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An extension of the notion of classical equivalence of equivalence in the Batalin–Vilkovisky (BV) and Batalin–Fradkin–Vilkovisky (BFV) frameworks for local Lagrangian field theory on manifolds possibly with boundary is discussed. Equivalence is phrased in both a strict and a lax sense, distinguished by the compatibility between the BV data for a field theory and its boundary BFV data, necessary for quantisation. In this context, the first- and second-order formulations of nonabelian Yang–Mills and of classical mechanics on curved backgrounds, all of which admit a strict BV–BFV description, are shown to be pairwise equivalent as strict BV–BFV theories. This in particular implies that their BV complexes are quasi-isomorphic. Furthermore, Jacobi theory and one-dimensional gravity coupled with scalar matter are compared as classically equivalent reparametrisation-invariant versions of classical mechanics, but such that only the latter admits a strict BV–BFV formulation. They are shown to be equivalent as lax BV–BFV theories and to have isomorphic BV cohomologies. This shows that strict BV–BFV equivalence is a strictly finer notion of equivalence of theories., Letters in Mathematical Physics, 113 (1), ISSN:0377-9017, ISSN:1573-0530

We study the quantum evolution of many-body Fermi gases in three dimensions, in arbitrarily large domains. We consider both particles with non-relativistic and with relativistic dispersion. We focus on the high-density regime, in the semiclassical scaling, and we consider a class of initial data describing zero-temperature states. In the non-relativistic case we prove that, as the density goes to infinity, the many-body evolution of the reduced one-particle density matrix converges to the solution of the time-dependent Hartree equation, for short macroscopic times. In the case of relativistic dispersion, we show convergence of the many-body evolution to the relativistic Hartree equation for all macroscopic times. With respect to previous work, the rate of convergence does not depend on the total number of particles, but only on the density: in particular, our result allows us to study the quantum dynamics of extensive many-body Fermi gases., 44 pages, no figures. The proof of the main result has been simplified and generalized. Furthermore, we included the derivation of the time-dependent relativistic Hartree equation, for all macroscopic times

We consider a system of $N$ bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in $N$ (Gross-Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit $N \to \infty$., 51 pages, typos corrected

Optoacoustic (OA, photoacoustic) imaging capitalizes on the low scattering of ultrasound within biological tissues to provide optical absorption-based contrast with high resolution at depths not reachable with optical microscopy. For deep tissue imaging applications, OA image formation commonly relies on acoustic inversion of time-resolved tomographic data. The excitation of OA responses and subsequent propagation of ultrasound waves can be mathematically described as a forward model enabling image reconstruction via algebraic inversion. These model-based reconstruction methods have been shown to outperform alternative inversion approaches and can further render OA images from incomplete datasets, strongly distorted signals or other suboptimally recorded data. Herein, we provide a general perspective on model-based OA reconstruction methods, review recent progress, and discuss the performance of the different algorithms under practical imaging scenarios., Frontiers in Physics, 10, ISSN:2296-424X

Coding theory where the alphabet is identified with the elements of a ring or a module has become an important research topic over the last 30 years. It has been well established that, with the generalization of the algebraic structure to rings, there is a need to also generalize the underlying metric beyond the usual Hamming weight used in traditional coding theory over finite fields. This paper introduces a generalization of the weight introduced by Shi, Wu and Krotov, called overweight. Additionally, this weight can be seen as a generalization of the Lee weight on the integers modulo 4 and as a generalization of Krotov’s weight over the integers modulo 2s for any positive integer s. For this weight, we provide a number of well-known bounds, including a Singleton bound, a Plotkin bound, a sphere-packing bound and a Gilbert–Varshamov bound. In addition to the overweight, we also study a well-known metric on finite rings, namely the homogeneous metric, which also extends the Lee metric over the integers modulo 4 and is thus heavily connected to the overweight. We provide a new bound that has been missing in the literature for homogeneous metric, namely the Johnson bound. To prove this bound, we use an upper estimate on the sum of the distances of all distinct codewords that depends only on the length, the average weight and the maximum weight of a codeword. An effective such bound is not known for the overweight.

