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The diffraction spectra of the Hat and Spectre monotile tilings, which are known to be pure point, are derived and computed explicitly. This is done via model set representatives of self-similar members in the topological conjugacy classes of the Hat and the Spectre tiling, which are the CAP and the CASPr tiling, respectively. This is followed by suitable reprojections of the model sets to represent the original Hat and Spectre tilings, which also allows to calculate their Fourier--Bohr coefficients explicitly. Since the windows of the underlying model sets have fractal boundaries, these coefficients need to be computed via an exact renormalisation cocycle in internal space., Comment: 35 pages, many figres

When an external parameter drives a system across a quantum phase transition at a finite rate, work is performed on the system and entropy is dissipated, due to the creation of excitations via the Kibble-Zurek mechanism. Although both the adiabatic and sudden-quench limits have been studied in detail, the quantum work statistics along the crossover connecting these limits has largely been an open question. Here we obtain exact scaling functions for the work statistics along the full crossover from adiabatic to sudden-quench limits for critical quantum impurity problems, by combining linear response theory, conformal field theory, and the numerical renormalization group. These predictions can be tested in charge-multichannel Kondo quantum dot devices, where the dissipated work corresponds to the creation of nontrivial excitations such as Majorana fermions or Fibonacci anyons.

Our aim in this paper is to outline how the design space for the ontologization process is richer than current practice would suggest. We point out that engineering processes as well as products need to be designed - and identify some components of the design. We investigate the possibility of designing a range of radically new practices, providing examples of the new practices from our work over the last three decades with an outlier methodology, bCLEARer. We also suggest that setting an evolutionary context for ontologization helps one to better understand the nature of these new practices and provides the conceptual scaffolding that shapes fertile processes. Where this evolutionary perspective positions digitalization (the evolutionary emergence of computing technologies) as the latest step in a long evolutionary trail of information transitions. This reframes ontologization as a strategic tool for leveraging the emerging opportunities offered by digitalization.

We present recent updates and results from QC$_2$D (Two Colour QCD) simulations at non-zero baryon density, including progress toward determining the speed of sound., Comment: 10 Pages, 7 figures, contribution to the 41st International Symposium on Lattice Field Theory (LATTICE2024), Liverpool, UK Speaker D. Lawlor

We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy are classified by invariance under an appropriate symmetry relation. All measures of maximal entropy are fully supported and they are generally not Gibbs measures. We prove that there is a unique measure of maximal entropy if and only if an associated Markov chain is ergodic in inverse time. This Markov chain has finitely many states and all transition matrices are explicitly computable. Thereby, we obtain several sufficient conditions for intrinsic ergodicity that are easy to verify. A practical way to compute the topological entropy in terms of inflation words is extended from previous work to a more general geometric setting., Comment: 30 pages, 2 figures

The probability that a configuration of a physical system reacts, or transitions from one metastable state to another, is quantified by the committor function. This function contains richly detailed mechanistic information about transition pathways, but a full parameterization of the committor requires building representing a high-dimensional function, a generically challenging task. Recent efforts to leverage neural networks as a means to solve high-dimensional partial differential equations, often called "physics-informed" machine learning, have brought the committor into computational reach. Here, we build on the semigroup approach to learning the committor and assess its utility for predicting dynamical quantities such as transition rates. We show that a careful reframing of the objective function and improved adaptive sampling strategies provide highly accurate representations of the committor. Furthermore, by directly applying the Hill relation, we show that these committors provide accurate transition rates for molecular system.

