Electron transport through Aharonov-Bohm interferometer with laterally coupled double quantum dots

We theoretically investigate electron transport through an Aharonov-Bohm interferometer containing laterally coupled double quantum dots. We introduce the indirect coupling parameter $\alpha$, which characterizes the strength of the coupling via the reservoirs between two quantum dots. $|\alpha|=1$ indicates the strongest coupling, where only a single mode contributes to the transport in the system. Two conduction modes exist in a system where $|\alpha|\neq 1$. The interference effects such as the Fano resonance and the Aharonov-Bohm oscillation are suppressed as the absolute value of the parameter $\alpha$ decreases from 1. The linear conductance does not depend on the flux when $\alpha=0$ since it corresponds to independent coupling of the dots to the reservoir modes.Comment: 15 pages, 13 figure

Non-equilibrium thermodynamical framework for rate- and state-dependent friction

Rate- and state-dependent friction law for velocity-step and healing are analysed from a thermodynamic point of view. Assuming a logarithmic deviation from steady-state a unification of the classical Dieterich and Ruina models of rock friction is proposed.Comment: 12 pages, 5 figure

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 $\alpha=0.23(3)$

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

Some properties of the resonant state in quantum mechanics and its computation

The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take account of the outgoing momentum flux; the number of particles would decay exponentially in a fixed volume of integration. Moreover, we introduce new numerical methods of treating the resonant state with the use of the effective potential. We first give a numerical method of finding a resonance pole in the complex energy plane. The method seeks an energy eigenvalue iteratively. We found that our method leads to a super-convergence, the convergence exponential with respect to the iteration step. The present method is completely independent of commonly used complex scaling. We also give a numerical trick for computing the time evolution of the resonant state in a limited spatial area. Since the wave function of the resonant state is diverging away from the scattering potential, it has been previously difficult to follow its time evolution numerically in a finite area.Comment: 20 pages, 12 figures embedde

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

Core structure of EAS in 10(15) to 10(17) eV

With the use of Akeno calorimeter, the attenuation of particles in concrete is analyzed as the function of the shower size of 10 to the 5th power to 10 to the 7th power. The attenuation length does not depend much on the shower size but depends a little on the shower age. The average value is approx. 150 g/sq cm for s = 0.5 to 0.85 and approx. 40 g/sq cm for s = 0.85 to 1.15. These values and their fluctuations are consistent with the equi-intensity curves of extensive air showers (EAS)