We are investigating the feasibility of using CMOS foundries to fabricate silicon detectors, both for pixels and for large-area strip sensors. The availability of multi-layer routing will provide the freedom to optimize the sensor geometry and the performance, with biasing structures in poly-silicon layers and MIM-capacitors allowing for AC coupling. A prototyping production of strip test-structures and RD53A compatible pixel sensors was recently completed at LFoundry in a 150 nm CMOS process. This paper will focus on the characterization of irradiated and non-irradiated pixel modules, composed by a CMOS passive sensor interconnected to a RD53A chip. The sensors are designed with a pixel cell of 25 × 100 μm2 in case of DC coupled devices and 50 × 50 μm2 for the AC coupled ones. Their performance in terms of charge collection, position resolution, and hit efficiency was studied with measurements performed in the laboratory and with beam tests. The RD53A modules with LFoundry silicon sensors were irradiated to fluences up to 1.0 × 1 0 16 n eq c m 2 ., Journal of Instrumentation, 17 (9), ISSN:1748-0221

In this note, we revisit the $\Theta$-invariant as defined by R. Bott and the first author. The $\Theta$-invariant is an invariant of rational homology 3-spheres with acyclic orthogonal local systems, which is a generalization of the 2-loop term of the Chern-Simons perturbation theory. The $\Theta$-invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the $\Theta$-invariant that we can define even if the cohomology group is not vanishing., Comment: 13 pages

We consider a Bose gas consisting of $N$ particles in $\mathbb{R}^3$, trapped by an external field and interacting through a two-body potential with scattering length of order $N^{-1}$. We prove that low energy states exhibit complete Bose-Einstein condensation with optimal rate, generalizing previous work in \cite{BBCS1, BBCS4}, restricted to translation invariant systems. This extends recent results in \cite{NNRT}, removing the smallness assumption on the size of the scattering length., 67 pages

We show that Bogoliubov theory correctly predicts the low-energy spectral properties of Bose gases in the Gross-Pitaevskii regime. We recover recent results from [6, 7]. While our main strategy is similar to the one developed in [6, 7], we combine it with new ideas, taken in part from [15, 25]; this makes our proof substantially simpler and shorter. As an important step towards the proof of Bogoliubov theory, we show that low-energy states exhibit complete Bose-Einstein condensation with optimal control over the number of orthogonal excitations.

We construct a formal global quantization of the Poisson Sigma Model in the BV-BFV formalism using the perturbative quantization of AKSZ theories on manifolds with boundary and analyze the properties of the boundary BFV operator. Moreover, we consider mixed boundary conditions and show that they lead to quantum anomalies, i.e. to a failure of the (modified differential) Quantum Master Equation. We show that it can be restored by adding boundary terms to the action, at the price of introducing corner terms in the boundary operator. We also show that the quantum GBFV operator on the total space of states is a differential, i.e. squares to zero, which is necessary for a well-defined BV cohomology., Comment: 56 pages, 22 figures, glossary added, presentation improved for non experts. Section 2 is very similar to Section 2 of our companion paper arXiv:1807.11782. Also Appendix A.1-3, on the compactification of configuration spaces of manifolds with boundary, are taken from there but Section A.4, on the case of manifolds with corners, is added. To appear in Commun. Math. Phys

We study four dimensional gauge theories in the context of an equivariant extension of the Batalin-Vilkovisky (BV) formalism. We discuss the embedding of BV Yang-Mills (YM) theory into a larger BV theory and their relation. Partial integration in the equivariant BV setting (BV push-forward map) is performed explicitly for the abelian case. As result, we obtain a non-local homological generalization of the Cartan calculus and a non-local extension of the abelian YM BV action which satisfies the equivariant master equation., Comment: 27 pages, refs added, published version

We describe the upgrade and performance of the high-purity germanium counting facility Gator, which is dedicated to low-background γ-ray spectrometry. Gator is operated at the Gran Sasso Underground Laboratory in Italy, at an average depth of 3600 meter water equivalent, and employed for material screening and selection in ultra-low background, rare-event search experiments in astroparticle physics. The detector is equipped with a passive shield made of layers of copper, lead and polyethylene, and the sample cavity is purged with gaseous nitrogen maintained at positive pressure for radon suppression. After upgrading its enclosure, the background rate is (82.0 ± 0.7) counts/(kg·day) in the energy region 100 keV to 2700 keV, a 20% reduction compared to the previously reported rate. We show the stability of various operation parameters as a function of time. We also summarize the sample analysis procedure, and demonstrate Gator's sensitivity by examining one material sample, a candidate photosensor for the DARWIN experiment.

