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We theoretically consider disorder and temperature effects on the integer quantum Hall effect (IQHE) using a variety of distinct and complementary analytical and numerical techniques. In particular, we address simple, physical, and experimentally relevant questions: How does disorder and/or temperature affect the IQHE plateau width? Does the plateau width increase or decrease with disorder and/or temperature? What happens to the peak in the longitudinal conductance with increasing disorder/temperature? Does the longitudinal conductance obey any universal scaling property? Is there "floating" with increasing disorder and/or decreasing magnetic field? Can disorder destroy the IQHE? Is there an IQHE to localization transition? What is the Landau level dependence of the plateau width? Our detailed theory provides answers to these and other related experimentally relevant questions. We discuss our results in the context of existing experimental results and suggest future experiments arising from our work. A key finding is that disorder and temperature are intrinsically connected in affecting IQHE, and there is an intricate interplay between them leading to nonmonotonicity in how the IQHE plateau width behaves as a function of increasing disorder. Both must be considered on an equal footing in understanding IQHE experiments., Comment: 24 pages, 18 figures

A recent experiment [Cohen et al., Science 382, 542 (2023)] observed a quantized $e^2/2h$ conductance tunneling into a fractional quantum hall edge in the strong coupling limit, which is consistent with the prediction of a quantum Hall transformer. We model this quantum point contact (QPC) as a quantum wire with a spatially-varying Luttinger parameter and a back-scattering impurity and use a numerical solution to find the wavepacket scattering and microwave (i.e. finite frequency) has conductance at the interface. We then compare the microwave conductance to an analytic solution of a Luttinger liquid with an abruptly varying Luttinger parameter and a back-scattering impurity, which is obtained by mapping the problem to a boundary sine-Gordon (BSG) model. Finally, we show that the quantum Hall transformer can survive the inclusion of the domain wall which is expected to occur in a wide QPC, which is experimentally relevant, provided the momentum change in the QPC is generated by electrostatics. We find that back-scattering generated by the domain wall is of an order of magnitude consistent with the experiment., Comment: 5 pages, 3 figures

In ergodic quantum spin chains, locally conserved quantities such as energy or particle number generically evolve according to hydrodynamic equations as they relax to equilibrium. We investigate the complexity of simulating hydrodynamics at infinite temperature with multiple methods: time evolving block decimation (TEBD), TEBD with density matrix truncation (DMT), the recursion method with a universal operator growth hypothesis (R-UOG), and operator-size truncated (OST) dynamics. Density matrix truncation and the OST dynamics give consistent dynamical correlations to $t=60/J$ and diffusion coefficients agreeing within 1%. TEBD only converges for $t\lesssim 20$, but still produces diffusion coefficients accurate within 1%. The universal operator growth hypothesis fails to converge and only matches other methods on short times. We see no evidence of long-time tails in either DMT or OST calculations of the current-current correlator, although we cannot rule out that they appear at longer times. We do observe power-law corrections to the energy density correlator. At finite wavelength, we observe a crossover from purely diffusive, overdamped decay of the energy density, to underdamped oscillatory behavior similar to that of cold atom experiments. We dub this behavior "hot band second sound" and offer a microscopically-motivated toy model., Comment: 18 pages, 13 figures

Discrete time crystals are novel phases of matter that break the discrete time translational symmetry of a periodically driven system. In this work, we propose a classical system of weakly-nonlinear parametrically-driven coupled oscillators as a testbed to understand these phases. Such a system of parametric oscillators can be used to model period-doubling instabilities of Josephson junction arrays as well as semiconductor lasers. To show that this instability leads to a discrete time crystal we first show that a certain limit of the system is close to Langevin dynamics in a symmetry breaking potential. We numerically show that this phase exists even in the presence of Ising symmetry breaking using a Glauber dynamics approximation. We then use a field theoretic argument to show that these results are robust to other approximations including the semiclassical limit when applied to dissipative quantum systems., Comment: 10 pages, 3 figures

The O(3) non-linear sigma model (NLSM) is a prototypical field theory for QCD and ferromagnetism, and provides a simple system in which to study topological effects. In lattice QCD, the gradient flow has been demonstrated to remove ultraviolet singularities from the topological susceptibility. In contrast, lattice simulations of the NLSM find that the topological susceptibility diverges in the continuum limit, even in the presence of the gradient flow. We introduce a $\theta$-term and analyze the topological charge as a function of $\theta$ under the gradient flow. Our results show that divergence persists in the presence of the flow, even at non-zero $\theta$., Comment: The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology

The handbook provides guidelines for the handling and storage of conventional NiCd flight batteries. The guidelines are based on many years of experience with ground and in-flight handling of batteries. The overall goal is to minimize the deterioration and irreversible effects of improper handling of NiCd flight batteries on flight performance. A secondary goal is to provide the reader with an understanding, in nonanalytical terms, of the degradation mechanisms of NiCd cells and how these mechanisms are affected by improper ground handling of flight hardware. Section 2 provides the reader with a brief introduction to NiCd cells. The effects of the environment on NiCd batteries are discussed in Section 3, and Section 4 contains 12 guidelines for battery handling and storage with supporting rationale for each guideline. The appendix provides a synopsis of NiCd cell design and evolution over 30 years of space flight on Goddard Space Flight Center (GSFC) satellites, along with a chronological review of key events that influenced the design of NiCd cells being flown today.

