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Relaxation to equilibrium in Bose-Hubbard rings is numerically investigated in the time domain. We show that for small mean site populations in the Mott insulator regime, characterized by strong onsite interaction as compared to hopping, equipartition starting from nonequilibrium initial states is significantly faster in these bosonic quantum many-body systems than in their classical counterparts, given by discrete Gross-Pitaevskii lattices. We attribute this phenomenon of thermalization enhancement to a genuine quantum transport mechanism akin to tunneling, allowing for pathways that are more efficient than chaotic diffusion across the ergodic domain of the classical systems., Comment: 12 pages, 6 figures

In a recent paper Zhuoke Yang, New approaches to ${\mathfrak gl}(N)$ weight system, Izvestiya Mathematics, 2023, vol. 77:6, 150--166; arXiv:2202.12225 (2022) a construction of a weight system, which unifies ${\mathfrak gl}(N)$ weight systems for $N=1,2,\dots$, has been suggested. The construction is based on an extension of the ${\mathfrak gl}(N)$ weight systems to permutations. This universal weight system takes values in the algebra of polynomials ${\mathbb C}[N;C_1,C_2,\dots]$ in infinitely many variables. We show that under the substitution $C_m=xN^{m-1}$, $m=1,2,\dots$, the leading term in $N$ of the value of the universal ${\mathfrak gl}$ weight system becomes the chromatic polynomial of the intersection graph of the chord diagram. Moreover, we show that under the substition $C_m=p_m N^{m-1}$, $m=1,2,\dots$, the leading term in $N$ of the value of the universal ${\mathfrak gl}$ weight system determines a flitered Hopf algebra homomorphism from the rotational Hopf algebra of permutations, which we construct in the present paper, to the Hopf algebra of polynomials ${\mathbb C}[p_1,p_2,\dots]$., Comment: 21 page

We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a transform order. Notably, this method exhibits broad applicability, particularly since several well-known nonparametric distribution families can be defined using relevant transform orders, including the convex and the star transform orders. In the context of convex-ordered families, we demonstrate that applying Jensen's inequality enables the derivation of bounds for the probability that a random variable exceeds the expected value of its corresponding order statistic.

Weight systems are functions on chord diagrams satisfying so-called Vassiliev's $4$-term relations. They are closely related to finite type knot invariants introduced by Vassiliev. Certain weight systems can be derived from graph invariants. Another main source of weight systems are Lie algebras. In recent papers, the weight systems associated to Lie algebras ${\mathfrak gl}(N)$ were unified in a universal ${\mathfrak gl}$-weight system, which takes values in the ring of polynomials in infinitely many variables. The unification has been achieved by extending the ${\mathfrak gl}(N)$-weight systems from chord diagrams to arbitrary permutations. A natural question then arises, namely, which already known weight systems can be obtained from the universal ${\mathfrak gl}$ weight system. In addition to understanding the internal relationship between weight systems, knowing that a given weight system can be induced from the ${\mathfrak gl}$-weight system would immediately lead to extending the former to arbitrary permutations. To each chord diagram, one can associate a graph, called the intersection graph of the chord diagram. Certain weight systems are completely determined by the intersection graphs. In general, the relationship between Lie algebra weight systems and polynomial graph invariants looks rather complicated. Our main result in the present paper consists in showing that the well-known graph and delta-matroid invariant, the interlace polynomial, can be induced from the universal ${\mathfrak gl}$-weight system. We provide an explicit substitution making the ${\mathfrak gl}$-weight system into the interlace polynomial for chord diagrams and their intersection graphs., Comment: 22 pages

Loudspeaker rendering techniques that create phantom sound sources often assume an equidistant loudspeaker layout. Typical home setups might not fulfill this condition as loudspeakers deviate from canonical positions, thus requiring a corresponding calibration. The standard approach is to compensate for delays and to match the loudness of each loudspeaker at the listener's location. It was found that a shift of the phantom image occurs when this calibration procedure is applied and one of a pair of loudspeakers is significantly closer to the listener than the other. In this paper, a novel approach to panning on non-equidistant loudspeaker layouts is presented whereby the panning position is governed by the direct sound and the perceived loudness is governed by the full impulse response. Subjective listening tests are presented that validate the approach and quantify the perceived effect of the compensation. In a setup where the standard calibration leads to an average error of 10 degrees, the proposed direct sound compensation largely returns the phantom source to its intended position., Comment: 10 pages. Accepted for presentation in AES Convention 155 (2023)

Given a pair of non-negative random variables $X$ and $Y$, we introduce a class of nonparametric tests for the null hypothesis that $X$ dominates $Y$ in the total time on test order. Critical values are determined using bootstrap-based inference, and the tests are shown to be consistent. The same approach is used to construct tests for the excess wealth order. As a byproduct, we also obtain a class of goodness-of-fit tests for the NBUE family of distributions.

