Fano interference in quantum resonances from angle-resolved elastic scattering

Asymmetric spectral line shapes are a hallmark of interference of a quasi-bound state with a continuum of states. Such line shapes are well known for multichannel systems, for example, in photoionization or Feshbach resonances in molecular scattering. On the other hand, in resonant single channel scattering, the signature of such interference may disappear due to the orthogonality of partial waves. Here, we show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles also in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules with detection angle, in excellent agreement with theoretical predictions from full quantum scattering calculations. Using a model description for the partial wave interference, we can disentangle the resonant and background contributions and extract the relative phase responsible for the characteristic Fano-like profiles from our experimental measurements.

The statistical mechanics of near-BPS black holes

Due to the failure of thermodynamics for low temperature near-extremal black holes, it has long been conjectured that a "thermodynamic mass gap'' exists between an extremal black hole and the lightest near-extremal state. For non-supersymmetric near-extremal black holes in Einstein gravity with an AdS2 throat, no such gap was found. Rather, at that energy scale, the spectrum exhibits a continuum of states, up to non-perturbative corrections. In this paper, we compute the partition function of near-BPS black holes in supergravity where the emergent, broken, symmetry is PSU(1,1|2). To reliably compute this partition function, we show that the gravitational path integral can be reduced to that of a N=4 supersymmetric extension of the Schwarzian theory, which we define and exactly quantize. In contrast to the non-supersymmetric case, we find that black holes in supergravity have a mass gap and a large extremal black hole degeneracy consistent with the Bekenstein-Hawking area. Our results verify a plethora of string theory conjectures, concerning the scale of the mass gap and the counting of extremal micro-states.

Dispersive bands of bound states in the continuum

Bound states in the continuum (BICs), i.e. highly-localized modes with energy embedded in the continuum of radiating waves, have provided in the past decade a new paradigm in optics and photonics, especially at the nanoscale, with a range of applications from nanophotonics to optical sensing and laser design. Here, we introduce the idea of a crystal made of BICs, in which an array of BICs is indirectly coupled via a common continuum of states resulting in a tight-binding dispersive energy miniband embedded in the spectrum of radiating waves. The results are illustrated for a chain of optical cavities side-coupled to a coupled-resonator optical waveguide with nonlocal contact points.

Loss and Dissipation: The RLC Circuit

The effects of energy loss or dissipation is well-known and understood in classical systems. It is the source of heat in LCR circuits and in the application of brakes in a vehicle or why a struck bell does not ring indefinitely. Understanding quantum behavior begins with understanding the Hamiltonian for the problem. Classically, loss arises from a coupling of the Hamiltonian for an isolated quantum system to a continuum of states. We look at such a Hamiltonian and develop the equations of motion following the rules of quantum mechanics and find that even in a quantum system, this coupling leads to loss and non-conservation of probability in the otherwise isolated quantum system. This is the Weisskopf–Wigner formalism that is then used to understand the quantum LCR circuit. The same formalism is used in Chapter 15 for the decay of isolated quantum systems by coupling to the quantum vacuum and the resulting emission of a photon.

Continuous flexibility analysis of SARS-CoV-2 spike prefusion structures

Using a new consensus-based image-processing approach together with principal component analysis, the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state have been analysed. These studies revealed concerted motions involving the receptor-binding domain (RBD), N-terminal domain, and subdomains 1 and 2 around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. It is shown that in this data set there are not well defined, stable spike conformations, but virtually a continuum of states. An ensemble map was obtained with minimum bias, from which the extremes of the change along the direction of maximal variance were modeled by flexible fitting. The results provide a warning of the potential image-processing classification instability of these complicated data sets, which has a direct impact on the interpretability of the results.

Analysis of Protein Disorder Predictions in the Light of a Protein Structural Alphabet

Intrinsically-disordered protein (IDP) characterization was an amazing change of paradigm in our classical sequence-structure-function theory. Moreover, IDPs are over-represented in major disease pathways and are now often targeted using small molecules for therapeutic purposes. This has had created a complex continuum from order-that encompasses rigid and flexible regions-to disorder regions; the latter being not accessible through classical crystallographic methodologies. In X-ray structures, the notion of order is dictated by access to resolved atom positions, providing rigidity and flexibility information with low and high experimental B-factors, while disorder is associated with the missing (non-resolved) residues. Nonetheless, some rigid regions can be found in disorder regions. Using ensembles of IDPs, their local conformations were analyzed in the light of a structural alphabet. An entropy index derived from this structural alphabet allowed us to propose a continuum of states from rigidity to flexibility and finally disorder. In this study, the analysis was extended to comparing these results to disorder predictions, underlying a limited correlation, and so opening new ideas to characterize and predict disorder.

Continuous flexibility analysis of SARS-CoV-2 Spike prefusion structures

With the help of novel processing workflows and algorithms, we have obtained a better understanding of the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state. We have re-analyzed previous cryo-EM data combining 3D clustering approaches with ways to explore a continuous flexibility space based on 3D Principal Component Analysis. These advanced analyses revealed a concerted motion involving the receptor-binding domain (RBD), N-terminal domain (NTD), and subdomain 1 and 2 (SD1 & SD2) around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. We show that in this dataset there are not well-defined, stable, spike conformations, but virtually a continuum of states moving in a concerted fashion. We obtained an improved resolution ensemble map with minimum bias, from which we model by flexible fitting the extremes of the change along the direction of maximal variance. Moreover, a high-resolution structure of a recently described biochemically stabilized form of the spike is shown to greatly reduce the dynamics observed for the wild-type spike. Our results provide new detailed avenues to potentially restrain the spike dynamics for structure-based drug and vaccine design and at the same time give a warning of the potential image processing classification instability of these complicated datasets, having a direct impact on the interpretability of the results.

A Versatile Stochastic Duel Game

This paper deals with a standard stochastic game model with a continuum of states under the duel-type setup. It newly proposes a hybrid model of game theory and the fluctuation process, which could be applied for various practical decision making situations. The unique theoretical stochastic game model is targeted to analyze a two-person duel-type game in the time domain. The parameters for strategic decisions including the moments of crossings, prior crossings, and the optimal number of iterations to get the highest winning chance are obtained by the compact closed joint functional. This paper also demonstrates the usage of a new time based stochastic game model by analyzing a conventional duel game model in the distance domain and briefly explains how to build strategies for an atypical business case to show how this theoretical model works.