Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice

We introduce an inhomogeneously-nonlinear Schr{\"o}dinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneous settings present vastly different dynamical behavior than the one expected in their homogeneous counterparts in the vicinity of the interface. We analyze the relevant stationary states, as well as their stability by means of perturbation theory and linear stability analysis. We find good agreement with the numerical findings in the vicinity of the anti-continuum limit. For larger values of the coupling, we follow the relevant branches numerically and show that they terminate at values of the coupling strength which are larger for more extended solutions. The dynamical development of relevant instabilities is also monitored in the case of unstable solutions.Comment: 14 pages, 4 figure

Choosing a basis that eliminates spurious solutions in k.p theory

A small change of basis in k.p theory yields a Kane-like Hamiltonian for the conduction and valence bands of narrow-gap semiconductors that has no spurious solutions, yet provides an accurate fit to all effective masses. The theory is shown to work in superlattices by direct comparison with first-principles density-functional calculations of the valence subband structure. A reinterpretation of the standard data-fitting procedures used in k.p theory is also proposed.Comment: 15 pages, 2 figures; v3: expanded with much new materia

Quadratic response theory for spin-orbit coupling in semiconductor heterostructures

This paper examines the properties of the self-energy operator in lattice-matched semiconductor heterostructures, focusing on nonanalytic behavior at small values of the crystal momentum, which gives rise to long-range Coulomb potentials. A nonlinear response theory is developed for nonlocal spin-dependent perturbing potentials. The ionic pseudopotential of the heterostructure is treated as a perturbation of a bulk reference crystal, and the self-energy is derived to second order in the perturbation. If spin-orbit coupling is neglected outside the atomic cores, the problem can be analyzed as if the perturbation were a local spin scalar, since the nonlocal spin-dependent part of the pseudopotential merely renormalizes the results obtained from a local perturbation. The spin-dependent terms in the self-energy therefore fall into two classes: short-range potentials that are analytic in momentum space, and long-range nonanalytic terms that arise from the screened Coulomb potential multiplied by a spin-dependent vertex function. For an insulator at zero temperature, it is shown that the electronic charge induced by a given perturbation is exactly linearly proportional to the charge of the perturbing potential. These results are used in a subsequent paper to develop a first-principles effective-mass theory with generalized Rashba spin-orbit coupling.Comment: 20 pages, no figures, RevTeX4; v2: final published versio

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

In this paper a multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent heterostructures with macroscopically neutral interfaces and no spontaneous bulk polarization. The key assumption -- proved in earlier numerical studies -- is that the heterostructure can be treated as a weak perturbation with respect to some periodic reference crystal, with the nonlinear response small in comparison to the linear response. Quadratic response theory is then used in conjunction with k.p perturbation theory to develop a multi-band effective-mass Hamiltonian (for slowly varying envelope functions) in which all interface band-mixing effects are determined by the linear response. To within terms of the same order as the position dependence of the effective mass, the quadratic response contributes only a bulk band offset term and an interface dipole term, both of which are diagonal in the effective-mass Hamiltonian. Long-range multipole Coulomb fields arise in quantum wires or dots, but have no qualitative effect in two-dimensional systems beyond a dipole contribution to the band offsets.Comment: 25 pages, no figures, RevTeX4; v3: final published versio

Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−1710^{-17}

The phase coherence of an ultrastable optical frequency reference is fully maintained over actively stabilized fiber networks of lengths exceeding 30 km. For a 7-km link installed in an urban environment, the transfer instability is $6 \times 10^{-18}$ at 1-s. The excess phase noise of 0.15 rad, integrated from 8 mHz to 25 MHz, yields a total timing jitter of 0.085 fs. A 32-km link achieves similar performance. Using frequency combs at each end of the coherent-transfer fiber link, a heterodyne beat between two independent ultrastable lasers, separated by 3.5 km and 163 THz, achieves a 1-Hz linewidth.Comment: 4 pages, 4 figure

Long-distance remote comparison of ultrastable optical frequencies with 1e-15 instability in fractions of a second

