Analytical Arguments Research Articles

Fading ergodicity

Eigenstate thermalization hypothesis (ETH) represents a breakthrough in many-body physics since it allows us to link thermalization of physical observables with the applicability of random matrix theory (RMT). Recent years were also extremely fruitful in exploring possible counterexamples to thermalization, ranging, among others, from integrability, single-particle chaos, many-body localization, many-body scars, to Hilbert-space fragmentation. In all these cases the conventional ETH is violated. However, it remains elusive how the conventional ETH breaks down when one approaches the boundaries of ergodicity, and whether the range of validity of the conventional ETH coincides with the validity of RMT-like spectral statistics. Here we bridge this gap and we introduce a scenario of the ETH breakdown in many-body quantum systems, dubbed fading ergodicity regime, which establishes a link between the conventional ETH and nonergodic behavior. We conjecture this scenario to be relevant for the description of finite many-body systems at the boundaries of ergodicity, and we provide numerical and analytical arguments for its validity in the quantum sun model of ergodicity-breaking phase transition. For the latter, we provide evidence that the breakdown of the conventional ETH is not associated with the breakdown of the RMT-like spectral statistics. Published by the American Physical Society 2024

Stark many-body localization under periodic driving

We study the stability of localization under periodic driving in Stark many-body systems. We find that localization is stable except near special resonant frequencies, where resonances cause delocalization. We provide approximate analytical arguments and numerical evidence in support of these results. This shows that disorder-free broken ergodicity is stable to driving, opening up the way to studying nonequilibrium driven physics in a different setting. Published by the American Physical Society 2024

Strange-metal behavior without fine tuning in PrV2Al20

Strange-metal behavior observed in the praseodymium-based heavy-fermion material PrV2Al20 has been tentatively interpreted in the framework of proximity to a quantum critical point (QCP) associated with quadrupolar ordering. Here, we demonstrate that an alternative, natural explanation exists without invoking a QCP, in terms of the unconventional nature of the quadrupolar Kondo effect taking place in non-Kramers ions. Using a combination of density-functional theory calculations and analytical arguments, we construct a periodic Anderson model with realistic parameters to describe PrV2Al20. We solve the model using dynamical mean-field theory preserving the model symmetries and demonstrate the non-Fermi liquid strange-metal behavior stemming from the two-channel nature of the quadrupolar Kondo effect. Our calculations provide an explanation for the puzzling temperature dependence in the magnetic susceptibility and provide a basis for analyzing future photoemission experiments. Published by the American Physical Society 2024

Basis Set Extrapolation from the Vanishing Counterpoise Correction Condition.

Basis set extrapolations are typically rationalized either from analytical arguments involving the partial-wave or principal expansions of the correlation energy in helium-like systems or from fitting extrapolation parameters to reference energetics for a small(ish) training set. Seeking to avoid both, we explore a third alternative: extracting extrapolation parameters from the requirement that the BSSE (basis set superposition error) should vanish at the complete basis set limit. We find this to be a viable approach provided that the underlying basis sets are not too small and reasonably well balanced. For basis sets not augmented by diffuse functions, BSSE minimization and energy fitting yield quite similar parameters.

Tunneling away the relic neutrino asymmetry

The Earth acts as a matter potential for relic neutrinos which modifies their index of refraction from vacuum by δ∼10−8. It has been argued that the refractive effects from this potential should lead to a large O(δ) neutrino-antineutrino asymmetry at the surface of the Earth. This result was computed by treating the Earth as flat. In this work, we revisit this calculation in the context of a perfectly spherical Earth. We demonstrate, both numerically and through analytic arguments, that the flat-Earth result is only recovered under the condition δ3/2kR≫1, where k is the typical momentum of the relic neutrinos and R is the radius of the Earth. This condition is required to prevent antineutrinos from tunneling into classically inaccessible trajectories below the Earth’s surface and washing away the large asymmetry. As the physical parameters of the Earth do not satisfy this condition, we find that the asymmetry at the surface should only be O(δ). While the asphericity of the Earth may serve as a loophole to our conclusions, we argue that it is still difficult to generate a large asymmetry even in the presence of local terrain. Published by the American Physical Society 2024

Beyond directed hypergraphs: heterogeneous hypergraphs and spectral centralities

Abstract The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article, we introduce the notion of heterogeneous hypergraphs from an algebraic point of view, which have traditional directed hypergraphs as a particular case. We furthermore analytically study the spectral centralities associated to some types of heterogeneous hypergraphs, extending previously defined eigenvector-like centrality measures to this new realm. We supplement the analytical arguments with some numerical comparisons of pairwise and higher order rankings, and we construct directed higher order networks from real data, which we then use for discussion and analysis.

