Interactions and Mobility Edges: Observing the Generalized Aubry-André Model.

Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge protected by a duality symmetry. These one-dimensional tight-binding models can be viewed as a generalization of the well-known Aubry-André model, with an energy-dependent self-duality condition that constitutes an analytical mobility edge relation. By adiabatically preparing low and high energy eigenstates of this model system and performing microscopic measurements of their participation ratio, we track the evolution of the mobility edge as the energy-dependent density of states is modified by the model's tuning parameter. Our results show strong deviations from single-particle predictions, consistent with attractive interactions causing both enhanced localization of the lowest energy state due to self-trapping and inhibited localization of high energy states due to screening. This study paves the way for quantitative studies of interaction effects on self-duality induced mobility edges.

Surveying the Side-Chain Network Approach to Protein Structure and Dynamics: The SARS-CoV-2 Spike Protein as an Illustrative Case.

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.

Quasinormal Modes and the Hawking-Unruh Effect in Quantum Hall Systems: Lessons from Black Hole Phenomena.

In this work, we propose the quantum Hall system as a platform for exploring black hole phenomena. By exhibiting deep rooted commonalities between the 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, bear 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.

From Quantum Chemistry to Networks in Biology: A Graph Spectral Approach to Protein Structure Analyses.

In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum chemistry, biology of polymer conformations, matrix mathematics, and percolation theory. We then explicitly provide the method for constructing the protein structure network in terms of noncovalently interacting amino acid side chains and show how a mine of information can be obtained from the graph spectra of these networks. Employing suitable mathematical approaches, such as the use of a weighted, Laplacian matrix to generate the spectra, enables us to develop rigorous methods for network comparison and to identify crucial nodes responsible for the network integrity through a perturbation approach. Our scoring methods have several applications in structural biology that are elusive to conventional methods of analyses. Here, we discuss the instances of (a) protein structure comparison that includes the details of side chain connectivity, (b) contribution to node clustering as a function of bound ligand, explaining the global effect of local changes in phenomena such as allostery, and (c) identification of crucial amino acids for structural integrity, derived purely from the spectra of the graph. We demonstrate how our method enables us to obtain valuable information on key proteins involved in cellular functions and diseases such as GPCR and HIV protease and discuss the biological implications. We then briefly describe how concepts from percolation theory further augment our analyses. In our concluding perspective for future developments, we suggest a further unifying approach to protein structure analyses and a judicious choice of questions to employ our methods for larger, more complex networks, such as metabolic and disease networks.

Charge fractionalization in a mesoscopic ring.

We study the fractionalization of an electron tunneling into a strongly interacting electronic one-dimensional ring. As a complement to transport measurements in quantum wires connected to leads, we propose noninvasive measures involving the magnetic field profile around the ring to probe this fractionalization. In particular, we show that the magnetic field squared produced by the electron and the power that it would induce in a detector exhibit anisotropic profiles that depend on the degree of fractionalization. We contrast true fractionalization with two other scenarios which could mimic it-quantum superposition and classical probabilistic electron insertion. We show that the proposed field-dependent measures and those of the persistent current can distinguish between these three scenarios.

Majorana fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials.

We present a unified study of the effect of periodic, quasiperiodic, and disordered potentials on topological phases that are characterized by Majorana end modes in one-dimensional p-wave superconducting systems. We define a topological invariant derived from the equations of motion for Majorana modes and, as our first application, employ it to characterize the phase diagram for simple periodic structures. Our general result is a relation between the topological invariant and the normal state localization length. This link allows us to leverage the considerable literature on localization physics and obtain the topological phase diagrams and their salient features for quasiperiodic and disordered systems for the entire region of parameter space.

Topological insulator magnetic tunnel junctions: quantum Hall effect and fractional charge via folding.

We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized fractional charge, also taking into account interaction effects for the 2D case. We show that the effects of tunneling are topologically equivalent to a certain deformation or folding of the sample geometry. Our key advance is the realization that the quantum Hall or fractional charge physics can appear in the presence of only a single magnet unlike previous proposals which involve magnetic domain walls on the surface or edges of topological insulators, respectively. We give illustrative topological folding arguments to prove our results and show that for the 2D case our results are robust even in the presence of interactions.

A glimpse of quantum phenomena in optical lattices.

Optical lattices in cold atomic systems offer an excellent setting for realizing quantum condensed matter phenomena. Here, a glimpse of such a setting is provided for the non-specialist. Some basic aspects of cold atomic gases and optical lattices are reviewed. Quantum many-body physics is explored in the case of interacting bosons on a lattice. Quantum behaviour in the presence of a potential landscape is examined for three different cases: a hexagonal lattice potential, a quasi-periodic potential and a disorder potential.

