Non-ergodic phenomena in many-body quantum systems

The assumption of ergodicity is the cornerstone of conventional thermodynamics, connecting the equilibrium properties of macroscopic systems to the chaotic nature of the underlying microscopic dynamics, which eventuates in thermalization and the scrambling of information contained in any generic initial condition. The modern understanding of ergodicity in a quantum mechanical framework is encapsulated in the so-called eigenstate thermalization hypothesis, which asserts that thermalization of an isolated quantum system is a manifestation of the random-like character of individual eigenstates in the bulk of the spectrum of the system's Hamiltonian. In this work, we consider two major exceptions to the rule of generic thermalization in interacting many-body quantum systems: many-body localization, and quantum spin glasses. In the first part, we debate the possibility of localization in a system endowed with a non-Abelian symmetry. We show that, in line with proposed theoretical arguments, such a system is probably delocalized in the thermodynamic limit, but the ergodization length scale is anomalously large, explaining the non-ergodic behavior observed in previous experimental and numerical works. A crucial feature of this system is the quasi-tensor-network nature of its eigenstates, which is dictated by the presence of nontrivial symmetry multiplets. As a consequence, ergodicity may only be restored by extensively large cascades of resonating spins, explaining the system's resistance to delocalization. In the second part, we study the effects of non-ergodic behavior in glassy systems in relation to the possibility of speeding up classical algorithms via quantum resources, namely tunneling across tall free energy barriers. First, we define a pseudo-tunneling event in classical diffusion Monte Carlo (DMC) and characterize the corresponding tunneling rate. Our findings suggest that DMC is very efficient at tunneling in stoquastic problems even in the presence of frustrated couplings, asymptotically outperforming incoherent quantum tunneling. We also analyze in detail the impact of importance sampling, finding that it does not alter the scaling. Next, we study the so-called population transfer (PT) algorithm applied to the problem of energy matching in combinatorial problems. After summarizing some known results on a simpler model, we take the quantum random energy model as a testbed for a thorough, model-agnostic numerical characterization of the algorithm, including parameter setting and quality assessment. From the accessible system sizes, we observe no meaningful asymptotic speedup, but argue in favor of a better performance in more realistic energy landscapes

Theory of robust quantum many-body scars in long-range interacting systems

Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special non-equilibrium initial states. Their various systematic constructions require fine-tuning of local Hamiltonian parameters. In this work we demonstrate that the setting of long-range interacting quantum spin systems generically hosts robust QMBS. We analyze spectral properties upon raising the power-law decay exponent $\alpha$ of spin-spin interactions from the solvable permutationally-symmetric limit $\alpha=0$. First, we numerically establish that despite spectral signatures of chaos appear for infinitesimal $\alpha$, the towers of $\alpha=0$ energy eigenstates with large collective spin are smoothly deformed as $\alpha$ is increased, and exhibit characteristic QMBS features. To elucidate the nature and fate of these states in larger systems, we introduce an analytical approach based on mapping the spin Hamiltonian onto a relativistic quantum rotor non-linearly coupled to an extensive set of bosonic modes. We exactly solve for the eigenstates of this interacting impurity model, and show their self-consistent localization in large-spin sectors of the original Hamiltonian for $0<\alpha<d$. Our theory unveils the stability mechanism of such QMBS for arbitrary system size and predicts instances of its breakdown e.g. near dynamical critical points or in presence of semiclassical chaos, which we verify numerically in long-range quantum Ising chains. As a byproduct, we find a predictive criterion for presence or absence of heating under periodic driving for $0<\alpha<d$, beyond existing Floquet-prethermalization theorems. Broader perspectives of this work range from independent applications of the technical toolbox developed here to informing experimental routes to metrologically useful multipartite entanglement.Comment: 25+13 pages, 15+3 figure

TGF-β concentrations and activity are down-regulated in the aqueous humor of patients with neovascular age-related macular degeneration

