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Contrary to fermions and bosons, anyons are quasiparticles that keep a robust memory of particle exchanges via a braiding phase factor. This provides them with unique dynamical properties so far unexplored. When an anyon excitation is emitted toward a quantum point contact (QPC) in a fractional quantum Hall (FQH) fluid, this memory translates into tunneling events that may occur long after the anyon excitation has exited the QPC. Here, we use triggered anyon pulses incident on a QPC in a $\nu= 1/3$ FQH fluid to investigate anyon tunneling in the time domain. We observe that braiding increases the tunneling timescale, which is set by the temperature and the anyon scaling dimension that characterizes the edge state dynamics. This contrasts with the electron behavior where braiding is absent and the tunneling timescale is set by the temporal width of the generated electron pulses. Our experiment introduces time-domain measurements for characterizing the braiding phase and scaling dimension of anyons.

Characterizing quantum states of the electromagnetic field at microwave frequencies requires fast and sensitive detectors that can simultaneously probe the field time-dependent amplitude and its quantum fluctuations. In this work, we demonstrate a quantum sensor that exploits the phase of a single electron wavefunction, measured in an electronic Fabry-Perot interferometer, to detect a classical time-dependent electric field. The time resolution, limited by the temporal width of the electronic wavepacket, is a few tens of picoseconds. The interferometry technique provides a voltage resolution of a few tens of microvolts, corresponding to a few microwave photons. Importantly, our detector simultaneously probes the amplitude of the field from the phase of the measured interference pattern and its fluctuations from the interference contrast. This capability paves the way for on-chip detection of quantum radiation, such as squeezed or Fock states., Comment: Main (8 pages and 3 figures) and supplementary files (17 pages and 12 figures)

The rise of Artificial Intelligence (AI) and Generative Artificial Intelligence (GenAI) in higher education necessitates assessment reform. This study addresses a critical gap by exploring student and academic staff experiences with AI and GenAI tools, focusing on their familiarity and comfort with current and potential future applications in learning and assessment. An online survey collected data from 35 academic staff and 282 students across two universities in Vietnam and one in Singapore, examining GenAI familiarity, perceptions of its use in assessment marking and feedback, knowledge checking and participation, and experiences of GenAI text detection. Descriptive statistics and reflexive thematic analysis revealed a generally low familiarity with GenAI among both groups. GenAI feedback was viewed negatively; however, it was viewed more positively when combined with instructor feedback. Academic staff were more accepting of GenAI text detection tools and grade adjustments based on detection results compared to students. Qualitative analysis identified three themes: unclear understanding of text detection tools, variability in experiences with GenAI detectors, and mixed feelings about GenAI's future impact on educational assessment. These findings have major implications regarding the development of policies and practices for GenAI-enabled assessment and feedback in higher education.

Quantum Hall systems are platforms of choice when it comes to study topological properties of condensed matter systems and anyonic exchange statistics. In this work we have developed a tunable radiofrequency edge magnetoplasmonic resonator meant to serve as a versatile platform for future interferometric devices. The resonance frequency of the system is controlled by both the magnetic field and a set of electrostatic gates. The gates allow us to change both the size of the resonant cavity and the electronic density of the two-dimensional electron gas. We show that we can continuously control the frequency response of our resonator, making it possible to develop an edge magnetoplasmon interferometer. As we reach smaller sizes of our resonator, finite size effects caused by the measurement probes manifest. We present a theoretical description of the system taking into account the spatial extension of the probing gates. In the future, such device will be a valuable tool to investigate the properties of non-abelian anyons in the fractional quantum Hall regime.

We review the connections between the octahedral recurrence, $\lambda$-determinants and tiling problems. This provides in particular a direct combinatorial interpretation of the $\lambda$-determinant (and generalizations thereof) of an arbitrary matrix in terms of domino tilings of Aztec diamonds. We also reinterpret the general Robbins-Rumsey formula for the rational function of consecutive minors, given by a summation over pairs of compatible alternating sign matrices, as the partition function for tilings of Aztec diamonds equipped with a general measure., Comment: 31 pages, published version; v2 slightly augmented with relations to Somos-4 sequences (see end of section 3.2 and appendix)