We study the disorder-induced crossover between the two recently discovered thermalization slowing-down universality classes -- characterized by long- and short-range coupling -- in classical unitary circuits maps close to integrability. We compute Lyapunov spectra, which display qualitatively distinct features depending on whether the proximity to the integrable limit is short or long ranged. For sufficiently small nonlinearity, translationally invariant systems fall into the long-range class. Adding disorder to such a system triggers a transition to the short-range class -- implying a breaking of this invariance -- and in the very limit of vanishing non-linearity Anderson localization emerges. The crossover from long- to short-range class is attained by tuning the localization length, $\xi$, from $\xi \approx N$ to $\xi \ll N$, where $N$ is the system size. As a consequence, the Lyapunov spectrum becomes exponentially suppressed, depending on how strongly its translational invariance is destroyed. We expect that this disorder-induced crossover will lead to prethermalized phases and, following quantization, to many-body localization.

We study the time evolution of mean values of quantum operators in a regime plagued by two difficulties: The smallness of $\hbar$ and the presence of strong and ubiquitous classical chaos. While numerics become too computationally expensive for purely quantum calculations as $\hbar \to 0$, methods that take advantage of the smallness of $\hbar$ -- that is, semiclassical methods -- suffer from both conceptual and practical difficulties in the deep chaotic regime. We implement an approach which addresses these conceptual problems, leading to a deeper understanding of the origin of the interference contributions to the operator's mean value. We show that in the deep chaotic regime our approach is capable of unprecedented accuracy, while a standard semiclassical method (the Herman-Kluk propagator) produces only numerical noise. Our work paves the way to the development and employment of more efficient and accurate methods for quantum simulations of systems with strongly chaotic classical limits., Comment: 6+9 pages, 3+5 figures. Published version

Given samples from two non-negative random variables, we propose a family of tests for the null hypothesis that one random variable stochastically dominates the other at the second order. Test statistics are obtained as functionals of the difference between the identity and the Lorenz P-P plot, defined as the composition between the inverse unscaled Lorenz curve of one distribution and the unscaled Lorenz curve of the other. We determine upper bounds for such test statistics under the null hypothesis and derive their limit distribution, to be approximated via bootstrap procedures. We then establish the asymptotic validity of the tests under relatively mild conditions and investigate finite sample properties through simulations. The results show that our testing approach can be a valid alternative to classic methods based on the difference of the integrals of the cumulative distribution functions, which require bounded support and struggle to detect departures from the null in some cases.

We characterize thermalization slowing-down of Josephson junction networks in 1, 2 and 3 spatial dimensions for systems with hundreds of sites by computing their entire Lyapunov spectra. The ratio of Josephson coupling $E_J$ to energy density $h$ controls two different universality classes of thermalization slowing-down, namely the weak coupling regime, $E_J/h \rightarrow 0$, and the strong coupling regime, $E_J/h \rightarrow \infty$. We analyze the Lyapunov spectrum by measuring the largest Lyapunov exponent and by fitting the rescaled spectrum with a general ansatz. We then extract two scales: the Lyapunov time (inverse of the largest exponent) and the exponent for the decay of the rescaled spectrum. The two universality classes, which exist irrespective of network dimension, are characterized by different ways the extracted scales diverge. The universality class corresponding to the weak-coupling regime allows for the coexistence of chaos with a large number of near-conserved quantities and is shown to be characterized by universal critical exponents, in contrast with the strong-coupling regime. We expect our findings, which we explain using perturbation theory arguments, to be a general feature of diverse Hamiltonian systems., Comment: 6+8 pages, 3+6 figures. Published version

We describe recent achievements in the theory of weight systems, which are functions on chord diagrams satisfying so-called $4$-term relations. Our main attention is devoted to constructions of weight systems. The two main sources of these constructions that are discussed in the paper are invariants of intersection graphs of chord diagrams that satisfy $4$-term relations for graphs and metrized Lie algebras. For the simplest nontrivial metrized Lie algebra $\mathfrak {sl}(2)$, we present recent results about the explicit form of generating functions for the values of the corresponding weight system on important families of chord diagrams. We also explain another recent result: construction of recurrence relations for computing the values of the $\mathfrak{gl}(N)$-weight system. These relations are based on M. Kazarian's extension of the $\mathfrak{gl}(N)$-weight system to arbitrary permutations. Certain recent papers suggest an approach to extending weight systems and graph invariants to arbitrary embedded graphs, which is based on the study of the corresponding Hopf algebra structures; we describe this approach. Weight systems defined on arbitrary embedded graphs correspond to finite type invariants of links (multicomponent knots)., Comment: 46 pages, 11 figures

