CLL) theory. One attractive feature of this theory is that due to the chirality, the interaction parameter of the CLL is often tied to the robust topological properties of the bulk and is independent of the details of electron interaction and edge confining potential; studying the physics at the edge thus offers an important probe of the bulk physics. It turns out, however, that the CLL ground state may not always be stable.2,3 On the microscopic level, the instability is driven by Coulomb interactions and leads to the change of the structure of the edge. This effect has been termed "edge reconstruction". One of its manifestations is the appearance of new low-energy excitations of the edge not present in the original CLL theory.Previous numerical studies 4,5 have suggested that the phenomenon of edge reconstruction can be understood as an instability of the original edge mode described by the CLL theory. This instability occurs as a result of increasing curvature of the edge spectrum as the edge confining potential softens. The spectrum curves down at high values of momenta until it touches zero at the transition point. This signals