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A Bloch decomposition-based stochastic Galerkin method for quantum dynamics with a random external potential

In this paper, we consider the numerical solution of the one-dimensional Schrödinger equation with a periodic lattice potential and a random external potential. This is an important model in solid state physics where the randomness results from complicated phenomena that are not exactly known. Here we generalize the Bloch decomposition-based time-splitting pseudospectral method to the stochastic setting using the generalized polynomial chaos with a Galerkin procedure so that the main effects of dispersion and periodic potential are still computed together. We prove that our method is unconditionally stable and numerical examples show that it has other nice properties and is more efficient than the traditional method. Finally, we give some numerical evidence for the well-known phenomenon of Anderson localization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

International Conference on Vacuum Ultraviolet Radiation Physics, 8th, Lunds Universitet, Sweden, Aug. 4-8, 1986, Proceedings

The interactions of VUV radiation with solids are explored in reviews and reports of recent theoretical and experimental investigations from the fields of atomic and molecular physics, solid-state physics, and VUV instrumentation. Topics examined include photoabsorption and photoionization, multiphoton processes, plasma physics, VUV lasers, time-resolved spectroscopy, synchrotron radiation centers, solid-state spectroscopy, and dynamical processes involving localized levels. Consideration is given to the fundamental principles of photoemission, spin-polarized photoemission, inverse photoemission, semiconductors, organic materials, and adsorbates.

Nilsson, Per-Olof↗

The Center for Applied Physics and Superconducting Technologies (CAPST)

The Department of Energy’s Fermi National Accelerator Laboratory and Northwestern University have established a new collaboration that enhances both institutions’ scientific research portfolios. The Center for Applied Physics and Superconducting Technologies (CAPST) focuses on the science and applications of superconductivity, with expected advances in the fields of particle physics, solid-state physics, materials science, medicine, energy and environmental sciences. CAPST formally recognizes a broad intersection of scientific pursuits and complementary state-of-the-art facilities. The center lays the groundwork for the cross-utilization of technical expertise, facilities, and equipment and establishes a partnership that will foster joint scientific research, mentorship, and new opportunities for researchers, graduate students, and postdoctoral fellows.

36 MATERIALS SCIENCE↗

Nuclear resonance scattering of synchrotron radiation as a unique electronic, structural and thermodynamic probe

Discovery of Moessbauer effect in a nuclear transition was a remarkable development. It revealed how long-lived nuclear states with relatively low energies in the kiloelectron volt (keV) region can be excited without recoil. This new effect had a unique feature involving a coupling between nuclear physics and solid-state physics, both in terms of physics and sociology. Physics coupling originates from the fact that recoilless emission and absorption or resonance is only possible if the requirement that nuclei have to be bound in a lattice with quantized vibrational states is fulfilled, and that the finite electron density on the nucleus couples to nuclear degrees of freedom leading to hyperfine interactions. thus, Moessbauer spectroscopy allows peering into solid-state effects using unique nuclear transitions. Sociological aspects of this coupling had been equally startling and fruitful. The interaction between diverse scientific communities, who learned to use Moessbauer spectroscopy proved to be very valuable. For example, biologists, geologists, chemists, physics, materials scientists, and archeologists, all sharing a common spectroscopic technique, also learned to appreciate the beauty and intricacies of each other's fields. As a laboratory-based technique, Moessbauer spectroscopy matured by the end of the 1970s. Further exciting developments took place when accelerator-based techniques were employed, like synchrotron radiation or 'in-beam'Moessbauer experiments with implanted radioactive ions. More recently, two Moessbauer spectrometers on the surface of the Mars kept the technique vibrant and viable up until present time. In this chapter, the authors look into some of the unique aspects of nuclear resonance excited with synchrotron radiation as a probe of condensed matter, including magnetism, valence, vibrations, and lattice dynamics, and review the development of nuclear resonance inelastic x-ray scattering (NRIXS) and synchrotron Moessbauer spectroscopy (SMS). However, to place these two techniques into some perspective with respect to other methods that yield related information, they display their version of a frequently used map of momentum and energy transfer diagram in figure 17.1. Here, various probes like electrons, neutrons, or light, i.e., Brillouin or Raman, and relatively newer forms of X-ray scattering are placed according to their range of energy and momentum transfer taking place during the measurements. Accordingly, NRIXS is a method that needs to be considered as a complementary probe to inelastic neutron and X-ray scattering, while SMS occupies a unique space due to its sensitivity to magnetism, structural deformations, valence, and spin states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The Superconductor-Superinsulator Transition: S-duality and the QCD on the Desktop