Future energy systems rely mostly on supply-dependent resources like wind and solar energy. Since most of the produced energy from distributed renewable sources arises as electricity, electrification of energy consumers and producers, called prosumers, expands. In this context, multi-modal distribution grids make use of the storage capabilities of other energy sectors like heat, and abolish the supply-dependency and uncertainty of the feed-in of decentralized generators. This provides flexibility in the energy system, which increases security of supply and at the same time ensures economical energy provision. The subject of this paper is to exploit the flexibility of such a multi-modal energy system for operation in an optimal way. The cellular approach serves here as the energy system architecture. Aim is to provide flexibility with a cell by optimally distributing a flexibility request to subordinate prosumers changing their active and reactive power. The load change is hereby to be optimally dispatched to the different components of the prosumers under consideration of technical restrictions and dynamic behavior of components, the grids and economical aspects. For dynamic modelling and simulation the open-source modelling language Modelica is used. Using a low-voltage benchmark model expanded by multi-modal technologies, the proposed methodology shows that the cells are capable of providing flexibility to the overlying grid with high accuracy at low costs., Comment: Submitted to VDE ETG Congress 2023

To improve nonparametric estimates of lifetime distributions, we propose using the increasing odds rate (IOR) model as an alternative to other popular, but more restrictive, ``adverse ageing'' models, such as the increasing hazard rate one. This extends the scope of applicability of some methods for statistical inference under order restrictions, since the IOR model is compatible with heavy-tailed and bathtub distributions. We study a strongly uniformly consistent estimator of the cumulative distribution function of interest under the IOR constraint. Numerical evidence shows that this estimator often outperforms the classic empirical distribution function when the underlying model does belong to the IOR family. We also study two different tests, aimed at detecting deviations from the IOR property, and we establish their consistency. The performance of these tests is also evaluated through simulations.

Matter wave revivals depend on a delicate interplay of constructive many-body quantum interferences in the developing dynamics of an ultracold bosonic system in an optical lattice. It is shown that the interplay between weak intersite tunneling and strong onsite interactions can lead to the quantum dynamics of a density wave displaying several features not found in the mean-field limit: occupancy oscillations, resurgent revivals, and a (anti-) synchronization of revival peaks and occupancy oscillation peaks. This implies cooperative interference effects that alternate between constructive and destructive features leading to the peak revival behaviors. These many-body quantum interference phenomena create striking features in various observables, which are accessible in experimental measurements., Comment: 6 pages, 4 figures

We introduce a new one-variable polynomial invariant of graphs, which we call the skew characteristic polynomial. For an oriented simple graph, this is just the characteristic polynomial of its anti-symmetric adjacency matrix. For nonoriented simple graphs the definition is different, but for a certain class of graphs (namely, for intersection graphs of chord diagrams), it gives the same answer if we endow such a graph with an orientation induced by the chord diagram. We prove that this invariant satisfies Vassiliev's $4$-term relations and determines therefore a finite type knot invariant. We investigate the behaviour of the polynomial with respect to the Hopf algebra structure on the space of graphs and show that it takes a constant value on any primitive element in this Hopf algebra. We also provide a two-variable extension of the skew characteristic polynomial to embedded graphs and delta-matroids. The $4$-term relations for the extended polynomial prove that it determines a finite type invariant of multicomponent links.

Classically allowed transport is shown to compete with quantum tunneling during the ionization of atoms by ultrashort and intense laser pulses, despite Keldysh parameters smaller than unity. This is done by comparing exact probability densities with the ones obtained from purely classical propagation using the Truncated Wigner Approximation. Not only is classical transport capable of moving trajectories away from the core, but it can also furnish ionization probabilities of the same order as the quantum ones for intensities currently employed in experiments. Our results have implications ranging from a conceptual correction to semiclassical step models in strong-field physics to the ongoing debate about tunneling time measurements in attoclock experiments., Comment: Small modifications to the text after feedback from readers. Layout of figures updated. Integration of Hamilton's equations updated to include automatic stiffness detection

In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of the usual stochastic order. For this purpose, we introduce a generalized family of stochastic orders, which is referred to as transform orders, showing that it provides a flexible framework for deriving stochastic monotonicity results. Given that our general definition makes it possible to obtain some well-known ordering relations as particular cases, we can easily apply our method to different families of functionals. These include some prominent inequality measures, such as the generalized entropy, the Gini index, and its generalizations. We also illustrate the applicability of our approach by determining the least favorable distribution, and the behavior of some bootstrap statistics, in some goodness-of-fit testing procedures.