Quantum systems used for metrology can offer enhanced precision over their classical counterparts. The design of quantum sensors can be optimized by maximizing the quantum Fisher information (QFI), which characterizes the precision of parameter estimation for an ideal measurement. Here we consider the response of a quantum system as a means to estimate the strength of an external perturbation that has been switched on slowly. General expressions for the QFI are derived, which also hold for interacting many-body systems in the thermodynamic limit at finite temperatures, and can be related to linear-response transport coefficients. For quantum dot nanoelectronics devices, we show that electron interactions can lead to exponential scaling of the QFI with system size, highlighting that quantum resources can be utilized in the full Fock space. The precision estimation of voltages and fields can also be achieved by practical global measurements, such as the electric current, making quantum circuits good candidates for metrological applications., Comment: 4+ pages plus supplementary material

We live in a rich and varied acoustic world, which is experienced by individuals or communities as a soundscape. Computational auditory scene analysis, disentangling acoustic scenes by detecting and classifying events, focuses on objective attributes of sounds, such as their category and temporal characteristics, ignoring their effects on people, such as the emotions they evoke within a context. To fill this gap, we propose the soundscape captioning task, which enables automated soundscape analysis, thus avoiding labour-intensive subjective ratings and surveys in conventional methods. With soundscape captioning, context-aware descriptions are generated for soundscape by capturing the acoustic scene, event information, and the corresponding human affective qualities (AQs). To this end, we propose an automatic soundscape captioner (SoundSCaper) system composed of an acoustic model, i.e. SoundAQnet, and a large language model (LLM). SoundAQnet simultaneously models multi-scale information about acoustic scenes, events, and perceived AQs, while the LLM describes the soundscape with captions by parsing the information captured with SoundAQnet. The soundscape caption's quality is assessed by a jury of 16 audio/soundscape experts. The average score (out of 5) of SoundSCaper-generated captions is lower than the score of captions generated by two soundscape experts by 0.21 and 0.25, respectively, on the evaluation set and the model-unknown mixed external dataset with varying lengths and acoustic properties, but the differences are not statistically significant. Overall, the proposed SoundSCaper shows promising performance, with captions generated being comparable to those annotated by soundscape experts. The code of models, LLM scripts, human assessment data and instructions, and expert evaluation statistics are all publicly available., Comment: Code: https://github.com/Yuanbo2020/SoundSCaper

We present an in-depth analysis of a single-electron box (SEB) biased through a floating node technique that is common in charge-coupled devices (CCDs). The device is analyzed and characterized in the context of single-electron charge-sensing techniques for integrated silicon quantum dots (QD). The unique aspect of our SEB design is the incorporation of a metallic floating node, strategically employed for sensing and precise injection of electrons into an electrostatically formed QD. To analyse the SEB, we propose an extended multi-orbital Anderson impurity model (MOAIM), adapted to our nanoscale SEB system, that is used to predict theoretically the behaviour of the SEB in the context of a charge-sensing application. The validation of the model and the sensing technique has been carried out on a QD fabricated in a fully depleted silicon on insulator (FDSOI) process on a 22-nm technological node. We demonstrate the MOAIM's efficacy in predicting the observed electronic behavior and elucidating the complex electron dynamics and correlations in the SEB. The results of our study reinforce the versatility and precision of the model in the realm of nanoelectronics and highlight the practical utility of the metallic floating node as a mechanism for charge injection and detection in integrated QDs. Finally, we identify the limitations of our model in capturing higher-order effects observed in our measurements and propose future outlooks to reconcile some of these discrepancies., Comment: 7 pages, 3 figures

Generalized quantum impurity models -- which feature a few localized and strongly-correlated degrees of freedom coupled to itinerant conduction electrons -- describe diverse physical systems, from magnetic moments in metals to nanoelectronics quantum devices such as quantum dots or single-molecule transistors. Correlated materials can also be understood as self-consistent impurity models through dynamical mean field theory. Accurate simulation of such models is challenging, especially at low temperatures, due to many-body effects from electronic interactions, resulting in strong renormalization. In particular, the interplay between local impurity complexity and Kondo physics is highly nontrivial. A common approach, which we further develop in this work, is to consider instead a simpler effective impurity model that still captures the low-energy physics of interest. The mapping from bare to effective model is typically done perturbatively, but even this can be difficult for complex systems, and the resulting effective model parameters can anyway be quite inaccurate. Here we develop a non-perturbative, unsupervised machine learning approach to systematically obtain low-energy effective impurity-type models, based on the renormalization group framework. The method is shown to be general and flexible, as well as accurate and systematically improvable. We benchmark the method against exact results for the Anderson impurity model, and provide an outlook for more complex models beyond the reach of existing methods., Comment: 28 pages, 8 figures

