Off-diagonal disorder in the Anderson model of localization

We examine the localization properties of the Anderson Hamiltonian with additional off-diagonal disorder using the transfer-matrix method and finite-size scaling. We compute the localization lengths and study the metal-insulator transition (MIT) as a function of diagonal disorder, as well as its energy dependence. Furthermore we investigate the different influence of odd and even system sizes on the localization properties in quasi one-dimensional systems. Applying the finite-size scaling approach in conjunction with a nonlinear fitting procedure yields the critical parameters of the MIT. In three dimensions, we find that the resulting critical exponent of the localization length agrees with the exponent for the Anderson model with pure diagonal disorder.Comment: 12 pages including 4 EPS figures, accepted for publication in phys. stat. sol. (b

Existence of a spectral gap in the Affleck-Kennedy-Lieb-Tasaki model on the hexagonal lattice

The S=1 Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the S=3/2 AKLT model on the hexagonal lattice is also in a gapped phase has remained open, despite being a fundamental problem of ongoing relevance to condensed-matter physics and quantum information theory. Here we confirm this conjecture by demonstrating the size-independent lower bound Δ>0.006 on the spectral gap of the hexagonal model with periodic boundary conditions in the thermodynamic limit. Our approach consists of two steps combining mathematical physics and high-precision computational physics. We first prove a mathematical finite-size criterion which gives an analytical, size-independent bound on the spectral gap if the gap of a particular cut-out subsystem of 36 spins exceeds a certain threshold value. Then we verify the finite-size criterion numerically by performing state-of-the-art DMRG calculations on the subsystem.Accepted manuscrip

Motives for choosing university and specialty applicants Ukraine (for example, students NTU "KPI")

Стаття присвячена аналізу портрета абітурієнта НТУ "ХПІ", де, крім визначення мотивів професійного вибору, самооцінки особистих здібностей, розглядаються і основні цілі навчання в НТУ "ХПІ". У статті підкреслюється, що проблема професійного самовизначення стояла перед молоддю завжди, а сьогодні вона особливо актуальна, тому що сучасні умови ринку праці ведуть до того, що більшість випускників не мають ясної життєвої перспективи. Аналізуються мотиви отримання абітурієнтами вищої освіти, мотивація вступу до НТУ "ХПІ", мотиви вибору спеціальності, період формування професійного інтересу. Проаналізовано мотиви професійного вибору абітурієнтів; період формування інтересу молодих людей до обраної спеціальності (процес самовизначення, коли здійснено вибір спеціальності, ВНЗ); специфіку вибору ВНЗ (яким за рахунком був ХПІ, хто допоміг визначитися з вибором); уявлення про процес навчання в університеті; відповідність уявлень про навчання в університеті реаліям університетського життя.This article analyzes portrait applicant NTU "KPI", where in addition to determining the reasons professional choice, self-personal skills, and discusses the main goals of training at NTU "KPI". The article highlights the problem of professional self -determination was always the youth, and today it is particularly urgent because the current labor market conditions lead to the fact that most graduates do not have a clear life perspective. Analyzed the motives of applicants receiving higher education, motivation admission to NTU "KPI" motives choice of specialty, during the formation of professional interest. Analyzed the motives of professional selection of applicants; during the formation of young people's interest to the chosen profession (the process of self-selection made when specialty Universities); the specific choice of university (how the account was HPI, who helped to choose); understanding of the learning process at the university; line ideas about university studies realities of university life

Quantum Bayes rule

We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state of the N copies is exchangeable. As an illustration, we apply the rule to N qubits. Finally, we show that quantum state estimates derived via the principle of maximum entropy are fundamentally different from those obtained via the quantum Bayes rule.Comment: REVTEX, 9 page

The role of frictional power dissipation (as a function of frequency) and test temperature on contact temperature and the subsequent wear behaviour in a stainless steel contact in fretting