Nickel-hydrogen (NiH2) batteries are finding more applications in the aerospace energy storage. Since 1983, NiH2 batteries have become the primary energy storage system used for Geosynchronous-Orbit (GEO) Satellites. The first NASA application for NiH2 batteries was the Low Earth Orbit (LEO) Hubble Space Telescope Satellite launched in 1990. The handbook was prepared as a reference book to aid in the application of this technology. That is, to aid in the cell and battery design, procurement, testing, and handling of NiH2 batteries. The design of individual pressure vessel NiH2 cells is covered in Chapter l. LEO and GEO applications and their requirements are discussed in Chapter 2. The design of NiH2 batteries for both GEO and LEO applications is discussed in Chapter 3. Advanced design concepts such as the common pressure vessel and bipolar NiH2 batteries are described in Chapter 4. Performance data are presented in Chapter 5. Storage and handling of the NiH2 cells and batteries are discussed in Chapter 6. Standard test procedures are presented in Chapter 7. Cell and battery procurements are discussed in Chapter 8. Finally, safety procedures are discussed in Chapter 9.

Over the past 5 years, COMSAT has performed numerous destructive physical analyses (DPA's) on NASA-Goddard-supplied nickel-cadmium (Ni/Cd) cells. The samples included activated but uncycled cells, wet stored cells, cycled cells, and anomalous cells. The DPA's provided visual, morphological, and chemical analyses of the cell components. The DPA data for the analyzed cells are presented. For the cells investigated, the leading cause of poor performance, as determined by DPA, has been poor negative electrode utilization, which resulted in negative-electrode-limiting operation.

This document contains the proceedings of the 20th annual Battery Workshop held at Goddard Space Flight Center, Greenbelt, Maryland on November 4-5, 1987. The workshop attendees included manufacturers, users, and government representatives interested in the latest developments in battery technology as they relate to high reliability operations and aerospace use. The subjects covered included lithium cell technology and safety improvements, nickel-cadmium electrode technology along with associated modifications, flight experience and life testing of nickel-cadmium cells, and nickel-hydrogen applications and technology.

This document contains the proceedings of the 21st annual Battery Workshop held at Goddard Space Flight Center, Greenbelt, Maryland on November 1-3, 1988. The Workshop attendees included manufacturers, users, and government representatives interested in the latest developments in battery technology as they relate to high reliability operations and aerospace use. The subjects covered included battery testing methodologies and criteria, life testing of nickel-cadmium cells, testing and operation of nickel-hydrogen batteries in low earth orbit, and nickel-hydrogen technology issues and concerns.

The following topics are presented in viewgraph format: Cosmic Background Explorer (COBE) mission background; battery background and specifications; cell history; battery mechanical/structural design; battery test data; and flowcharts of the various battery approval procedures.

The following topics are covered in viewgraph format: Solar Maximum Mission (SSM) background; battery background and specifications; and battery rundown tests.

A survey of the batteries used in the LEO and GEO missions at the Goddard Space Flight Center is described. For each spacecraft, a tentative launch date is given, along with relevant battery parameters including battery size and description, depth-of-discharge, predicted mission temperature, and life requirement.

A survey of the batteries used in the low earth orbit (LEO) and geosynchronous earth orbit (GEO) missions at the Goddard Space Flight Center is described. For each spacecraft, tentative launch date is given, along with relevant battery parameters including battery size and description, depth-of-discharge, predicted mission temperature, and life requirement.

Evaluation of the long term effects on aerospace nickel cadmium cells is described. A number of 6Ah and 12Ah capacity cells which were stored in shorted condition for 9 to 11 years at the Goddard Space Flight Center were selected for the study. Of the three tests which were initiated (initial and final destruction analyses of the test cells, electrical characterization tests, and life cycling tests) only the electrical characterization tests are completed; the other tests are scheduled to be completed by February 1987. The preliminary electrial performance data from the life cycling test and chemical composition data from the destructive testing indicate no anomalous behavior.

The subjects covered include: lithium cell technology and safety improvements; nickel-cadmium separator and electrode technology along with associated modifications; flight experience and life testing of nickel-cadmium cell; and nickel-hydrogen applications and technology.