We prove an upper bound for the ground state energy of a Bose gas consisting of $N$ hard spheres with radius $\mathfrak{a}/N$, moving in the three-dimensional unit torus $\Lambda$. Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit $N \to \infty$. The proof is based on the construction of an appropriate trial state, given by the product of a Jastrow factor (describing two-particle correlations on short scales) and of a wave function constructed through a (generalized) Bogoliubov transformation, generating orthogonal excitations of the Bose-Einstein condensate and describing correlations on large scales., Comment: Final version, 58 pages

In the search for a monochromatic peak as the signature of neutrinoless double beta decay an excellent energy resolution and an ultra-low background around the $Q$-value of the decay are essential. The LEGEND-200 experiment performs such a search with high-purity germanium detectors enriched in $^{76}$Ge immersed in liquid argon. To determine and monitor the stability of the energy scale and resolution of the germanium diodes, custom-made, low-neutron emission $^{228}$Th sources are regularly deployed in the vicinity of the crystals. Here we describe the production process of the 17 sources available for installation in the experiment, the measurements of their alpha- and gamma-activities, as well as the determination of the neutron emission rates with a low-background LiI(Eu) detector operated deep underground. With a flux of $\left( 4.27 \pm 0.60_{\rm stat} \pm 0.92_{\rm syst} \right) \times 10^{-4} ~\text{n / (kBq$\cdot$s)}$, approximately one order of magnitude below that of commercial sources, the neutron-induced background rate, mainly from the activation of $^{76}$Ge, is negligible compared to other background sources in LEGEND-200., Comment: 13 pages + references; typos corrected, comments from journal referee's implemented

In this study, we analyse the aggregated transaction networks of Ether (the native cryptocurrency in Ethereum) and the three most market-capitalised ERC-20 tokens in this platform at the time of writing: Binance, USDT, and Chainlink. We analyse a comprehensive dataset from 2015 to 2020 (encompassing 87,780,546 nodes and 856,207,725 transactions) to understand the mechanism that drives their growth. In a seminal analysis, Kondor et al. (PLoS ONE, 2014, 9: e86197) showed that during its first year, the aggregated Bitcoin transaction network grew following linear preferential attachment. For the Ethereum-based cryptoassets, we find that they present in general super-linear preferential attachment, i.e., the probability for a node to receive a new incoming link is proportional to kα, where k is the node’s degree. Specifically, we find an exponent α = 1.2 for Binance and Chainlink, for Ether α = 1.1, and for USDT α = 1.05. These results reveal that few nodes become hubs rapidly. We then analyse wealth and degree correlation between tokens since many nodes are active simultaneously in different networks. We conclude that, similarly to what happens in Bitcoin, “the rich indeed get richer” in Ethereum and related tokens as well, with wealth much more concentrated than in-degree and out-degree.

A construction of gauge-invariant observables is suggested for a class of topological field theories, the AKSZ sigma-models. The observables are associated to extensions of the target Q-manifold of the sigma model to a Q-bundle over it with additional Hamiltonian structure in fibers., Comment: 36 pages

The oriented graph complexes $${GC^{or}_n}$$ are complexes of directed graphs without directed cycles. They govern, for example, the quantization of Lie bialgebras and infinite dimensional deformation quantization. Similar to the ordinary graph complexes GC n introduced by Kontsevich they come in two essentially different versions, depending on the parity of n. It is shown that, surprisingly, the oriented graph complex $${GC^{or}_n}$$ is quasi-isomorphic to the ordinary commutative graph complex of opposite parity GC n-1, up to some known classes. This yields in particular a combinatorial description of the action of $${\mathfrak{grt}_{1} \cong H^0({\rm GC}_2)}$$ on Lie bialgebras, and shows that a cycle-free formality morphism in the sense of Shoikhet can be constructed rationally without reference to configuration space integrals. Curiously, the obstruction class in the oriented graph complex found by Shoikhet corresponds to the well known theta graph in the ordinary graph complex.