We image and characterize the mechanical modes of a 2D drum resonator made of hBN suspended over a high-stress Si$_3$N$_4$ membrane. Our measurements demonstrate hybridization between various modes of the hBN resonator and those of the Si$_3$N$_4$ membrane. The measured resonance frequencies and spatial profiles of the modes are consistent with finite-element simulations based on an idealized geometry. Spectra of the thermal motion reveal that, depending on the degree of hybridization with modes of the heavier and higher-quality-factor Si$_3$N$_4$ membrane, the quality factors and the motional mass of the hBN drum modes can be shifted by orders of magnitude. This effect could be exploited to engineer hybrid drum/membrane modes that combine the low motional mass of 2D materials with the high quality factor of Si$_3$N$_4$ membranes for optomechanical or sensing applications., Comment: 16 pages, 4 figure, 1 supplementary section (6 pages, 3 figures)

Domino tilings of Aztec diamonds are known to exhibit an arctic phenomenon, namely a separation between frozen regions (in which all the dominoes have the same orientation) and a central disordered region (where dominoes are found without any apparent order). This separation was proved to converge, under a suitable rescaling, to the Airy process whose $1$-point distribution is the Tracy-Widom distribution. In this work, we conjecture, by means of numerical analysis, that the boundary between the frozen and disordered regions, converges, for the same rescaling, to the Airy line ensemble, a generalisation of the Airy process., Comment: Accepted for publication in the Belgian Journal of Physics

Anyon collision experiments have recently demonstrated the ability to discriminate between fermionic and anyonic statistics. However, only one type of anyons associated with the simple Laughlin state at filling factor $\nu=1/3$ has been probed so far. It is now important to establish anyon collisions as quantitative probes of fractional statistics for more complex topological orders, with the ability to distinguish between different species of anyons with different statistics. In this work, we use the anyon collider to compare the Laughlin $\nu=1/3$ state, which is used as the reference state, with the more complex Jain state at $\nu=2/5$, where low energy excitations are carried by two co-propagating edge channels. We demonstrate that anyons generated on the outer channel of the $\nu=2/5$ state (with a fractional charge $e^*=e/3$) have a similar behavior compared to $\nu=1/3$, showing the robustness of anyon collision signals for anyons of the same type. In contrast, anyons emitted on the inner channel of $\nu=2/5$ (with a fractional charge $e^*=e/5$) exhibit a reduced degree of bunching compared to the $\nu=1/3$ case, demonstrating the ability of the anyon collider to discriminate not only between anyons and fermions, but also between different species of anyons associated with different topological orders of the bulk. Our experimental results for the inner channel of $\nu=2/5$ also point towards an influence of interchannel interactions in anyon collision experiments when several co-propagating edge channels are present. A quantitative understanding of these effects will be important for extensions of anyon collisions to non-abelian topological orders, where several charged and neutral modes propagate at the edge., Comment: 17 pages, 5 figures

We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning of the human brain privileges concept naming and short formulations. This leads to organizing mathematical knowledge structurally. We consider briefly the problem of non-mathematical sciences., Comment: 6 pages

We use the octahedron recurrence, which generalizes the quadratic recurrence found by Kuo for standard Aztec diamonds, in order to compute boundary one-refined and two-refined partition functions for two-periodic Aztec diamonds. In a first approach, the geometric tangent method allows to derive the parametric form of the arctic curve, separating the solid and liquid phases. This is done by using the recently reformulation of the tangent method and the one-refined partition functions without extension of the domain. In a second part, we use the two-refined tangent method to rederive the arctic curve from the boundary two-refined partition functions, which we compute exactly on the lattice. The curve satisfies the known algebraic equation of degree 8, of which either tangent method gives an explicit parametrization., Comment: 29 pages; v2: final version, 36 pages : improved presentation + expanded with two new sections (comparison of the tangent methods with and without extension of the domain + discussion of Aztec diamonds with higher periodicity)

We describe an apparatus for the implementation of hybrid optomechanical systems at 4 K. The platform is based on a high-finesse, micrometer-scale fiber Fabry-Perot cavity, which can be widely tuned using piezoelectric positioners. A mechanical resonator can be positioned within the cavity in the object-in-the-middle configuration by a second set of positioners. A high level of stability is achieved without sacrificing either performance or tunability, through the combination of a stiff mechanical design, passive vibration isolation, and an active Pound-Drever-Hall feedback lock incorporating a reconfigurable digital filter. The stability of the cavity length is demonstrated to be better than a few picometers over many hours both at room temperature and at 4 K., Comment: 10 pages, 6 figures, 1 table

Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex ($6$V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is defined on a $s\times n$ square lattice ($s\leq n$). In this paper, we derive the analytic expression of the arctic curve, for $a=b=1$ and $c=\sqrt{2}$ ($\Delta=0$), while keeping the ratio $s/n \,\in [0,1]$ as a free parameter. The computation relies on the tangent method. We also consider domino tilings of double Aztec rectangles and show via the tangent method that, for particular parameters, the arctic curve is identical to that of the $6$V model with partial DWBC. Our results are confirmed by extensive numerical simulations., Comment: 42 pages, 18 figures

Superradiance and subradiance occur in quantum optics when the emission rate of photons from multiple atoms is enhanced and diminished, respectively, owing to interaction between neighboring atoms. We here demonstrate a classical analog thereof in a theoretical model of droplets walking on a vibrating bath. Two droplets are confined to identical two-level systems, a pair of wells between which the drops may tunnel, joined by an intervening coupling cavity. The resulting classical superradiance is rationalized in terms of the system's non-Markovian, pilot-wave dynamics.

When applied to statistical systems showing an arctic curve phenomenon, the tangent method assumes that a modification of the most external path does not affect the arctic curve. We strengthen this statement and also make it more concrete by observing a factorization property: if $Z^{}_{n+k}$ denotes a refined partition function of a system of $n+k$ non-crossing paths, with the endpoints of the $k$ most external paths possibly displaced, then at dominant order in $n$, it factorizes as $Z^{}_{n+k} \simeq Z^{}_{n} Z_k^{\rm out}$ where $Z_k^{\rm out}$ is the contribution of the $k$ most external paths. Moreover if the shape of the arctic curve is known, we find that the asymptotic value of $Z_k^{\rm out}$ is fully computable in terms of the large deviation function $L$ introduced in \cite{DGR19} (also called Lagrangean function). We present detailed verifications of the factorization in the Aztec diamond and for alternating sign matrices by using exact lattice results. Reversing the argument, we reformulate the tangent method in a way that no longer requires an extension of the domain, and which reveals the hidden role of the $L$ function. As a by-product, the factorization property provides an efficient way to conjecture the asymptotics of multirefined partition functions., Comment: 28 pages, 8 figures

Climate change poses a major challenge to humanity, especially in its impact on agriculture, a challenge that a responsible AI should meet. In this paper, we examine a CBR system (PBI-CBR) designed to aid sustainable dairy farming by supporting grassland management, through accurate crop growth prediction. As climate changes, PBI-CBRs historical cases become less useful in predicting future grass growth. Hence, we extend PBI-CBR using data augmentation, to specifically handle disruptive climate events, using a counterfactual method (from XAI). Study 1 shows that historical, extreme climate-events (climate outlier cases) tend to be used by PBI-CBR to predict grass growth during climate disrupted periods. Study 2 shows that synthetic outliers, generated as counterfactuals on a outlier-boundary, improve the predictive accuracy of PBICBR, during the drought of 2018. This study also shows that an instance-based counterfactual method does better than a benchmark, constraint-guided method., Comment: 15 pages, 6 figures, 3 tables

This contribution is a review of the deep and powerful connection between the large scale properties of critical systems and their description in terms of a field theory. Although largely applicable to many other models, the details of this connection are illustrated in the class of two-dimensional Abelian sandpile models. Bulk and boundary height variables, spanning tree related observables, boundary conditions and dissipation are all discussed in this context and found to have a proper match in the field theoretic description., Comment: Invited contribution to the Research Topic "Self-Organized Criticality, Three Decades Later" (Frontiers in Physics), 55 pages