Random network behaviour of protein structures.

Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus imperative that, apart from the protein backbone, other tunable degrees of freedom be accountable. Here, we focus on side-chain interactions, which non-covalently link amino acids in folded proteins to form a network structure. At a coarse-grained level, we show that the network conforms remarkably well to realizations of random graphs and displays associated percolation behavior. Thus, within the rigid framework of the protein backbone that restricts the structure space, the side-chain interactions exhibit an element of randomness, which account for the functional flexibility and diversity shown by proteins. However, at a finer level, the network exhibits deviations from these random graphs which, as we demonstrate for a few specific examples, reflect the intrinsic uniqueness in the structure and stability, and perhaps specificity in the functioning of biological proteins.

Understanding protein structure from a percolation perspective.

Underlying the unique structures and diverse functions of proteins are a vast range of amino-acid sequences and a highly limited number of folds taken up by the polypeptide backbone. By investigating the role of noncovalent connections at the backbone level and at the detailed side-chain level, we show that these unique structures emerge from interplay between random and selected features. Primarily, the protein structure network formed by these connections shows simple (bond) and higher order (clique) percolation behavior distinctly reminiscent of random network models. However, the clique percolation specific to the side-chain interaction network bears signatures unique to proteins characterized by a larger degree of connectivity than in random networks. These studies reflect some salient features of the manner in which amino acid sequences select the unique structure of proteins from the pool of a limited number of available folds.

Correlators and fractional statistics in the quantum Hall bulk.

We derive one-particle and two-particle correlators of anyons in the lowest Landau level. We show that the two-particle correlator exhibits signatures of fractional statistics which can distinguish anyons from their fermionic and bosonic counterparts. These signatures include the zeros of the two-particle correlator and its exclusion behavior. We find that the one-particle correlator in finite geometries carries valuable information relevant to experiments in which quasiparticles on the edge of a quantum Hall system tunnel through its bulk.

Signatures of fractional statistics in noise experiments in quantum Hall fluids.

The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross-current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a bunching effect, while for higher states in the Jain sequences they should exhibit an "antibunching" effect.

h/e magnetic flux modulation of the energy gap in nanotube quantum dots.

We report experiments on quantum dot single-electron-tunneling (SET) transistors made from short multiwall nanotubes and threaded by magnetic flux. Such systems allow us to probe the electronic energy spectrum of the nanotube and its dependence on the magnetic field. Evidence is provided for the interconversion between gapped (semiconducting) and ungapped (metallic) states. Our tubes exhibit h/e-period magnetic flux dependence, in agreement with simple tight-binding calculations.

Critical dynamics of superconductors in the charged regime.

We investigate the finite temperature critical dynamics of three-dimensional superconductors in the charged regime, described by a transverse gauge field coupling to the superconducting order parameter. Assuming relaxational dynamics for both the order parameter and the gauge fields, within a dynamical renormalization group scheme, we find a new dynamic universality class characterized by a finite fixed point ratio between the transport coefficients associated with the order parameter and gauge fields, respectively. We find signatures of this universality class in various measurable physical quantities, and in the existence of a universal amplitude ratio formed by a combination of physical quantities.

Cooper-pair tunneling in junctions of singlet quantum Hall States and superconductors.

We propose tunnel junctions of a Hall bar and a superconducting lead for observing Cooper-pair tunneling into singlet fractional quantum Hall edge states. These tunnel junctions provide a natural means of extracting precise information of the spin polarization and the filling factor of the state. The low energy regime of one of the setups is governed by a novel quantum entangled fixed point.

Revisiting the Hanbury Brown-Twiss setup for fractional statistics.

The Hanbury Brown-Twiss experiment has proved to be an effective means of probing statistics of particles. Here, in a setup involving edge-state quasiparticles in a fractional quantum Hall system, we show that a variant of the experiment composed of two sources and two sinks can be used to unearth fractional statistics. We find a clearcut signature of the statistics in the equal-time current-current correlation function for quasiparticle currents emerging from the two sources and collected at the sinks.

Quantum entanglement in carbon nanotubes.

With the surge of research in quantum information, the issue of producing entangled states has gained prominence. Here, we show that judiciously bringing together two systems of strongly interacting electrons with vastly differing ground states-the gapped BCS superconductor and the Luttinger liquid-can result in quantum entanglement. We propose three sets of measurements involving single-walled metallic carbon nanotubes which have been shown to exhibit Luttinger liquid physics, to test our claim and as nanoscience experiments of interest in and of themselves.