We consider the many-body quantum evolution of a factorized initial data, in the mean-field regime. We show that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates, that are consistent with central limit theorems that have been established in the last years., 21 pages, small changes in the introduction

In this paper we obtain the following stability result for periodic multi-solitons of the KdV equation: We prove that under any given semilinear Hamiltonian perturbation of small size $\varepsilon > 0$, a large class of periodic multi-solitons of the KdV equation, including ones of large amplitude, are orbitally stable for a time interval of length at least $O(\varepsilon^{-2})$. To the best of our knowledge, this is the first stability result of such type for periodic multi-solitons of large size of an integrable PDE., The title has been changed. Other minor changes in the text

We discuss observables of an equivariant extension of the A-model in the framework of the AKSZ construction. We introduce the A-model observables, a class of observables that are homotopically equivalent to the canonical AKSZ observables but are better behaved in the gauge fixing. We discuss them for two different choices of gauge fixing: the first one is conjectured to compute the correlators of the A-model with target the Marsden-Weinstein reduced space; in the second one we recover the topological Yang-Mills action coupled with A-model so that the A-model observables are closed under supersymmetry., Comment: 16 pages; minor corrections

Construct recursively a long string of words w1. .. wn, such that at each step k, w k+1 is a new word with a fixed probability p $\in$ (0, 1), and repeats some preceding word with complementary probability 1 -- p. More precisely, given a repetition occurs, w k+1 repeats the j-th word with probability proportional to j $\alpha$ for j = 1,. .. , k. We show that the proportion of distinct words occurring exactly times converges as the length n of the string goes to infinity to some probability mass function in the variable $\ge$ 1, whose tail decays as a power function when 1 -- p > $\alpha$/(1 + $\alpha$), and exponentially fast when 1 -- p < $\alpha$/(1 + $\alpha$).

Bitcoin is built on a blockchain, an immutable decentralised ledger that allows entities (users) to exchange Bitcoins in a pseudonymous manner. Bitcoins are associated with alpha-numeric addresses and are transferred via transactions. Each transaction is composed of a set of input addresses (associated with unspent outputs received from previous transactions) and a set of output addresses (to which Bitcoins are transferred). Despite Bitcoin was designed with anonymity in mind, different heuristic approaches exist to detect which addresses in a specific transaction belong to the same entity. By applying these heuristics, we build an Address Correspondence Network: in this representation, addresses are nodes are connected with edges if at least one heuristic detects them as belonging to the same entity. %addresses are nodes and edges are drawn between addresses detected as belonging to the same entity by at least one heuristic. %nodes represent addresses and edges model the likelihood that two nodes belong to the same entity %In this network, connected components represent sets of addresses controlled by the same entity. In this paper, we analyse for the first time the Address Correspondence Network and show it is characterised by a complex topology, signalled by a broad, skewed degree distribution and a power-law component size distribution. Using a large-scale dataset of addresses for which the controlling entities are known, we show that a combination of external data coupled with standard community detection algorithms can reliably identify entities. The complex nature of the Address Correspondence Network reveals that usage patterns of individual entities create statistical regularities; and that these regularities can be leveraged to more accurately identify entities and gain a deeper understanding of the Bitcoin economy as a whole., 21 pages, 13 figures

We study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

We consider systems of N bosons trapped on the two-dimensional unit torus, in the Gross-Pitaevskii regime, where the scattering length of the repulsive interaction is exponentially small in the number of particles. We show that low-energy states exhibit complete Bose-Einstein condensation, with almost optimal bounds on the number of orthogonal excitations., 72 pages, improved rate of condensation

We extend the classical one-parameter Yule-Simon law to a version depending on two parameters, which in part appeared in Bertoin [2019] in the context of a preferential attachment algorithm with fading memory. By making the link to a general branching process with age-dependent reproduction rate, we study the tail-asymptotic behavior of the two-parameter Yule-Simon law, as it was already initiated in the mentioned paper. Finally, by superposing mutations to the branching process, we propose a model which leads to the full two-parameter range of the Yule-Simon law, generalizing thereby the work of Simon [1955] on limiting word frequencies., Comment: 19 pages

We establish an upper bound for the ground state energy per unit volume of a dilute Bose gas in the thermodynamic limit, capturing the correct second-order term, as predicted by the Lee–Huang–Yang formula. This result was first established in [20] by H.-T. Yau and J. Yin. Our proof, which applies to repulsive and compactly supported $V \in L^3 (\mathbb {R}^3)$ , gives better rates and, in our opinion, is substantially simpler.

