Tolerating Inconsistencies: A Study of Logic of Moral Conflicts

Moral conflicts are the situations which emerge as a response to deal with conflicting obligations or duties. An interesting case arises when an agent thinks that two obligations A and B are equally important, but yet fails to choose one obligation over the other. Despite the fact that the systematic study and the resolution of moral conflicts finds prominence in our linguistic discourse, standard deontic logic when used to represent moral conflicts, implies the impossibility of moral conflicts. This presents a conundrum for appropriate logic to address these moral conflicts. We frequently believe that there is a close connection between tolerating inconsistencies and conflicting moral obligations. In paraconsistent logics, we tolerate inconsistencies by treating them to be both true and false. In this paper, we analyze Graham Priest’s paraconsistent logic LP, and extend our examination to the deontic extension of LP known as DLP. We illustrate our work, with a classic example from the famous Indian epic Mahabharata, where the protagonist Arjuna faces a moral conflict in the battlefield of Kurukshetra. The paper aims to avoid deontic explosion and allows to accommodate Arjuna’s moral conflict in paraconsistent deontic logics. Our analysis is expected to provide novel tools towards the logical representation of moral conflicts and to shed some light on the context-sensitive paraconsistent deontic logic

Inelastic lifetimes of confined two-component electron systems in semiconductor quantum wire and quantum well structures

We calculate Coulomb scattering lifetimes of electrons in two-subband quantum wires and in double-layer quantum wells by obtaining the quasiparticle self-energy within the framework of the random-phase approximation for the dynamical dielectric function. We show that, in contrast to a single-subband quantum wire, the scattering rate in a two-subband quantum wire contains contributions from both particle-hole excitations and plasmon excitations. For double-layer quantum well structures, we examine individual contributions to the scattering rate from quasiparticle as well as acoustic and optical plasmon excitations at different electron densities and layer separations. We find that the acoustic plasmon contribution in the two-component electron system does not introduce any qualitatively new correction to the low energy inelastic lifetime, and, in particular, does not produce the linear energy dependence of carrier scattering rate as observed in the normal state of high-$T_c$ superconductors.Comment: 16 pages, RevTeX, 7 figures. Also available at http://www-cmg.physics.umd.edu/~lzheng

Theory of nuclear induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots

We propose a model for spectral diffusion of localized spins in semiconductors due to the dipolar fluctuations of lattice nuclear spins. Each nuclear spin flip-flop is assumed to be independent, the rate for this process being calculated by a method of moments. Our calculated spin decoherence time $T_{M}=0.64$ ms for donor electron spins in Si:P is a factor of two longer than spin echo decay measurements. For $^{31}$P nuclear spins we show that spectral diffusion is well into the motional narrowing regime. The calculation for GaAs quantum dots gives $T_{M}=10-50$ $\mu$s depending on the quantum dot size. Our theory indicates that nuclear induced spectral diffusion should not be a serious problem in developing spin-based semiconductor quantum computer architectures.Comment: 15 pages, 9 figures. Accepted for publication in Phys. Rev.

Coulomb scattering lifetime of a two-dimensional electron gas

Motivated by a recent tunneling experiment in a double quantum-well system, which reports an anomalously enhanced electronic scattering rate in a clean two-dimensional electron gas, we calculate the inelastic quasiparticle lifetime due to electron-electron interaction in a single loop dynamically screened Coulomb interaction within the random-phase-approximation. We obtain excellent quantitative agreement with the inelastic scattering rates in the tunneling experiment without any adjustable parameter, finding that the reported large ($\geq$ a factor of six) disagreement between theory and experiment arises from quantitative errors in the existing theoretical work and from the off-shell energy dependence of the electron self-energy.Comment: 11 pages, RevTex, figures included. Also available at http://www-cmg.physics.umd.edu/~lzheng

Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions

We have studied a quantum Hamiltonian that models an array of ultrasmall Josephson junctions with short range Josephson couplings, $E_J$, and charging energies, $E_C$, due to the small capacitance of the junctions. We derive a new effective quantum spherical model for the array Hamiltonian. As an application we start by approximating the capacitance matrix by its self-capacitive limit and in the presence of an external uniform background of charges, $q_x$. In this limit we obtain the zero-temperature superconductor-insulator phase diagram, $E_J^{\rm crit}(E_C,q_x)$, that improves upon previous theoretical results that used a mean field theory approximation. Next we obtain a closed-form expression for the conductivity of a square array, and derive a universal scaling relation valid about the zero--temperature quantum critical point. In the latter regime the energy scale is determined by temperature and we establish universal scaling forms for the frequency dependence of the conductivity.Comment: 18 pages, four Postscript figures, REVTEX style, Physical Review B 1999. We have added one important reference to this version of the pape

Electron spin coherence in semiconductors: Considerations for a spin-based solid state quantum computer architecture

We theoretically consider coherence times for spins in two quantum computer architectures, where the qubit is the spin of an electron bound to a P donor impurity in Si or within a GaAs quantum dot. We show that low temperature decoherence is dominated by spin-spin interactions, through spectral diffusion and dipolar flip-flop mechanisms. These contributions lead to 1-100 $\mu$s calculated spin coherence times for a wide range of parameters, much higher than former estimates based on $T_{2}^{*}$ measurements.Comment: Role of the dipolar interaction clarified; Included discussion on the approximations employed in the spectral diffusion calculation. Final version to appear in Phys. Rev.

Nuclear spin relaxation probed by a single quantum dot

We present measurements on nuclear spin relaxation probed by a single quantum dot in a high-mobility electron gas. Current passing through the dot leads to a spin transfer from the electronic to the nuclear spin system. Applying electron spin resonance the transfer mechanism can directly be tuned. Additionally, the dependence of nuclear spin relaxation on the dot gate voltage is observed. We find electron-nuclear relaxation times of the order of 10 minutes

Competing orders in a magnetic field: spin and charge order in the cuprate superconductors

We describe two-dimensional quantum spin fluctuations in a superconducting Abrikosov flux lattice induced by a magnetic field applied to a doped Mott insulator. Complete numerical solutions of a self-consistent large N theory provide detailed information on the phase diagram and on the spatial structure of the dynamic spin spectrum. Our results apply to phases with and without long-range spin density wave order and to the magnetic quantum critical point separating these phases. We discuss the relationship of our results to a number of recent neutron scattering measurements on the cuprate superconductors in the presence of an applied field. We compute the pinning of static charge order by the vortex cores in the `spin gap' phase where the spin order remains dynamically fluctuating, and argue that these results apply to recent scanning tunnelling microscopy (STM) measurements. We show that with a single typical set of values for the coupling constants, our model describes the field dependence of the elastic neutron scattering intensities, the absence of satellite Bragg peaks associated with the vortex lattice in existing neutron scattering observations, and the spatial extent of charge order in STM observations. We mention implications of our theory for NMR experiments. We also present a theoretical discussion of more exotic states that can be built out of the spin and charge order parameters, including spin nematics and phases with `exciton fractionalization'.Comment: 36 pages, 33 figures; for a popular introduction, see http://onsager.physics.yale.edu/superflow.html; (v2) Added reference to new work of Chen and Ting; (v3) reorganized presentation for improved clarity, and added new appendix on microscopic origin; (v4) final published version with minor change

Electron spin as a spectrometer of nuclear spin noise and other fluctuations

This chapter describes the relationship between low frequency noise and coherence decay of localized spins in semiconductors. Section 2 establishes a direct relationship between an arbitrary noise spectral function and spin coherence as measured by a number of pulse spin resonance sequences. Section 3 describes the electron-nuclear spin Hamiltonian, including isotropic and anisotropic hyperfine interactions, inter-nuclear dipolar interactions, and the effective Hamiltonian for nuclear-nuclear coupling mediated by the electron spin hyperfine interaction. Section 4 describes a microscopic calculation of the nuclear spin noise spectrum arising due to nuclear spin dipolar flip-flops with quasiparticle broadening included. Section 5 compares our explicit numerical results to electron spin echo decay experiments for phosphorus doped silicon in natural and nuclear spin enriched samples.Comment: Book chapter in "Electron spin resonance and related phenomena in low dimensional structures", edited by Marco Fanciulli. To be published by Springer-Verlag in the TAP series. 35 pages, 9 figure