Quantum effects in glasses at ultra-low temperatures

Glasses at ultra-low temperatures present several puzzling phenomena. A notable example is the anomalous (i.e., non-Debye) behavior of thermodynamic quantities at temperatures lower than 1 K. A comprehensive quantum theory able to explain these phenomena has not been developed so far. In this thesis, we tackle this long-standing problem with different and innovative perspectives, employing various physical models, and several analytical and numerical techniques. We mainly explore two different but complementary approaches. In the first approach, we investigate the thermodynamics of models for ultra-low temperature glasses, with particular attention to mean-field models. Specifically, exploiting hard-sphere systems and constraint satisfaction problems as a minimal model for structural glasses, we explore their jamming transition both in the classical and the quantum regime. In the second approach, we focus on finite-dimensional models. We analyze the quantum dynamics of the two-level system model for glasses and generic many-body localized systems, providing clues for the presence of a deep connection between glasses and quantum many-body localized systems. This thesis aims at estimating both qualitatively and quantitatively the effects of quantum mechanics on glasses at ultra-low temperatures. In the literature, only a few studies have considered glasses deep in their quantum regime, partly due to the analytical and computational challenges this posits. Nevertheless, this perspective promises to have wide-ranging applications. One of our ambitious goals is to take a first, substantial step to unveil the possible origin of long-standing discrepancies observed between theory and experiments in ultra-low temperature glasses. Moreover, we would like to predict the presence of new experimental regimes that might be interesting to investigate

An exploratory study of the glassy landscape near jamming

We present the study of the landscape structure of athermal soft spheres both as a function of the packing fraction and of the energy. We find that, on approaching the jamming transition, the number of different configurations available to the system has a steep increase and that a hierarchical organization of the landscape emerges. We use the knowledge of the structure of the landscape to predict the values of thermodynamic observables on the edge of the transition

Spatio-temporal heterogeneity of entanglement in many-body localized systems

We propose a spatio-temporal characterization of the entanglement dynamics in many-body localized (MBL) systems, which exhibits a striking resemblance with dynamical heterogeneity in classical glasses. Specifically, we find that the relaxation times of local entanglement, as measured by the concurrence, are spatially correlated yielding a dynamical length scale for quantum entanglement. As a consequence of this spatio-temporal analysis, we observe that the considered MBL system is made up of dynamically correlated clusters with a size set by this entanglement length scale. The system decomposes into compartments of different activity such as active regions with fast quantum entanglement dynamics and inactive regions where the dynamics is slow. We further find that the relaxation times of the on-site concurrence become broader distributed and more spatially correlated, as disorder increases or the energy of the initial state decreases. Through this spatio-temporal characterization of entanglement, our work unravels a previously unrecognized connection between the behavior of classical glasses and the genuine quantum dynamics of MBL systems.Comment: 12 pages, 8 figure

CALiPPSO: A Linear Programming Algorithm for Jamming Hard Spheres

The jamming transition is ubiquitous. It is present in granular matter, foams, colloids, structural glasses, and many other systems. Yet, it defines a critical point whose properties still need to be fully understood. Recently, a major breakthrough came about when the replica formalism was extended to build a mean-field theory that provides an exact description of the jamming transition of spherical particles in the infinite-dimensional limit. While such theory explains the jamming critical behavior of both soft and hard spheres (HS), investigating these two kinds of particles in finite dimensions poses very different problems, particularly from the numerical point of view. Soft particles are modeled by a continuous potential; thus, their jamming point can be reached through efficient energy minimization algorithms. In contrast, such methods are inapplicable in HS systems because the interaction energy among the particles is always zero by construction. To overcome this difficulty, here we recast HS jamming as a constrained optimization problem and introduce the CALiPPSO algorithm, capable of readily producing jammed packings of HS without including any effective potential. This algorithm brings a HS configuration of arbitrary dimensions to its jamming point by solving a chain of linear optimization problems. We show that there is a strict correspondence between the force balance conditions of jammed packings and the properties of the optimal solutions of CALiPPSO, whence we prove analytically that our packings are always isostatic and in mechanical equilibrium. Furthermore, using extensive numerical simulations, we show that our algorithm is able to probe the complex structure of the free energy landscape, finding qualitative agreement with mean-field predictions. We also characterize the algorithmic complexity of CALiPPSO and provide an open-source implementation of it.Comment: Version accepted in Phys Rev E. Find our own implementation of the algorithm here: https://github.com/rdhr/CALiPPS