We study interacting Bose gases in thermal equilibrium on a lattice. We establish convergence of the grand canonical Gibbs states of such gases to their mean-field (classical field) and large-mass (classical particle) limits. The former is a classical field theory for a complex scalar field with quartic self-interaction. The latter is a classical theory of point particles with two-body interactions. Our analysis is based on representations in terms of ensembles of interacting random loops, the Ginibre loop ensemble for Bose gases and the Symanzik loop ensemble for classical scalar field theories. For small enough interactions, our results also hold in infinite volume., Revised version

Cryptocurrencies are distributed systems that allow exchanges of native (and non-) tokens among participants. The complete historical bookkeeping and its wide availability opens up an unprecedented possibility, i.e. that of understanding the evolution of their network structure while gaining useful insight on the relationships between user' behaviour and cryptocurrency pricing in exchange markets. In this contribution we review some of the most recent results concerning the structural properties of Bitcoin Transaction Networks, a generic name referring to a set of different constructs: the Bitcoin Address Network, the Bitcoin User Network and the Bitcoin Lightning Network. The picture that emerges is that of system growing over time, which becomes increasingly sparse and whose mesoscopic structural organization is characterised by the presence of an increasingly significant core-periphery structure. Such a peculiar topology is matched by a highly uneven distribution of bitcoins, a result suggesting that Bitcoin is becoming an increasingly centralized system at different levels., Comment: 15 pages, 7 figures

We study an equivariant extension of the Batalin-Vilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation, and we apply it to the natural equivariant extension of AKSZ solutions of the classical master equation (CME). As examples of the construction, we recover the equivariant extension of supersymmetric Yang-Mills in 2d and of Donaldson-Witten theory., Comment: 22 pages, refs added, typos corrected, the final published version in J.Geom.Phys

We consider systems of bosons trapped in a box, in the Gross-Pitaevskii regime. We show that low-energy states exhibit complete Bose-Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in \cite{BBCS1}, removing the assumption of small interaction potential., 99 pages, typos corrected

These notes give an introduction to the mathematical framework of the Batalin-Vilkovisky and Batalin-Fradkin-Vilkovisky formalisms. Some of the presented content was given as a mini course by the first author at the 2018 QSPACE conference in Benasque., 63 pages, 10 figures, minor changes made (added some references, corrected some typos and some small mistakes)

Dark Matter In CCDs (DAMIC) is a silicon detector apparatus used primarily for searching for low-mass dark matter using the silicon bulk of Charge-Coupled Devices (CCDs) as targets. The silicon target within each CCD is \SI{675}{\micro\meter} thick and its top surface is divided into over 16 million \SI{15}{\micro\meter} $\times$ \SI{15}{\micro\meter} pixels. The DAMIC collaboration has installed a number of these CCDs at SNOLAB. As of 2019, DAMIC at SNOLAB has reached operational conditions with leakage current less than \SI{8.2e-22}{\ampere\per\centi\meter\squared} and a readout noise of \SI{1.6}{\electron}, achieved with 5 CCDs. A new DAMIC apparatus will be installed at Laboratoire Souterrain de Modane in a few years. The DAMIC at Modane (DAMIC-M) collaboration will be using an improved version of CCDs designed by Lawrence Berkeley National Laboratory with skipper amplifiers that use non-destructive readout with multiple-sampling, enabling the CCDs to achieve a readout noise of \SI{0.068}{\electron}. The low readout noise, in conjunction with low leakage current of these skipper CCDs, will allow DAMIC-M to observe physics processes with collisions energies as low as \SI{1}{\electronvolt}. The DAMIC-M experiment will consist of an array of 50 large-area skipper CCDs with more than 36 million pixels in each CCD. The following proceeding will introduce the DAMIC apparatus at SNOLAB and its results and as well as the capabilities and the status of the new DAMIC-M experiment., Proceeding for the IPRD19 conference

In this note the AKSZ construction is applied to the BFV description of the reduced phase space of the Einstein–Hilbert and of the Palatini–Cartan theories in every space-time dimension greater than two. In the former case one obtains a BV theory for the first-order formulation of Einstein–Hilbert theory, in the latter a BV theory for Palatini–Cartan theory with a partial implementation of the torsion-free condition already on the space of fields. All theories described here are BV versions of the same classical system on cylinders. The AKSZ implementations we present have the advantage of yielding a compatible BV–BFV description, which is the required starting point for a quantization in presence of a boundary., Communications in Mathematical Physics, 385, ISSN:1432-0916, ISSN:0010-3616