Let $z$ be the activity of point particles described by classical equilibrium statistical mechanics in ${\bf R}^\nu$. The correlation functions $\rho^z(x_1,\dots,x_k)$ denote the probability densities of finding $k$ particles at $x_1,\dots,x_k$. Letting $\phi^z(x_1,\dots,x_k)$ be the cluster functions corresponding to the $\rho^z(x_1,\dots,x_k)/z^k$ we prove identities of the type $$ \phi^{z_0+z'}(x_1,\dots,x_k) $$ $$ =\sum_{n=0}^\infty{z'^n\over n!}\int dx_{k+1}\dots\int dx_{k+n}\,\phi^{z_0}(x_1,\dots,x_{k+n}) $$ It is then non-rigorously argued that, assuming a suitable cluster property (decay of correlations) for a crystal state, the pressure and the translation invariant correlation functions \- $\rho^z(x_1,\dots,x_k)$ are real analytic functions of $z$., Comment: 8 pages

The tangent method has recently been devised by Colomo and Sportiello (arXiv:1605.01388 [math-ph]) as an efficient way to determine the shape of arctic curves. Largely conjectural, it has been tested successfully in a variety of models. However no proof and no general geometric insight have been given so far, either to show its validity or to allow for an understanding of why the method actually works. In this paper, we propose a universal framework which accounts for the tangency part of the tangent method, whenever a formulation in terms of directed lattice paths is available. Our analysis shows that the key factor responsible for the tangency property is the concavity of the entropy (also called the Lagrangean function) of long random lattice paths. We extend the proof of the tangency to $q$-deformed paths., Comment: published version, 22 pages

We investigate the bipartite fidelity $\mathcal F_d$ for a lattice model described by a logarithmic CFT: the model of critical dense polymers. We define this observable in terms of a partition function on the pants geometry, where $d$ defects enter at the top of the pants lattice and exit in one of the legs. Using the correspondence with the XX spin chain, we obtain an exact closed-form expression for $\mathcal F_d$ and compute the leading terms in its $1/N$ asymptotic expansion as a function of $x = N_A/N$, where $N$ is the lattice width at the top of the pants and $N_A$ is the width of the leg where the defects exit. We find an agreement with the results of St\'ephan and Dubail for rational CFTs, with the central charge and conformal weights specialised to $c=-2$ and $\Delta = \Delta_{1,d+1} = d(d-2)/8$. We compute a second instance $\mathcal {\tilde F}_2$ of the bipartite fidelity for $d=2$ by imposing a different rule for the connection of the defects. In the conformal setting, this choice corresponds to inserting two boundary condition changing fields of weight $\Delta = 0$ that are logarithmic instead of primary. We compute the asymptotic expansion in this case as well and find a simple additive correction compared to $\mathcal F_2$, of the form $-2\log((1+x)/(2\sqrt{x}))$. We confirm this lattice result with a CFT derivation and find that this correction term is identical for all logarithmic theories, independently of $c$ and $\Delta$., Comment: 35 pages. v2: minor changes

We realize mirror templates on the tips of optical fibers using a single-shot CO$_2$ laser ablation procedure. We perform a systematic study of the influence of the pulse power, pulse duration, and laser spot size on the radius of curvature, depth, and diameter of the mirror templates. We find that these geometrical characteristics can be tuned to a larger extent than has been previously reported, and notably observe that compound convex-concave shapes can be obtained. This detailed investigation should help further the understanding of the physics of CO$_2$ laser ablation processes and help improve current models. We additionally identify regimes of ablation parameters that lead to mirror templates with favorable geometries for use in cavity quantum electrodynamics and optomechanics.

In the paper arXiv:1803.11463, the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for portions of arctic curve in terms of an arbitrary piecewise differentiable function that describes the defect distribution. When this distribution presents "freezing" intervals, other portions of arctic curve appear and typically have a cusp. These freezing boundaries can be of two types, respectively with maximal or minimal density of defects. Our purpose here is to extend the tangent method derivation of arXiv:1803.11463 to include these portions, hence answering the open question stated in arXiv:1803.11463., Comment: published version, 12 pages, 6 figures

If ${\cal F}$ is a set of subgraphs $F$ of a finite graph $E$ we define a graph-counting polynomial $$ p_{\cal F}(z)=\sum_{F\in{\cal F}}z^{|F|} $$ In the present note we consider oriented graphs and discuss some cases where ${\cal F}$ consists of unbranched subgraphs $E$. We find several situations where something can be said about the location of the zeros of $p_{\cal F}$., Comment: 6 pages

