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Quantized classical response from spectral winding topology.

ABSTRACT: Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge states as their topological winding. In this work, we discover the totally new paradigm of quantized classical response, which is based on the spectral winding number in the complex spectral plane, rather than the winding of eigenstates in momentum space. Such quantized response is classical insofar as it applies to phenomenological non-Hermitian setting, arises from fundamental mathematical properties of the Green's function, and shows up in steady-state response, without invoking a conventional linear response theory. Specifically, the ratio of the change in one quantity depicting signal amplification to the variation in one imaginary flux-like parameter is found to display fascinating plateaus, with their quantized values given by the spectral winding numbers as the topological invariants.

SUBMITTER: Li L

PROVIDER: S-EPMC8421445 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Studies in our laboratory over the last three decades have shown that the Chinese hamster dihydrofolate reductase (DHFR) origin of replication corresponds to a broad zone of inefficient initiation sites distributed throughout the spacer between the convergently transcribed DHFR and 2BE2121 genes. It is clear from mutational analysis that none of these sites is genetically required for controlling origin activity. However, the integrity of the promoter of the DHFR gene is needed to activate the downstream origin, while the 3' processing signals prevent invasion and inactivation of the downstream origin by transcription forks. Several other origins in metazoans have been shown to correspond to zones of inefficient sites, while a different subset appears to be similar to the fixed replicators that characterize origins in S. cerevisiae and lower organisms. These observations have led us to suggest a model in which the mammalian genome is dotted with a hierarchy of degenerate, redundant, and inefficient replicators at intervals of a kilobase or less, some of which may have evolved to be highly circumscribed and efficient. The activities of initiation sites are proposed to be largely regulated by local transcription and chromatin architecture. Recently, we and others have devised strategies for identifying active origins on a genome-wide scale in order to define their distributions between fixed and dispersive origin types and to detect relationships among origins, genes, and epigenetic markers. The global pictures emerging are suggestive but far from complete and appear to be plagued by some of the same uncertainties that have led to conflicting views of individual origins in the past (particularly DHFR). In this paper, we will trace the history of origin discovery in mammalian genomes, primarily using the well-studied DHFR origin as a model, because it has been analyzed by nearly every available origin mapping technique in several different laboratories, while many origins have been identified by only one. We will address the strengths and shortcomings of the various methods utilized to identify and characterize origins in complex genomes and will point out how we and others were sometimes led astray by false assumptions and biases, as well as insufficient information. The goal is to help guide future experiments that will provide a truly comprehensive and accurate portrait of origins and their regulation. After all, in the words of George Santayana, "Those who do not learn from history are doomed to repeat it."

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Quantized classical response from spectral winding topology.

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