Self-adjointness of Dirac operators via Hardy-Dirac inequalities

Distinguished selfadjoint extensions of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, $-|x|^{-1}$. The method uses Hardy-Dirac inequalities and quadratic form techniques.Comment: PACS 03.65.P, 03.3

Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes

We discuss and review several thermodynamic criteria that have been introduced to characterize the thermal stability of a self-correcting quantum memory. We first examine the use of symmetry-breaking fields in analyzing the properties of self-correcting quantum memories in the thermodynamic limit: we show that the thermal expectation values of all logical operators vanish for any stabilizer and any subsystem code in any spatial dimension. On the positive side, we generalize the results in [R. Alicki et al., arXiv:0811.0033] to obtain a general upper bound on the relaxation rate of a quantum memory at nonzero temperature, assuming that the quantum memory interacts via a Markovian master equation with a thermal bath. This upper bound is applicable to quantum memories based on either stabilizer or subsystem codes.Comment: 23 pages. v2: revised introduction, various additional comments, and a new section on gapped hamiltonian

Effect of strain on hyperfine-induced hole-spin decoherence in quantum dots

We theoretically consider the effect of strain on the spin dynamics of a single heavy-hole (HH) confined to a self-assembled quantum dot and interacting with the surrounding nuclei via hyperfine interaction. Confinement and strain hybridize the HH states, which show an exponential decay for a narrowed nuclear spin bath. For different strain configurations within the dot, the dependence of the spin decoherence time $T_2$ on external parameters is shifted and the non-monotonic dependence of the peak is altered. Application of external strain yields considerable shifts in the dependence of $T_2$ on external parameters. We find that external strain affects mostly the effective hyperfine coupling strength of the conduction band (CB), indicating that the CB admixture of the hybridized HH states plays a crucial role in the sensitivity of $T_2$ on strain

Resonant spin polarization and spin current in a two-dimensional electron gas

We study the spin polarization and its associated spin-Hall current due to EDSR in disordered two-dimensional electron systems. We show that the disorder induced damping of the resonant spin polarization can be strongly reduced by an optimal field configuration that exploits the interference between Rashba and Dresselhaus spin-orbit interaction. This leads to a striking enhancement of the spin susceptibility while the spin-Hall current vanishes at the same time. We give an interpretation of the spin current in geometrical terms which are associated with the trajectories the polarization describes in spin space.Comment: (5 pages), updated references, corrected typo

Coulomb scattering cross-section in a 2D electron gas and production of entangled electrons

We calculate the Coulomb scattering amplitude for two electrons injected with opposite momenta in an interacting 2DEG. We include the effect of the Fermi liquid background by solving the 2D Bethe-Salpeter equation for the two-particle Green function vertex, in the ladder and random phase approximations. This result is used to discuss the feasibility of producing spin EPR pairs in a 2DEG by collecting electrons emerging from collisions at a pi/2 scattering angle, where only the entangled spin-singlets avoid the destructive interference resulting from quantum indistinguishability. Furthermore, we study the effective 2D electron-electron interaction due to the exchange of virtual acoustic and optical phonons, and compare it to the Coulomb interaction. Finally, we show that the 2D Kohn-Luttinger pairing instability for the scattering electrons is negligible in a GaAs 2DEG.Comment: 19 pages, 10 figure

Observing the Berry phase in diffusive conductors: Necessary conditions for adiabaticity

In a recent preprint (cond-mat/9803170), van~Langen, Knops, Paasschens and Beenakker attempt to re-analyze the proposal of Loss, Schoeller and Goldbart (LSG) [Phys. Rev. B~48, 15218 (1993)] concerning Berry phase effects in the magnetoconductance of diffusive systems. Van Langen et al. claim that the adiabatic approximation for the Cooperon previously derived by LSG is not valid in the adiabatic regime identified by LSG. It is shown that the claim of van~Langen et al. is not correct, and that, on the contrary, the magnetoconductance does exhibit the Berry phase effect within the LSG regime of adiabaticity. The conclusion reached by van~Langen et al. is based on a misinterpretation of field-induced dephasing effects, which can mask the Berry phase (and any other phase coherent phenomena) for certain parameter values.Comment: 25 pages, 9 figure