Temperature is known to affect the fretting wear behaviour of metals; generally, a critical temperature is observed, above which there are substantial reductions in wear rate, with these being associated with the development of protective oxide beds in the fretting contact. This work has examined the gross sliding fretting behaviour of a stainless steel as a function of bulk temperature and fretting frequency(with changes in the fretting frequency altering the frictional power dissipated in the contact amongst other things). An analytical model has been developed which has suggested that at 200 Hz, an increase in the contact temperature of more than 70°C can be expected, associated with the high frictional power dissipation at this frequency (compared to that dissipated at a fretting frequency of 20 Hz). With the bulk temperature at either room temperature or 275°C, the increase in contact temperature does not result in a transition across the critical temperature (and thus fretting behaviour at these temperatures is relatively insensitive to fretting frequency). However, with a bulk temperature of 150°C, the increase in temperature associated with the increased frictional power dissipation at the higher frequency results in the critical temperature being exceeded, and in significant differences in fretting behaviour

A Generalized Framework for Quantifying the Dynamics of EEG Event-Related Desynchronization

Brains were built by evolution to react swiftly to environmental challenges. Thus, sensory stimuli must be processed ad hoc, i.e., independent—to a large extent—from the momentary brain state incidentally prevailing during stimulus occurrence. Accordingly, computational neuroscience strives to model the robust processing of stimuli in the presence of dynamical cortical states. A pivotal feature of ongoing brain activity is the regional predominance of EEG eigenrhythms, such as the occipital alpha or the pericentral mu rhythm, both peaking spectrally at 10 Hz. Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states. Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics. Moreover, this computational approach also encompasses the more general notion of a “conditional ERD,” through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study. Thus, the generalized ERD represents a powerful novel analysis tool for extending our understanding of inter-trial variability of evoked responses and therefore the robust processing of environmental stimuli

Safety and immunogenicity of a self-amplifying RNA vaccine against COVID-19: COVAC1, a phase I, dose-ranging trial

Background: Lipid nanoparticle (LNP) encapsulated self-amplifying RNA (saRNA) is a novel technology formulated as a low dose vaccine against COVID-19. Methods: A phase I first-in-human dose-ranging trial of a saRNA COVID-19 vaccine candidate LNP-nCoVsaRNA, was conducted at Imperial Clinical Research Facility, and participating centres in London, UK, between 19th June to 28th October 2020. Participants received two intramuscular (IM) injections of LNP-nCoVsaRNA at six different dose levels, 0.1-10.0μg, given four weeks apart. An open-label dose escalation was followed by a dose evaluation. Solicited adverse events (AEs) were collected for one week from enrolment, with follow-up at regular intervals (1-8 weeks). The binding and neutralisation capacity of anti-SARS-CoV-2 antibody raised in participant sera was measured by means of an anti-Spike (S) IgG ELISA, immunoblot, SARS-CoV-2 pseudoneutralisation and wild type neutralisation assays. (The trial is registered: ISRCTN17072692, EudraCT 2020-001646-20). Findings: 192 healthy individuals with no history or serological evidence of COVID-19, aged 18-45 years were enrolled. The vaccine was well tolerated with no serious adverse events related to vaccination. Seroconversion at week six whether measured by ELISA or immunoblot was related to dose (both p<0.001), ranging from 8% (3/39; 0.1μg) to 61% (14/23; 10.0μg) in ELISA and 46% (18/39; 0.3μg) to 87% (20/23; 5.0μg and 10.0μg) in a post-hoc immunoblot assay. Geometric mean (GM) anti-S IgG concentrations ranged from 74 (95% CI, 45-119) at 0.1μg to 1023 (468-2236) ng/mL at 5.0μg (p<0.001) and was not higher at 10.0μg. Neutralisation of SARS-CoV-2 by participant sera was measurable in 15% (6/39; 0.1μg) to 48% (11/23; 5.0μg) depending on dose level received. Interpretation: Encapsulated saRNA is safe for clinical development, is immunogenic at low dose levels but failed to induce 100% seroconversion. Modifications to optimise humoral responses are required to realise its potential as an effective vaccine against SARS-CoV-2. Funding: This study was co-funded by grants and gifts from the Medical Research Council UKRI (MC_PC_19076), and the National Institute Health Research/Vaccine Task Force, Partners of Citadel and Citadel Securities, Sir Joseph Hotung Charitable Settlement, Jon Moulton Charity Trust, Pierre Andurand, Restore the Earth