This note presents a non-rigorous study of the linear response for an SRB (or `natural physical') measure $\rho$ of a diffeomorphism $f$ in the presence of tangencies of the stable and unstable manifolds of $\rho$. We propose that generically, if $\rho$ has no zero Lyapunov exponent, if its stable dimension is sufficiently large (greater than 1/2 or perhaps 3/2) and if it is exponentially mixing in a suitable sense, then the following formal expression for the first derivative of $\rho(\phi)$ with respect to $f$ along $X$ is convergent: $$ \Psi(z)=\sum_{n=0}^\infty z^n\int\rho(dx)\,X(x)\cdot\nabla_x(\phi\circ f^n)\qquad{\rm for}\qquad z=1 $$ This suggests that an SRB measure may exist for small perturbations of $f$, with weak differentiability., Comment: 10 pages

A full equilibrium treatment of molecular aggregation is presented for prototypes of 1D and 3D aggregates, with and without nucleation. By skipping complex kinetic parameters like aggregate size-dependent diffusion, the equilibrium treatment allows to predict directly time-independent quantities such as critical concentrations. The relationships between the macroscopic equilibrium constants for the different paths are first established by statistical corrections and so as to comply with the detailed balance constraints imposed by nucleation, and the composition of the mixture resulting from homogeneous aggregation is then analyzed using the polylogarithm function. Several critical concentrations are distinguished: the residual monomer concentation in equilibrium (RMC) and the critical nucleation concentration (CNC), that is the threshold concentration of total subunits necessary for initiating aggregation. When increasing the concentration of total subunits, the RMC converges more strongly to its asymptotic value, the equilibrium constant of depolymerization, for 3D aggregates and in case of nucleation. The CNC moderately depends on the number of subunits in the nucleus, but sharply increases with the difference between the equilibrium constants of polymerization and nucleation. As the RMC and CNC can be numerically but not analytically determined, ansatz equations connecting them to thermodynamic parameters are proposed., Comment: 14 pages, 2 figures

We consider the Abelian sandpile model on triangular and hexagonal lattices. We compute several height probabilities on the full plane and on half-planes, and discuss some properties of the universality of the model., Comment: 26 pages, 12 figures. v2 and v3: minor corrections

We revisit the calculation of height correlations in the two-dimensional Abelian sandpile model by taking advantage of a technique developed recently by Kenyon and Wilson. The formalism requires to equip the usual graph Laplacian, ubiquitous in the context of cycle-rooted spanning forests, with a complex connection. In the case at hand, the connection is constant and localized along a semi-infinite defect line (zipper). In the appropriate limit of a trivial connection, it allows one to count spanning forests whose components contain prescribed sites, which are of direct relevance for height correlations in the sandpile model. Using this technique, we first rederive known 1- and 2-site lattice correlators on the plane and upper half-plane, more efficiently than what has been done so far. We also compute explicitly the (new) next-to-leading order in the distances ($r^{-4}$ for 1-site on the upper half-plane, $r^{-6}$ for 2-site on the plane). We extend these results by computing new correlators involving one arbitrary height and a few heights 1 on the plane and upper half-plane, for the open and closed boundary conditions. We examine our lattice results from the conformal point of view, and confirm the full consistency with the specific features currently conjectured to be present in the associated logarithmic conformal field theory., Comment: 60 pages, 21 figures. v2: reformulation of the grove theorem, minor corrections

In earlier papers we have studied the turbulent flow exponents $\zeta_p$, where $\langle|\Delta{\bf v}|^p\rangle\sim\ell^{\zeta_p}$ is the contribution to the fluid velocity at small scale $\ell$. Using ideas of non-equilibrium statistical mechanics we have found $$ \zeta_p={p\over3}-{1\over\ln\kappa}\ln\Gamma({p\over3}+1) $$ where $1/ln\kappa$ is experimentally $\approx 0.32\pm 0.01$. The purpose of the present note is to propose a somewhat more physical derivation of the formula for $\zeta_p$. We also present an estimate $\approx 100$ for the Reynolds number at the onset of turbulence., Comment: 6 pages

This note presents a minimal approach to the origin of life, following standard ideas. We pay special attention to the point of view of non-equilibrium statistical mechanics, and in particular to detailed balance. As a consequence we propose a characterization of pre-biological states., Comment: 10 pages