In this work, we propose the quantum Hall system as a platform for exploring black hole phenomena. By exhibiting deep rooted commonalities between lowest Landau level and spacetime symmetries, we show that features of both quantum Hall and gravitational systems can be elegantly captured by a simple quantum mechanical model, the inverted harmonic oscillator. Through this correspondence, we argue that radiation phenomena in gravitational situations, such as presented by W. G. Unruh and S. Hawking, bears a parallel with saddle-potential scattering of quantum Hall quasiparticles. We also find that scattering by the quantum Hall saddle potential can mimic the signature quasinormal modes in black holes, such as theoretically demonstrated through Gaussian scattering off a Schwarzschild black hole by C. V. Vishveshwara. We propose a realistic quantum Hall point contact setup for probing these temporally decaying modes in quasiparticle tunneling, offering a new mesoscopic parallel for black hole ringdown.
Network theory-based approaches provide valuable insights into the variations in global structural connectivity between different dynamical states of proteins. Our objective is to review network-based analyses to elucidate such variations, especially in the context of subtle conformational changes. We present technical details of the construction and analyses of protein structure networks, encompassing both the non-covalent connectivity and dynamics. We examine the selection of optimal criteria for connectivity based on the physical concept of percolation. We highlight the advantages of using side-chain-based network metrics in contrast to backbone measurements. As an illustrative example, we apply the described network approach to investigate the global conformational changes between the closed and partially open states of the SARS-CoV-2 spike protein. These conformational changes in the spike protein is crucial for coronavirus entry and fusion into human cells. Our analysis reveals global structural reorientations between the two states of the spike protein despite small changes between the two states at the backbone level. We also observe some differences at strategic locations in the structures, correlating with their functions, asserting the advantages of the side-chain network analysis. Finally, we present a view of allostery as a subtle synergistic-global change between the ligand and the receptor, the incorporation of which would enhance drug design strategies.
In this article, we present a systematic study of quantum statistics and dynamics of a pair of anyons in the lowerst Landau level (LLL), of direct relevance to quasiparticle excitations in the quantum Hall bulk. We develop the formalism for such a two-dimensional setting of two charged particles subject to a transverse field, including fractional angular momentum states and the related algebra stemming from the anyonic boundary condition, coherent state descriptions of localized anyons, and bunching features associated with such anyons. We analyze the dynamic motion of the anyons in a harmonic trap, emphasizing phase factors emerging from exchange statistics. We then describe non-equilibrium dynamics upon the application of a saddle potential, elaborating on its role as a squeezing operator acting on LLL coherent states, and its action as a beam splitter for anyons. Employing these potential landscapes as building blocks, we analyze anyon dynamics in a quantum Hall bulk interferometer. We discuss parallels between the presented LLL setting and other realms, extensively in the context of quantum optics, whose formalism we heavily borrow from, and briefly in that of black hole phenomena.
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