We consider the phase diagram of three dimensional topological insulators  and Weyl semimetal [2-4] in the disorder vs. mass parameter plane. The phase transition from Weyl/Dirac semimetals to metals is described by the scaling of density of states , where the critical exponents are expressed by the correlation exponent and the dynamical exponent. The scaling behaviors of conductivity and density of states across other phase boundaries, namely those across the Chern insulator and Weyl semimetal and those across the Chern insulator and metal are discussed in details [3,4]. The dynamics of wave packets in Weyl and Dirac semimetals is well described by the scaling of the velocity of the ballistic motion, which is numerically demonstrated to vanish toward the critical point . In addition, we demonstrate that the machine learning the wave functions of these systems enables us to draw the phase diagrams . We emphasize the advantage of using the wave functions in k-space.  K. Kobayashi, T. Ohtsuki, K.-I. Imura, Physical review letters 110, 236803 (2013).  S. Liu, T. Ohtsuki, R. Shindou, Physical Review Letters 116, 066401 (2016).  X. Luo, B. Xu, T. Ohtsuki, R. Shindou, Physical Review B 97, 045129 (2018).  A.L. Szabo, B. Roy, arXiv: 2002.09475.  K. Kobayashi, T. Ohtsuki, K.-I. Imura, I.F. Herbut, Physical review letters 112, 016402 (2014).  K. Kobayashi, M. Wada, and T. Ohtsuki, Phys. Rev. Research 2, 022061(R) (2020)  T. Ohtsuki, T Mano, Journal of the Physical Society of Japan 88, 123704 (2020).
We review the construction of a higher order topological Dirac semimetal (HOTDSM) by adding a time reversal and four-fold rotational symmetry breaking Wilson mass term to a first-order DSM. We examine the stability of such a system in the presence of random charge impurities. Just like its first-order counterpart, the HOTDSM proves to be stable at sufficiently weak disorder, and it undergoes a quantum phase transition into a diffusive metal phase at a critical disorder strength. At the same time the corresponding one-dimensional hinge modes gradually fade into the metallic bulk. The universality class of the metallic quantum critical point is the same within numerical accuracy, regardless of the order of the topological phase. This suggests an emergent superuniversality in the family of topological Dirac semimetals.
In genetic networks, information of relevance to the organism is represented by the concentrations of transcription factor molecules. In order to extract this information the cell must effectively “measure” these concentrations, but there are physical limits to the precision of these measurements. We explore this trading between bits of precision in measuring concentration and bits of relevant information that can be extracted, using the gap gene network in the early fruit fly embryo as an example. We argue that cells in the fly embryo can extract all the available information about their position if the concentration measurements approach the physical limits to information capacity, and that realistic molecular mechanisms can reach these abstract bounds if their parameters are selected appropriately.
As a global society we have been burning fossil fuels to meet our energy and transportation needs since the start of the industrial revolution. This has resulted in atmospheric CO2 concentrations much greater than at any other time during the last 650,000 years. That concentration reached a record 415 parts per million in May 2019. The replacement of fossil fuels with renewables, advances in energy efficiency, and carbon capture and storage are among the key strategies required to prevent warming beyond 2°C within this century. But they will not be enough. We need to ramp up our efforts in reducing CO2 emissions, and then we need to do even more. The Earth’s natural systems, such as forests and oceans, are capable of removing roughly half of global CO2 emissions each year, while the rest steadily accumulates in the atmosphere. Until now, our best approach to avoiding the worst impacts of climate change was simply to avoid such emissions in the first place. But because of our failure to act quickly and at a large enough scale, we are now faced with the need to go beyond that strategy—to actually start removing CO2 directly from the air. Trees and oceans already do this, but these systems are overwhelmed. Manufactured or synthetic removal systems are designed to pull CO2 from the atmosphere, and at a much faster rate than natural systems. This talk will review both the promise and pitfalls of this approach.