Controversy still exists regarding the role of the TGF-β in neovascular age-related macular degeneration (nAMD), a major cause of severe visual loss in the elderly in developed countries. Here, we measured the concentrations of active TGF-β1, TGF-β2, and TGF-β3 by ELISA in the aqueous humor of 20 patients affected by nAMD, who received 3 consecutive monthly intravitreal injections of anti-VEGF-A antibody. Samples were collected at baseline (before the first injection), month 1 (before the second injection), and month 2 (before the third injection). The same samples were used in a luciferase-based reporter assay to test the TGF-β pathway activation. Active TGF-β1 concentrations in the aqueous humor were below the minimum detectable dose. Active TGF-β2 concentrations were significantly lower at baseline and at month 1, compared to controls. No significant differences in active TGF-β3 concentration were found among the sample groups. Moreover, TGF-β pathway activation was significantly lower at baseline compared to controls. Our data corroborate an anti-angiogenic role for TGF-β2 in nAMD. This should be considered from the perspective of a therapy using TGF-β inhibitors

Understanding quantum tunneling using diffusion Monte Carlo simulations

In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as 1/\u3942, where \u394 is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests that there is no quantum advantage in using QAs with respect to quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model (Andriyash and Amin, arXiv:1703.09277), where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving open the possibility for potential quantum speedup, even for stoquastic models. In this work we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as 1/\u394, i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However, a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain indicates an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases

Matrix for Mucosal Regeneration in Transoral Glossectomy for Squamous Cell Carcinoma: Objective and Subjective Functional Evaluation

Background: Numerous options to manage local reconstruction following transoral partial glossectomy are possible. In this work, we present our experience using a matrix for mucosal regeneration, Integra®, after transoral resections of squamous cell carcinoma of the oral tongue. Methods: A retrospective analysis of patients treated for tongue carcinoma and reconstruction with Integra®, from September 2017 to September 2022. Functional outcomes were evaluated by measuring swallowing and speech abilities, tongue motility, and subjective quality of life. Results: The series accounts for 13 consecutive patients, staged from Tis to T3, no positive resection margins were found, average defect size was 17.8 cm2. The average histologically measured depth of invasion was 4.1 mm (range 2–12 mm), and no recurrences were observed during follow-up. All patients maintained excellent swallowing function, the average number of recognized words by an external listener during a phone call was 70.5 out of 75, the lingual motility test was good (a mean score of 4.5 out of 6 movements correctly executed) and subjective questionnaires results were optimal. Less satisfying functional results were recorded in elderly patients receiving a wider surgical resection. Conclusions: This reconstructive technique for allows obtaining optimal healing and functional outcomes in patients with tumors suitable for transoral glossectomy

LRG1 expression is elevated in the eyes of patients with neovascular age-related macular degeneration

Leucine-rich a-2-glycoprotein 1 (LRG1) is a candidate therapeutic target for treating the neovascular form of age-related macular degeneration (nvAMD). In this study we examined the expression of LRG1 in eyes of nvAMD patients. Choroidal neovascular membranes (CNVMs) from patients who underwent submacular surgery for retinal pigment epithelium–choroid graft trans plantation were collected from 5 nvAMD patients without any prior intravitreal anti-VEGF injection, and from six patients who received intravitreal anti-VEGF injections before surgery. As controls free of nvAMD, retina sections were obtained from the eyes resected from a patient with lacrimal sac tumor and from a patient with neuroblastoma. CNVMs were immunostained for CD34, LRG1, and α-smooth muscle actin (α-SMA). Aqueous humor samples were collected from 58 untreated-naïve nvAMD patients prior to the intravitreal injection of anti-VEGF and 51 age-matched cataract control patients, and LRG1 concentration was measured by ELISA. The level of LRG1 immunostaining is frequently high in both the endothelial cells of the blood vessels, and myofibroblasts in the surround ing tissue of CNVMs of treatment-naïve nvAMD patients. Furthermore, the average concentration of LRG1 was significantly higher in the aqueous humor of nvAMD patients than in controls. These observations provide a strong experimental basis and scientific rationale for the progression of a therapeutic anti-LRG1 monoclonal antibody into clinical trials with patients with nvAMD