We show that the nature of quantum phases around the superconductor-insulator transition (SIT) is controlled by charge-vortex topological interactions, and does not depend on the details of material parameters and disorder. We find three distinct phases, superconductor, superinsulator, and bosonic topological insulator. The superinsulator is a state of matter with infinite resistance in a finite temperature range, which is the S-dual of the superconductor and in which charge transport is prevented by electric strings binding charges of opposite sign. The electric strings ensuring linear confinement of charges are generated by instantons and are dual to superconducting Abrikosov vortices. Material parameters and disorder enter the London penetration depth of the superconductor, the string tension of the superinsulator and the quantum fluctuation parameter driving the transition between them. They are entirely encoded in four phenomenological parameters of a topological gauge theory of the SIT. Finally, we point out that, in the context of strong coupling gauge theories, the many-body localization phenomenon that is often referred to as an underlying mechanism for superinsulation is a mere transcription of the well-known phenomenon of confinement into solid-state physics language and is entirely driven by endogenous disorder embodied by instantons with no need of exogenous disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Gaps labeling theorem for the bubble-diamond self-similar graphs

Abstract Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.

Physics↗

Solving many-body Schrödinger equations with kinetic energy partition method

We present a general formulation of our previously developed kinetic energy partition (KEP) method for solving many-bodySchrödinger equations. In atomic physics, as well as in general molecular and solid state physics, solving many-electronSchrödinger equations is a very challenging task, often called Dirac’s challenge. The central problem is how to properly handle the electron–electron Coulomb repulsion interactions. Using the KEP solution scheme, in addition to dividing the kinetic energy into partial terms, the electron–electron Coulomb interaction is also separated into parts to be associated with a “negative mass” kinetic energy term. Therefore, the full Hamiltonian can be expressed as a simple sum of subsystem Hamiltonians, each representing an effective one-body problem. Using a Hartree-like product in constructing the wave-function, we achieve fast convergence in the calculations of the ground state energies. First, the model Moshinsky atoms are used to illustrate the solution procedure. We then apply this new KEP method to harmonium atoms and obtain precise energies with an error less than 5% using only two basis functions from each subsystem. It is thus very promising that this methodology, when further extended, can be useful for general many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Lattice Anharmonicity and Thermal Conductivity from Compressive Sensing of First-Principles Calculations

First-principles prediction of lattice thermal conductivity K L of strongly anharmonic crystals is a long-standing challenge in solid state physics. Using recent advances in information science, we propose a systematic and rigorous approach to this problem, compressive sensing lattice dynamics (CSLD). Compressive sensing is used to select the physically important terms in the lattice dynamics model and determine their values in one shot. Non-intuitively, high accuracy is achieved when the model is trained on first-principles forces in quasi-random atomic configurations. The method is demonstrated for Si, NaCl, and Cu 12 Sb 4 S 13 , an earth-abundant thermoelectric with strong phononphonon interactions that limit the room-temperature K L to values near the amorphous limit.

36 MATERIALS SCIENCE↗

Solid state crystal physics at very low temperatures

The properties of nearly perfect crystals was studied at cryogenic temperatures. A large Helium 3 and Helium 4 dilution refrigerator has been assembled, and is described. A cryostat suitable for cooling a 35 liter volume to .020 Kelvin was designed and constructed, together with instrumentation to observe the properties of nearly perfect crystals.

Davis, W.↗

Solid state crystal physics at very low temperatures

The mechanical dissipation (Q) and resonant frequency of a 15 kg silicon crystal were measured at cryogenic temperatures. In the experiment described, temperature control was incorporated to reduce the time derivative of the temperature. The results of the Q measurements with and without this temperature control are quite different. Measurements of the resonant frequency of the fundamental longitudinal mode of the silicon crystal from 6 to 300 Kelvin are presented and discussed with respect to temperature, df/dT. It is observed that frequency increases as temperature decreases down to about 16 Kelvin, i.e. dt/dT is negative. However, below this temperature the frequency decreases as temperature decreases, i.e. dt/dT is positive. It is suggested that this behavior is related to the coefficient of thermal contraction of silicon, which changes sign at 18 Kelvin. Continuation of these experiments to 20 mK is discussed.

Davis, W.↗