Rheology and dynamical heterogeneity in frictionless beads at jamming density

We investigate the rheological properties of an assembly of inelastic (but frictionless) particles close to the jamming density using numerical simulation, in which uniform steady states with a constant shear rate $\dot\gamma$ is realized. The system behaves as a power-law fluid and the relevant exponents are estimated; e.g., the shear stress is proportional to $\dot\gamma^{1/\delta_S}$, where $1/\delta_S=0.64(2)$. It is also found that the relaxation time $\tau$ and the correlation length $\xi$ of the velocity increase obeying power laws: $\tau\sim\dot\gamma^{-\beta}$ and $\xi\sim\dot\gamma^{-\alpha}$, where $\beta=0.27(3)$ and $\alpha=0.23(3)$

Scaling Theory of Antiferromagnetic Heisenberg Ladder Models

The $S=1/2$ antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd number of legs are distinguished clearly. In the former, the energy gap opens up as $\Delta E\sim{J_\perp}$, where ${J_\perp}$ is the strength of the antiferromagnetic inter-chain coupling. In the latter, the critical phase with the central charge $c=1$ extends over the whole region of ${J_\perp}>0$.Comment: 12 pages with 9 Postscript figures. To appear in J. Phys. A: Math. Ge

A variational approach to Ising spin glasses in finite dimensions

We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the lower level (cluster of a single spin) our approximation coincides with the SK model while at the highest level it coincides with the true $d$-dimensional system. The method is variational and it uses the replica approach to spin glasses and the Parisi ansatz for the order parameter. As a result we have rigorous bounds for the quenched free energy which become more and more precise when larger and larger clusters are considered.Comment: 16 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to J. Phys. A: Math. Ge

Maximization of thermal entanglement of arbitrarily interacting two qubits

We investigate the thermal entanglement of interacting two qubits. We maximize it by tuning a local Hamiltonian under a given interaction Hamiltonian. We prove that the optimizing local Hamiltonian takes a simple form which dose not depend on the temperature and that the corresponding optimized thermal entanglement decays as $1/(T log T)$ at high temperatures. We also find that at low temperatures the thermal entanglement is maximum without any local Hamiltonians and that the second derivative of the maximized thermal entanglement changes discontinuously at the boundary between the high- and low-temperature phases.Comment: 23 pages, 4 figure

Supernova Resonance-Scattering Profiles in the Presence of External Illumination

We discuss a simple model for the formation of a supernova spectral line by resonance scattering in the presence of external illumination of the line-forming region by light from circumstellar interaction (toplighting). The simple model provides a clear understanding of the most conspicuous toplighting effect: a rescaling or, as we prefer, a ``muting'' of the line profile relative to the continuum. This effect would be present in more realistic models, but would be harder to isolate. An analytic expression for a muting factor for a P-Cygni line is derived that depends on the ratio E of the toplighting specific intensity to the specific intensity from the supernova photosphere. If E<1, the line profile is reduced in scale or ``muted''. If E=1, the line profile vanishes altogether. If E>1, the line profile flips vertically: then having an absorption component near the observer-frame line center wavelength and a blueshifted emission component.Comment: accepted for publication in PAS

Complex periodic potentials with real band spectra

This paper demonstrates that complex PT-symmetric periodic potentials possess real band spectra. However, there are significant qualitative differences in the band structure for these potentials when compared with conventional real periodic potentials. For example, while the potentials V(x)=i\sin^{2N+1}(x), (N=0, 1, 2, ...), have infinitely many gaps, at the band edges there are periodic wave functions but no antiperiodic wave functions. Numerical analysis and higher-order WKB techniques are used to establish these results.Comment: 8 pages, 7 figures, LaTe

Electronic Structure of Multiple Dots

We calculate, via spin density functional theory (SDFT) and exact diagonalization, the eigenstates for electrons in a variety of external potentials, including double and triple dots. The SDFT calculations employ realistic wafer profiles and gate geometries and also serve as the basis for the exact diagonalization calculations. The exchange interaction J between electrons is the difference between singlet and triplet ground state energies and reflects competition between tunneling and the exchange matrix element, both of which result from overlap in the barrier. For double dots, a characteristic transition from singlet ground state to triplet ground state (positive to negative J) is calculated. For the triple dot geometry with 2 electrons we also find the electronic structure with exact diagonalization. For larger electron number (18 and 20) we use only SDFT. In contrast to the double dot case, the triple dot case shows a quasi-periodic fluctuation of J with magnetic field which we attribute to periodic variations of the basis states in response to changing flux quanta threading the triple dot structure.Comment: 3 pages, 4 figure

Non-Hermitian Delocalization and Eigenfunctions

Recent literature on delocalization in non-Hermitian systems has stressed criteria based on sensitivity of eigenvalues to boundary conditions and the existence of a non-zero current. We emphasize here that delocalization also shows up clearly in eigenfunctions, provided one studies the product of left- and right-eigenfunctions, as required on physical grounds, and not simply the squared modulii of the eigenfunctions themselves. We also discuss the right- and left-eigenfunctions of the ground state in the delocalized regime and suggest that the behavior of these functions, when considered separately, may be viewed as ``intermediate'' between localized and delocalized.Comment: 8 pages, 11 figures include

Semiconductor quantum dots for electron spin qubits

We report on our recent progress in applying semiconductor quantum dots for spin-based quantum computation, as proposed by Loss and DiVincenzo (1998 Phys. Rev. A 57 120). For the purpose of single-electron spin resonance, we study different types of single quantum dot devices that are designed for the generation of a local ac magnetic field in the vicinity of the dot. We observe photon-assisted tunnelling as well as pumping due to the ac voltage induced by the ac current driven through a wire in the vicinity of the dot, but no evidence for ESR so far. Analogue concepts for a double quantum dot and the hydrogen molecule are discussed in detail. Our experimental results in laterally coupled vertical double quantum dot device show that the Heitler–London model forms a good approximation of the two-electron wavefunction. The exchange coupling constant J is estimated. The relevance of this system for two-qubit gates, in particular the SWAP operation, is discussed. Density functional calculations reveal the importance of the gate electrode geometry in lateral quantum dots for the tunability of J in realistic two-qubit gates