Structural stability hypothesis of dual unitary quantum chaos

Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits—a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focusing on the , i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions. Published by the American Physical Society 2024

Spinning waveforms from the Kosower-Maybee-O’Connell formalism at leading order

We provide the analytic waveform in time domain for the scattering of two Kerr black holes at leading order in the post-Minkowskian (weak field, but generic velocity) expansion and up to fourth order in both spins. The result is obtained by the generalization of the Kosower-Maybee-O’Connell formalism to radiative observables, combined with the analytic continuation of the five-point scattering amplitude to complex kinematics. We use analyticity arguments to express the waveform directly in terms of the three-point coupling of the graviton to the spinning particles and the gravitational Compton amplitudes, completely bypassing the need to compute and integrate the five-point amplitude. In particular, this allows us to easily include higher-order spin contributions for any spinning compact body. Finally, in the spinless case, we find a new compact and gauge-invariant representation of the Kovacs-Thorne waveform. Published by the American Physical Society 2024

Modelling co-evolution of resource feedback and social network dynamics in human-environmental systems

Games with environmental feedback have become a crucial area of study across various scientific domains, modelling the dynamic interplay between human decisions and environmental changes, and highlighting the consequences of our choices on natural resources and biodiversity. In this work, we propose a co-evolutionary model for human-environment systems that incorporates the effects of knowledge feedback and social interaction on the sustainability of common pool resources (CPRs). The model represents consumers as agents who adjust their resource extraction based on the resource’s state. These agents are connected through social networks, where links symbolize either affinity or aversion among them. The interplay between social dynamics and resource dynamics is explored, with the system’s evolution analyzed across various network topologies and initial conditions. We find that knowledge feedback can independently sustain CPRs. However, the impact of social interactions on sustainability is dual-faceted: it can either support or impede sustainability, influenced by the network’s connectivity and heterogeneity. A notable finding is the identification of a critical network mean degree, beyond which a depletion/repletion transition parallels an absorbing/active state transition in social dynamics, i.e. individual agents and their connections are/are not prone to being frozen in their social states. Furthermore, the study examines the evolution of the social network, revealing the emergence of two polarized groups where agents within each community have the same affinity. Finally, we observe an inverse relationship between system complexity and sustainability. Comparative analyses using Monte–Carlo simulations and rate equations are employed, along with analytical arguments, to reinforce the study’s findings. The model successfully captures key aspects of the human-environment system, offering valuable insights to understand how both the spread of information and social dynamics may impact the sustainability of CPRs.

Quantum chaotic features of the spin-orbit coupled excitons in disordered two-dimensional insulators.

We study the synergy between disorder (phenomenologically modeled by the introduction of Riesz fractional derivative in the corresponding Schrödinger equation) and spin-orbit coupling (SOC) on the exciton spectra in two-dimensional (2D) semiconductor structures. We demonstrate that the joint impact of "fractionality" and SOC considerably modifies the spectrum of corresponding "ordinary" (i.e., without fractional derivatives) hydrogenic problem, leading to the non-Poissonian statistics of the adjacent level distance distribution. The latter fact is strong evidence of the possible emergence of quantum chaotic features in the system. Using analytical and numerical arguments, we discuss the possibilities to control the above chaotic features using the synergy of SOC, Coulomb interaction, and "fractionality," characterized by the Lévy index μ.

Covariance matrix filtering and portfolio optimisation: the average oracle vs non-linear shrinkage and all the variants of DCC-NLS

The Average Oracle, a simple and very fast covariance filtering method, is shown to yield superior Sharpe ratios than the current state-of-the-art (and complex) methods, Dynamic Conditional Covariance coupled to Non-Linear Shrinkage (DCC-NLS). We pit all the known variants of DCC-NLS (quadratic shrinkage, gross-leverage or turnover limitations, and factor-augmented NLS) against the Average Oracle in large-scale randomized experiments. We find generically that while some variants of DCC-NLS sometimes yield the lowest average realized volatility, albeit with a small improvement, their excessive gross leverage and investment concentration, and their 10-time larger turnover contribute to smaller average portfolio returns, which mechanically result in smaller realized Sharpe ratios than the Average Oracle. We also provide simple analytical arguments about the origin of the advantage of the Average Oracle over NLS in a changing world.

Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal

Realistic modeling of ecological population dynamics requires spatially explicit descriptions that can take into account spatial heterogeneity as well as long-distance dispersal. Here, we present Monte Carlo simulations and numerical renormalization group results for the paradigmatic model, the contact process, in the combined presence of these factors in both one and two-dimensional systems. Our results confirm our analytic arguments stating that the density vanishes smoothly at the extinction threshold, in a way characteristic of infinite-order transitions. This extremely smooth vanishing of the global density entails an enhanced exposure of the population to extinction events. At the same time, a reverse order parameter, the local persistence displays a discontinuity characteristic of mixed-order transitions, as it approaches a non-universal critical value algebraically with an exponent \beta_p'<1βp′<1.

Dilute Measurement-Induced Cooling into Many-Body Ground States

Cooling a quantum system to its ground state is important for the characterization of nontrivial interacting systems and in the context of a variety of quantum information platforms. It can be achieved by employing measurement-based passive steering protocols, where the steering steps are predetermined and are not based on measurement readouts. However, measurements realized by coupling the system to auxiliary quantum degrees of freedom (“detectors”) are rather costly and protocols in which the number of detectors scales with system size will have limited practical applicability. Here, we identify conditions under which measurement-based cooling protocols can be taken to the ultimate dilute limit where the number of detectors is independent of system size. For two examples of frustration-free one-dimensional spin chains, we show that steering on a single link is sufficient to cool these systems into their unique ground states. We corroborate our analytical arguments with finite-size numerical simulations and discuss further applications of dilute cooling. Published by the American Physical Society 2024

Increasing stability for inverse source problem with limited-aperture far field data at multi-frequencies

We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are given by the far field patterns u∞(xˆ,k) for all observation directions xˆ in some neighborhood of a fixed direction xˆ0 and for all wave numbers k belonging to a finite interval (0,K). In this paper, we discuss the increasing stability with respect to the width of the wavenumber interval K>1. In three dimensions we establish stability estimates of the L2-norm and H−1-norm of the source function from the far field data. The ill-posedness of the inverse source problem turns out to be of Hölder type while increasing the wavenumber band K. We also discuss an analytic continuation argument of the far-field data with respect to the wavenumbers at a fixed direction.

Dynamics of simplicial SEIRS epidemic model: global asymptotic stability and neural Lyapunov functions.

The transmission of infectious diseases on a particular network is ubiquitous in the physical world. Here, we investigate the transmission mechanism of infectious diseases with an incubation period using a networked compartment model that contains simplicial interactions, a typical high-order structure. We establish a simplicial SEIRS model and find that the proportion of infected individuals in equilibrium increases due to the many-body connections, regardless of the type of connections used. We analyze the dynamics of the established model, including existence and local asymptotic stability, and highlight differences from existing models. Significantly, we demonstrate global asymptotic stability using the neural Lyapunov function, a machine learning technique, with both numerical simulations and rigorous analytical arguments. We believe that our model owns the potential to provide valuable insights into transmission mechanisms of infectious diseases on high-order network structures, and that our approach and theory of using neural Lyapunov functions to validate model asymptotic stability can significantly advance investigations on complex dynamics of infectious disease.

Reaction-Driven Diffusiophoresis of Liquid Condensates: Potential Mechanisms for Intracellular Organization.

The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase separation. Cells show precise control over the position of such condensates. We demonstrate that organelle movement in external concentration gradients, diffusiophoresis, is distinct from the one of colloids because fluxes can remain finite inside the liquid-phase droplets and movement of the latter arises from incompressibility. Within cellular domains diffusiophoresis naturally arises from biochemical reactions that are driven by a chemical fuel and produce waste. Simulations and analytical arguments within a minimal model of reaction-driven phase separation reveal that the directed movement stems from two contributions: Fuel and waste are refilled or extracted at the boundary, resulting in concentration gradients, which (i) induce product fluxes via incompressibility and (ii) result in an asymmetric forward reaction in the droplet's surroundings (as well as asymmetric backward reaction inside the droplet), thereby shifting the droplet's position. We show that the former contribution dominates and sets the direction of the movement, toward or away from fuel source and waste sink, depending on the product molecules' affinity toward fuel and waste, respectively. The mechanism thus provides a simple means to organize condensates with different composition. Particle-based simulations and systems with more complex reaction cycles corroborate the robustness and universality of this mechanism.

Periodic orbits, pair nucleation, and unbinding of active nematic defects on cones.

Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the simultaneous impact of confinement together with curvature singularity by characterizing the dynamics of an active nematic on a cone. Here, the Born-Oppenheimer approximation means that textures can follow defect positions rapidly on the timescales of interest. Upon imposing strong anchoring boundary conditions at the base of a cone, we find a rich phase diagram of multidefect dynamics, including exotic periodic orbits of one or two +1/2 flank defects, depending on activity and nonquantized geometric charge at the cone apex. By characterizing the transitions between these ordered dynamical states, we present detailed understanding of (i) defect unbinding, (ii) defect absorption, and (iii) defect pair nucleation at the apex. Numerical simulations confirm theoretical predictions of not only the nature of the circular orbits but also defect unbinding from the apex.

