ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

Angle-resolved photoemission spectroscopy study of HgBa2_{2}CuO4+δ_{4+\delta}

HgBa$_{2}$CuO$_{4+\delta}$ (Hg1201) has been shown to be a model cuprate for scattering, optical, and transport experiments, but angle-resolved photoemission spectroscopy (ARPES) data are still lacking owing to the absence of a charge-neutral cleavage plane. We report on progress in achieving the experimental conditions for which quasiparticles can be observed in the near-nodal region of the Fermi surface. The d-wave superconducting gap is measured and found to have a maximum of 39 meV. At low temperature, a kink is detected in the nodal dispersion at approximately 51 meV below the Fermi level, an energy that is different from other cuprates with comparable T$_c$. The superconducting gap, Fermi surface, and nodal band renormalization measured here provide a crucial momentum-space complement to other experimental probes

Integrated silicon qubit platform with single-spin addressability, exchange control and robust single-shot singlet-triplet readout

Silicon quantum dot spin qubits provide a promising platform for large-scale quantum computation because of their compatibility with conventional CMOS manufacturing and the long coherence times accessible using $^{28}$Si enriched material. A scalable error-corrected quantum processor, however, will require control of many qubits in parallel, while performing error detection across the constituent qubits. Spin resonance techniques are a convenient path to parallel two-axis control, while Pauli spin blockade can be used to realize local parity measurements for error detection. Despite this, silicon qubit implementations have so far focused on either single-spin resonance control, or control and measurement via voltage-pulse detuning in the two-spin singlet-triplet basis, but not both simultaneously. Here, we demonstrate an integrated device platform incorporating a silicon metal-oxide-semiconductor double quantum dot that is capable of single-spin addressing and control via electron spin resonance, combined with high-fidelity spin readout in the singlet-triplet basis.Comment: 10 pages, 4 figure

Thermodynamics of the superfluid dilute Bose gas with disorder

We generalize the Beliaev-Popov diagrammatic technique for the problem of interacting dilute Bose gas with weak disorder. Averaging over disorder is implemented by the replica method. Low energy asymptotic form of the Green function confirms that the low energy excitations of the superfluid dirty Boson system are sound waves with velocity renormalized by the disorder and additional dissipation due to the impurity scattering. We find the thermodynamic potential and the superfluid density at any temperature below the superfluid transition temperature and derive the phase diagram in temperature vs. disorder plane.Comment: 4 page

Gravity from Quantum Information

It is suggested that the Einstein equation can be derived from Landauer's principle applied to an information erasing process at a local Rindler horizon and Jacobson's idea linking the Einstein equation with thermodynamics. When matter crosses the horizon, the information of the matter disappears and the horizon entanglement entropy increases to compensate the entropy reduction. The Einstein equation describes an information-energy relation during this process, which implies that entropic gravity is related to the quantum entanglement of the vacuum and has a quantum information theoretic origin.Comment: 7 pages, revtex4-1, 2 figures, recent supporting results adde

Black hole as an Information Eraser

We discuss the identity of black hole entropy and show that the first law of black hole thermodynamics, in the case of a Schwarzschild black hole, can be derived from Landauer's principle by assuming that the black hole is one of the most efficient information erasers in systems of a given temperature. The term "most efficient" implies that minimal energy is required to erase a given amount of information. We calculate the discrete mass spectra and the entropy of a Schwarzschild black hole assuming that the black hole processes information in unit of bits. The black hole entropy acquires a sub-leading contribution proportional to the logarithm of its mass-squared in addition to the usual mass-squared term without an artificial cutoff. We also argue that the minimum of the black hole mass is $\sqrt{\log 2/(8\pi)}M_P$.Comment: 12 pages, 4 figures, minor change