Lattice theory is proposed to provide a formalism for the knowledge base used as a mental model by the operator of a complex system. The ordering relation 'greater than or equal to' is interpreted as 'is caused by', and the lattice becomes a representation of the operator's causal hypotheses about the system. A given system can be thought of causally in different ways (purposes, mechanics, physical form, etc.). Each gives rise to a separate lattice. These are related to each other and to an objective description of the structure and function of the physical system by homomorphic mappings. Errors arise when nodes on the mental lattices are not connected in the same way as the physical system lattice; when the latter changes so that the mental lattice no longer provides an accurate map, even as a homomorphism; or when inverse one-to-many mapping gives rise to ambiguities. Some suggestions are made about the design of displays and decision aids to reduce error.
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http://dx.doi.org/10.1098/rstb.1990.0100 | DOI Listing |
Phys Rev Lett
December 2024
RIKEN, Condensed Matter Theory Laboratory, CPR, Wako, Saitama 351-0198, Japan.
We show that the ground-state expectation value of twisting operator is a topological order parameter for U(1)- and Z_{N}-symmetric symmetry-protected topological (SPT) phases in one-dimensional "spin" systems-it is quantized in the thermodynamic limit and can be used to identify different SPT phases and to diagnose phase transitions among them. We prove that this (nonlocal) order parameter must take values in Nth roots of unity, and its value can be changed by a generalized lattice translation acting as an N-ality transformation connecting distinct phases. This result also implies the Lieb-Schultz-Mattis (LSM) ingappability for SU(N) spins if we further impose a general translation symmetry.
View Article and Find Full Text PDFPhys Rev Lett
December 2024
Massachusetts Institute of Technology, Research Laboratory of Electronics, Cambridge, Massachusetts 02139, USA.
Classical transport of electrons and holes in nanoscale devices leads to heating that severely limits performance, reliability, and efficiency. In contrast, recent theory suggests that interband quantum tunneling and subsequent thermalization of carriers with the lattice results in local cooling of devices. However, internal cooling in nanoscale devices is largely unexplored.
View Article and Find Full Text PDFPhys Rev Lett
December 2024
National University of Singapore, Department of Materials Science and Engineering, 9 Engineering Drive 1, Singapore 117575.
By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moiré materials.
View Article and Find Full Text PDFBy utilizing the time inversion of radiation from spatial dipole arrays, we propose a method for constructing the spatial lattice-type skyrmion arrays under 4 focusing conditions, including Néel-, Bloch-, and Anti-skyrmions/merons. The Richards-Wolf vector diffraction theory is applied to analyze the radiation field emitted by dipole arrays, aiming to determine the incident field required under a high numerical aperture (NA=0.95).
View Article and Find Full Text PDFNPJ Comput Mater
January 2025
Computational Atomic-scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, Kgs. Lyngby, Denmark.
We conduct a systematic investigation of the role of Hubbard U corrections in electronic structure calculations of two-dimensional (2D) materials containing 3 transition metals. Specifically, we use density functional theory (DFT) with the PBE and PBE+U approximations to calculate the crystal structure, band gaps, and magnetic parameters of 638 monolayers. Based on a comprehensive comparison to experiments we first establish that the inclusion of the U correction worsens the accuracy for the lattice constants.
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