We demonstrate a fully optical, long-distance remote comparison of independent ultrastable optical frequencies reaching a short term stability that is superior to any reported remote comparison of optical frequencies. We use two ultrastable lasers, which are separated by a geographical distance of more than 50 km, and compare them via a 73 km long phase-stabilized fiber in a commercial telecommunication network. The remote characterization spans more than one optical octave and reaches a fractional frequency instability between the independent ultrastable laser systems of 3e-15 in 0.1 s. The achieved performance at 100 ms represents an improvement by one order of magnitude to any previously reported remote comparison of optical frequencies and enables future remote dissemination of the stability of 100 mHz linewidth lasers within seconds.Comment: 7 pages, 4 figure

Lattice Resistance and Peierls Stress in Finite-size Atomistic Dislocation Simulations

Atomistic computations of the Peierls stress in fcc metals are relatively scarce. By way of contrast, there are many more atomistic computations for bcc metals, as well as mixed discrete-continuum computations of the Peierls-Nabarro type for fcc metals. One of the reasons for this is the low Peierls stresses in fcc metals. Because atomistic computations of the Peierls stress take place in finite simulation cells, image forces caused by boundaries must either be relaxed or corrected for if system size independent results are to be obtained. One of the approaches that has been developed for treating such boundary forces is by computing them directly and subsequently subtracting their effects, as developed by V. B. Shenoy and R. Phillips [Phil. Mag. A, 76 (1997) 367]. That work was primarily analytic, and limited to screw dislocations and special symmetric geometries. We extend that work to edge and mixed dislocations, and to arbitrary two-dimensional geometries, through a numerical finite element computation. We also describe a method for estimating the boundary forces directly on the basis of atomistic calculations. We apply these methods to the numerical measurement of the Peierls stress and lattice resistance curves for a model aluminum (fcc) system using an embedded-atom potential.Comment: LaTeX 47 pages including 20 figure

Effective mass and band nonparabolicity in remote doped Si/Si0.8Ge0.2 quantum wells

The effective masses in remote doped Si/Si0.8Ge0.2/Si quantum wells having sheet densities, Ns in the range 2 × 1011–1.1 × 1012 cm – 2 have been determined from the temperature dependencies of the Shubnikov–de Haas oscillations. The values obtained increase with magnetic field and Ns. This behavior is taken as evidence for the nonparabolicity of the valence band and accounts for the discrepancies in previously reported masses. Self-consistent band structure calculations for a triangular confinement of the carriers have also been carried out and provide confirmation of the increase in mass with Ns. Theory and experiment give extrapolated Gamma point effective masses of 0.21 and 0.20 of the free-electron mass, respectively

Exploring the Symbolic/Subsymbolic Continuum: A case study of RAAM

Exoplanets orbiting pre-main-sequence stars are laboratories for studying planet evolution processes, including atmospheric loss, orbital migration, and radiative cooling. V1298 Tau, a young solar analog with an age of 23 ± 4 Myr, is one such laboratory. The star is already known to host a Jupiter-sized planet on a 24 day orbit. Here, we report the discovery of three additional planets—all between the sizes of Neptune and Saturn—based on our analysis of K2 Campaign 4 photometry. Planets c and d have sizes of 5.6 and 6.4 R⊕, respectively, and with orbital periods of 8.25 and 12.40 days reside 0.25% outside of the nominal 3:2 mean-motion resonance. Planet e is 8.7 R⊕ in size but only transited once in the K2 time series and thus has a period longer than 36 days, but likely shorter than 223 days. The V1298 Tau system may be a precursor to the compact multiplanet systems found to be common by the Kepler mission. However, the large planet sizes stand in sharp contrast to the vast majority of Kepler multiplanet systems, which have planets smaller than 3 R⊕. Simple dynamical arguments suggest total masses of <28 M⊕ and <120 M⊕ for the c–d and d–b planet pairs, respectively. The implied low masses suggest that the planets may still be radiatively cooling and contracting, and perhaps losing atmosphere. The V1298 Tau system offers rich prospects for further follow-up including atmospheric characterization by transmission or eclipse spectroscopy, dynamical characterization through transit-timing variations, and measurements of planet masses and obliquities by radial velocities