We develop a theory of Rauzy fractals for random substitutions, which are a generalisation of deterministic substitutions where the substituted image of a letter is determined by a Markov process. We show that a Rauzy fractal can be associated with a given random substitution in a canonical manner, under natural assumptions on the random substitution. Further, we show the existence of a natural measure supported on the Rauzy fractal, which we call the Rauzy measure, that captures geometric and dynamical information. We provide several different constructions for the Rauzy fractal and Rauzy measure, which we show coincide, and ascertain various analytic, dynamical and geometric properties. While the Rauzy fractal is independent of the choice of (non-degenerate) probabilities assigned to a given random substitution, the Rauzy measure captures the explicit choice of probabilities. Moreover, Rauzy measures vary continuously with the choice of probabilities, thus provide a natural means of interpolating between Rauzy fractals of deterministic substitutions., Comment: 30 pages, 4 figures

Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin-1/2 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo (2IK) model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular -- even though the parameters to be estimated are independent -- resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters., Comment: 19 pages, 9 figures

Soundscape studies typically attempt to capture the perception and understanding of sonic environments by surveying users. However, for long-term monitoring or assessing interventions, sound-signal-based approaches are required. To this end, most previous research focused on psycho-acoustic quantities or automatic sound recognition. Few attempts were made to include appraisal (e.g., in circumplex frameworks). This paper proposes an artificial intelligence (AI)-based dual-branch convolutional neural network with cross-attention-based fusion (DCNN-CaF) to analyze automatic soundscape characterization, including sound recognition and appraisal. Using the DeLTA dataset containing human-annotated sound source labels and perceived annoyance, the DCNN-CaF is proposed to perform sound source classification (SSC) and human-perceived annoyance rating prediction (ARP). Experimental findings indicate that (1) the proposed DCNN-CaF using loudness and Mel features outperforms the DCNN-CaF using only one of them. (2) The proposed DCNN-CaF with cross-attention fusion outperforms other typical AI-based models and soundscape-related traditional machine learning methods on the SSC and ARP tasks. (3) Correlation analysis reveals that the relationship between sound sources and annoyance is similar for humans and the proposed AI-based DCNN-CaF model. (4) Generalization tests show that the proposed model's ARP in the presence of model-unknown sound sources is consistent with expert expectations and can explain previous findings from the literature on sound-scape augmentation., Comment: The Journal of the Acoustical Society of America, 154 (5), 3145

In this paper, we present the novel task of estimating the extrinsic parameters of a virtual camera relative to a real camera in exercise videos with a mirror. This task poses a significant challenge in scenarios where the views from the real and mirrored cameras have no overlap or share salient features. To address this issue, prior knowledge of a human body and 2D joint locations are utilized to estimate the camera extrinsic parameters when a person is in front of a mirror. We devise a modified eight-point algorithm to obtain an initial estimation from 2D joint locations. The 2D joint locations are then refined subject to human body constraints. Finally, a RANSAC algorithm is employed to remove outliers by comparing their epipolar distances to a predetermined threshold. MirrorCalib achieves a rotation error of 1.82{\deg} and a translation error of 69.51 mm on a collected real-world dataset, which outperforms the state-of-art method., Comment: Accepted by AVSS2024

