Related papers: Higher-order correlations for group actions
Condensed ionic systems are described in the framework of a combined approach that takes into account both long-range and short-range interactions. Short-range interaction is expressed in terms of mean potentials and long-range interaction…
We write down a series of basic laws for (strict) higher-order circuit diagrams. More precisely, we define higher-order circuit theories in terms of: (a) nesting, (b) temporal and spatial composition, and (c) equivalence between lower-order…
We analyse systems described by first order actions using the Hamilton-Jacobi (HJ) formalism for singular systems. In this study we verify that generalized brackets appear in a natural way in HJ approach, showing us the existence of a…
We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
In this thesis, we have investigated the spreading of quantum correlations in isolated lattice models with short- or long-range interactions driven far from equilibrium via sudden global quenches. A general theoretical approach relying on a…
We consider the problem of under and over-approximating the image of general vector-valued functions over bounded sets, and apply the proposed solution to the estimation of reachable sets of uncertain non-linear discrete-time dynamical…
Higher-order networks are gaining significant scientific attention due to their ability to encode the many-body interactions present in complex systems. However, higher-order networks have the limitation that they only capture many-body…
This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory's…
This paper pursues an investigation on groups equipped with an $L$-ordered relation, where $L$ is a fixed complete complete Heyting algebra. First, by the concept of join and meet on an $L$-ordered set, the notion of an $L$-lattice is…
The higher order moments of the fluctuations for the thermodynamical systems in the presence of fields are investigated in the framework of a theoretical method. The metod uses a generalized statistical ensemble consonant with the adequate…
We supply the mathematical arguments required to complete the proofs of two previously published results: Lieb-Robinson bounds for the dynamics of quantum lattice systems with unbounded on-site terms in the Hamiltonian and the existence of…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
Galton's rank order statistic is one of the oldest statistical tools for two-sample comparisons. It is also a very natural index to measure departures from stochastic dominance. Yet, its asymptotic behaviour has been investigated only…
We study noisy majority-rule dynamics on annealed hypergraphs to clarify how variability in group interaction sizes reshapes collective ordering. At each update, a group is sampled from a prescribed size distribution and either follows the…
We define an 't Hooft anomaly index for a group acting on a 2d quantum lattice system by finite-depth circuits. It takes values in the degree-4 cohomology of the group and is an obstruction to on-siteability of the group action. We…
When exposed to a contagion phenomenon, individuals may respond to the perceived risk of infection by adopting behavioral changes, aiming to reduce their exposure or their risk of infecting others. The social cost of such adaptive behaviors…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
Systems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled…
Understanding the emergence of novel collective behaviors in strongly interacting systems lies at the heart of quantum many-body physics. Valuable insight comes from examining how few-body correlations manifest in many-body systems,…