Perspectives and consensus among international orthopaedic surgeons during initial and mid-lockdown phases of coronavirus disease

With a lot of uncertainty, unclear, and frequently changing management protocols, COVID-19 has significantly impacted the orthopaedic surgical practice during this pandemic crisis. Surgeons around the world needed closed introspection, contemplation, and prospective consensual recommendations for safe surgical practice and prevention of viral contamination. One hundred orthopaedic surgeons from 50 countries were sent a Google online form with a questionnaire explicating protocols for admission, surgeries, discharge, follow-up, relevant information affecting their surgical practices, difficulties faced, and many more important issues that happened during and after the lockdown. Ten surgeons critically construed and interpreted the data to form rationale guidelines and recommendations. Of the total, hand and microsurgery surgeons (52%), trauma surgeons (32%), joint replacement surgeons (20%), and arthroscopy surgeons (14%) actively participated in the survey. Surgeons from national public health care/government college hospitals (44%) and private/semiprivate practitioners (54%) were involved in the study. Countries had lockdown started as early as January 3, 2020 with the implementation of partial or complete lifting of lockdown in few countries while writing this article. Surgeons (58%) did not stop their surgical practice or clinics but preferred only emergency cases during the lockdown. Most of the surgeons (49%) had three-fourths reduction in their total patients turn-up and the remaining cases were managed by conservative (54%) methods. There was a 50 to 75% reduction in the number of surgeries. Surgeons did perform emergency procedures without COVID-19 tests but preferred reverse transcription polymerase chain reaction (RT-PCR; 77%) and computed tomography (CT) scan chest (12%) tests for all elective surgical cases. Open fracture and emergency procedures (60%) and distal radius (55%) fractures were the most commonly performed surgeries. Surgeons preferred full personal protection equipment kits (69%) with a respirator (N95/FFP3), but in the case of unavailability, they used surgical masks and normal gowns. Regional/local anesthesia (70%) remained their choice for surgery to prevent the aerosolized risk of contaminations. Essential surgical follow-up with limited persons and visits was encouraged by 70% of the surgeons, whereas teleconsultation and telerehabilitation by 30% of the surgeons. Despite the protective equipment, one-third of the surgeons were afraid of getting infected and 56% feared of infecting their near and dear ones. Orthopaedic surgeons in private practice did face 50 to 75% financial loss and have to furlough 25% staff and 50% paramedical persons. Orthopaedics meetings were cancelled, and virtual meetings have become the preferred mode of sharing the knowledge and experiences avoiding human contacts. Staying at home, reading, and writing manuscripts became more interesting and an interesting lifestyle change is seen among the surgeons. Unanimously and without any doubt all accepted the fact that COVID-19 pandemic has reached an unprecedented level where personal hygiene, hand washing, social distancing, and safe surgical practices are the viable antidotes, and they have all slowly integrated these practices into their lives. Strict adherence to local authority recommendations and guidelines, uniform and standardized norms for admission, inpatient, and discharge, mandatory RT-PCR tests before surgery and in selective cases with CT scan chest, optimizing and regularizing the surgeries, avoiding and delaying nonemergency surgeries and follow-up protocols, use of teleconsultations cautiously, and working in close association with the World Health Organization and national health care systems will provide a conducive and safe working environment for orthopaedic surgeons and their fraternity and also will prevent the resurgence of COVID-19