Molecular junctions -- whether actual single molecules in nanowire break junctions or artificial molecules realized in coupled quantum dot devices -- offer unique functionality due to their orbital complexity, strong electron interactions, gate control, and many-body effects from hybridization with the external electronic circuit. Inverse design involves finding candidate structures that perform a desired function optimally. Here we develop an inverse design strategy for generalized quantum impurity models describing molecular junctions, and as an example, use it to demonstrate that many-body quantum interference can be leveraged to realize the two-channel Kondo critical point in simple 4- or 5-site molecular moieties. We show that remarkably high Kondo temperatures can be achieved, meaning that entropy and transport signatures should be experimentally accessible., Comment: 4.5 pages + supplementary material

Sound events in daily life carry rich information about the objective world. The composition of these sounds affects the mood of people in a soundscape. Most previous approaches only focus on classifying and detecting audio events and scenes, but may ignore their perceptual quality that may impact humans' listening mood for the environment, e.g. annoyance. To this end, this paper proposes a novel hierarchical graph representation learning (HGRL) approach which links objective audio events (AE) with subjective annoyance ratings (AR) of the soundscape perceived by humans. The hierarchical graph consists of fine-grained event (fAE) embeddings with single-class event semantics, coarse-grained event (cAE) embeddings with multi-class event semantics, and AR embeddings. Experiments show the proposed HGRL successfully integrates AE with AR for AEC and ARP tasks, while coordinating the relations between cAE and fAE and further aligning the two different grains of AE information with the AR., Comment: INTERSPEECH 2023, Code and models: https://github.com/Yuanbo2020/HGRL

We consider word complexity and topological entropy for random substitution subshifts. In contrast to previous work, we do not assume that the underlying random substitution is compatible. We show that the subshift of a primitive random substitution has zero topological entropy if and only if it can be obtained as the subshift of a deterministic substitution, answering in the affirmative an open question of Rust and Spindeler. For constant length primitive random substitutions, we develop a systematic approach to calculating the topological entropy of the associated subshift. Further, we prove lower and upper bounds that hold even without primitivity. For subshifts of non-primitive random substitutions, we show that the complexity function can exhibit features not possible in the deterministic or primitive random setting, such as intermediate growth, and provide a partial classification of the permissible complexity functions for subshifts of constant length random substitutions., Comment: 14 pages. Fixed a small gap in the proof of Proposition 4.6, some other minor changes. To appear in Proc. Amer. Math. Soc

The emergence of flat bands in twisted bilayer graphene at the magic angle can be understood in terms of a vanishing Fermi velocity of the Dirac cone. This is associated with van Hove singularities approaching the Fermi energy and becoming higher-order. In the density of states this is reflected by flanking logarithmic van Hove divergences pinching off the central Dirac cone in energy space. The low-energy pseudogap of the Dirac cone away from the magic angle is replaced by a power-law divergence due to the higher-order van Hove singularity at the magic angle. This plays an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. Here we investigate one such correlation effect -- the Kondo effect due to a magnetic impurity embedded in twisted bilayer graphene. We use the Bistritzer-MacDonald model to extract the low-energy density of states of the material as a function of twist angle, and study the resulting quantum impurity physics using perturbative and numerical renormalization group methods. Although at zero temperature the impurity is only Kondo screened precisely at the magic angle, we find highly nontrivial behavior at finite temperatures relevant to experiment, due to the complex interplay between Dirac, van Hove, and Kondo physics., Comment: 16 pages, 8 figures

We study regularity properties of frequency measures arising from random substitutions, which are a generalisation of (deterministic) substitutions where the substituted image of each letter is chosen independently from a fixed finite set. In particular, for a natural class of such measures, we derive a closed-form analytic formula for the $L^q$-spectrum and prove that the multifractal formalism holds. This provides an interesting new class of measures satisfying the multifractal formalism. More generally, we establish results concerning the $L^q$-spectrum of a broad class of frequency measures. We introduce a new notion called the inflation word $L^q$-spectrum of a random substitution and show that this coincides with the $L^q$-spectrum of the corresponding frequency measure for all $q \geq 0$. As an application, we obtain closed-form formulas under separation conditions and recover known results for topological and measure theoretic entropy., Comment: 49 pages, 3 figures. Minor typo fixes and updated references. To appear in Comm. Math. Phys