Unlearnable Games and “Satisficing” Decisions: A Simple Model for a Complex World

As a schematic model of the complexity economic agents are confronted with, we introduce the “Sherrington-Kirkpatrick game,” a discrete time binary choice model inspired from mean-field spin glasses. We show that, even in a completely static environment, agents are unable to learn collectively optimal strategies. This is either because the learning process gets trapped in a suboptimal fixed point or because learning never converges and leads to a never-ending evolution of agent intentions. Contrarily to the hope that learning might save the standard “rational expectation” framework in economics, we argue that complex situations are generically and agents must do with solutions, as argued long ago by Simon []. Only a centralized, omniscient agent endowed with enormous computing power could qualify to determine the optimal strategy of all agents. Using a mix of analytical arguments and numerical simulations, we find that (i) long memory of past rewards is beneficial to learning, whereas overreaction to recent past is detrimental and leads to cycles or chaos; (ii) increased competition (nonreciprocity) destabilizes fixed points and leads first to chaos and, in the high competition limit, to quasicycles; (iii) some amount of randomness in the learning process, perhaps paradoxically, allows the system to reach better collective decisions; (iv) nonstationary, “aging” behavior spontaneously emerges in a large swath of parameter space of our complex but static world. On the positive side, we find that the learning process allows cooperative systems to coordinate around satisficing solutions with rather high (but markedly suboptimal) average reward. However, hypersensitivity to the game parameters makes it impossible to predict who will be better or worse off in our stylized economy. The statistical description of the space of satisficing solutions is an open problem. Published by the American Physical Society 2024

Causal definitions versus casual estimation: Reply to Valente et al. (2022).

In this response to Valente et al. (2022), I am discussing the plausibility and applicability of the proposed mediation model and its causal effects estimation for single case experimental designs (SCEDs). I will focus on the underlying assumptions that the authors use to identify the causal effects. These assumptions include the particularly problematic assumption of sequential ignorability or no-unmeasured confounders. First, I will discuss the plausibility of the assumption in general and then particularly for SCEDs by providing an analytic argument and a reanalysis of the empirical example in Valente et al. (2022). Second, I will provide a simulation that reproduces the design by Valente et al. (2022) with the exception that, for a more realistic depiction of empirical data, an unmeasured confounder affects the mediator and outcome variables. The results of this simulation study indicate that even minor violations will lead to Type I error rates up to 100% and coverage rates as low as 0% for the defined causal direct and indirect effects. Third, using historical data on the effect of birth control on stork population and birth rates, I will show that mediation models like the proposed method can lead to surprising artifacts. These artifacts can hardly be identified with statistically means including methods such as sensitivity analyses. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

The rise and fall of the Standard-Model Higgs: electroweak vacuum stability during kination

In this paper we investigate the vacuum stability of the non-minimally coupled Standard-Model Higgs during a phase of kinetic domination following the end of inflation. The non-minimal coupling to curvature stabilises the Higgs fluctuations during inflation while driving them towards the instability scale during kination, when they can classically overcome the potential barrier separating the false electroweak vacuum from the true one at super-Planckian field values. Avoiding the instability of the Standard-Model vacuum sets an upper bound on the inflationary scale that depends both on the strength of the non-minimal interaction and on the top quark Yukawa coupling. Classical vacuum stability is guaranteed if the gravitationally-produced energy density is smaller than the height of barrier in the effective potential. Interestingly enough, thanks to the explosive particle production in the tachyonic phase, the Higgs itself can be also appointed to the role of reheaton field responsible for the onset of the hot Big Bang era, setting an additional lower bound on the inflationary scale Hinf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{H}}_{\ extrm{inf}} $$\\end{document} ≳ 105.5 GeV. Overall, these constraints favour lower masses for the top quark, in agreement with the current measurements of the top quark pole mass. We perform our analysis semi-analytically in terms of the one-loop and three-loop running of the Standard-Model Higgs self-coupling and make use of lattice-based parametric formulas for studying the (re)heating phase derived in arXiv:2307.03774. For a specific choice of mt = 171.3 GeV we perform also an extensive numerical scanning of the parameter space via classical lattice simulations, identifying stable/unstable regions and supporting the previous analytical arguments. For this fiducial value, the heating of the Universe is achieved at temperatures in the range 10−2–109 GeV.