We study quantum impurity models as a platform for quantum thermometry. A single quantum spin-1/2 impurity is coupled to an explicit, structured, fermionic thermal environment which we refer to as the environment or bath. We critically assess the thermometric capabilities of the impurity as a probe, when its coupling to the environment is of Ising or Kondo exchange type. In the Ising case, we find sensitivity equivalent to that of an idealized two-level system, with peak thermometric performance obtained at a temperature that scales linearly in the applied control field, independent of the coupling strength and environment spectral features. By contrast, a richer thermometric response can be realized for Kondo impurities, since strong probe-environment entanglement can then develop. At low temperatures, we uncover a regime with a universal thermometric response that is independent of microscopic details, controlled only by the low-energy spectral features of the environment. The many-body entanglement that develops in this regime means that low-temperature thermometry with a weakly applied control field is inherently less sensitive, while optimal sensitivity is recovered by suppressing the entanglement with stronger fields., Comment: 16 pages, 5 figures. Close to published version

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [arXiv:2108.12691] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a $\mathbb{Z}_3$ parafermion emerges at the critical point, characterized by a fractional $\tfrac{1}{2}\ln(3)$ residual entropy, and scattering fractional charges $e/3$. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results., Comment: 5 pages+, 3 figures

Nanoelectronics devices, such as quantum dot systems or single-molecule transistors, consist of a quantum nanostructure coupled to a macroscopic external electronic circuit. Thermoelectric transport between source and drain leads is controlled by the quantum dynamics of the lead-coupled nanostructure, through which a current must pass. Strong electron interactions due to quantum confinement on the nanostructure produce nontrivial conductance signatures such as Coulomb blockade and Kondo effects, which become especially pronounced at low temperatures. In this work we first provide a modern review of standard quantum transport techniques, focusing on the linear response regime, and highlight the strengths and limitations of each. In the second part, we develop an improved numerical scheme for calculation of the ac linear electrical conductance through generic interacting nanostructures, based on the numerical renormalization group (NRG) method, and explicitly demonstrate its utility in terms of accuracy and efficiency. In the third part we derive low-energy effective models valid in various commonly-encountered situations, and from them we obtain simple analytical expressions for the low-temperature conductance. This indirect route via effective models, although approximate, allows certain limitations of conventional methodologies to be overcome, and provides physical insights into transport mechanisms. Finally, we apply and compare the various techniques, taking the two-terminal triple quantum dot and the serial multi-level double dot devices as nontrivial benchmark systems., Comment: Pre-submission draft. All comments or missing references welcome

Nanoelectronic quantum dot devices exploiting the charge-Kondo paradigm have been established as versatile and accurate analog quantum simulators of fundamental quantum impurity models. In particular, hybrid metal-semiconductor dots connected to two metallic leads realize the two-channel Kondo (2CK) model, in which Kondo screening of the dot charge pseudospin is frustrated. Here, we consider theoretically a two-channel charge-Kondo device made instead from graphene components, realizing a pseudogapped version of the 2CK model. We solve the model using Wilson's Numerical Renormalization Group method, and uncover a rich phase diagram as a function of dot-lead coupling strength, channel asymmetry, and potential scattering. The complex physics of this system is explored through its thermodynamic properties, scattering T-matrix, and experimentally measurable conductance. We find that the strong coupling pseudogap Kondo phase persists in the channel-asymmetric two-channel context, while in the channel-symmetric case frustration results in a novel quantum phase transition. Remarkably, despite the vanishing density of states in the graphene leads at low energies, we find a finite linear conductance at zero temperature at the frustrated critical point, which is of non-Fermi liquid type. Our results suggest that the graphene charge-Kondo platform offers a unique possibility to access multichannel pseudogap Kondo physics., Comment: 12 pages, 4 figures