Related papers: Nontrivial Causal Structures Engendered by Knotted…
In this review, we trace the evolution of the quantum spin-wave theory treating non-collinear spin configurations. Non-collinear spin configurations are consequences of the frustration created by competing interactions. They include simple…
It is shown that in the 4d Euclidean space there are two causal structures defined by the temporal field. One of them is well-known Minkowski spacetime. In this case the gravitational potential (the positive definite Riemann metric) and…
A structural causal model is made of endogenous (manifest) and exogenous (latent) variables. We show that endogenous observations induce linear constraints on the probabilities of the exogenous variables. This allows to exactly map a causal…
Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad…
Using numerical simulations of the full nonlinear equations of motion we investigate topological solitons of a modified O(3) sigma model in three space dimensions, in which the solitons are stabilized by the Hopf charge. We find that for…
Inferring the effect of interventions within complex systems is a fundamental problem of statistics. A widely studied approach employs structural causal models that postulate noisy functional relations among a set of interacting variables.…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
We associate a noncommutative curve to a periodic, bipartite, planar dimer model with polygonal boundary. It determines the inverse Kasteleyn matrix and hence all correlations. It may be seen as a quantization of the limit shape…
The causal assumptions, the study design and the data are the elements required for scientific inference in empirical research. The research is adequately communicated only if all of these elements and their relations are described…
We compare the structures and methods in the theory of causal fermion systems with generalized trace dynamics and non-commutative geometry. Although the three theories differ on many aspects, they agree in that the geometric structure to be…
We discuss the geometry of trees endowed with a causal structure using the conventional framework of equilibrium statistical mechanics. We show how this ensemble is related to popular growing network models. In particular we demonstrate…
A quantum causal topology is presented. This is modeled after a non-commutative scheme type of theory for the curved finitary spacetime sheaves of the non-abelian incidence Rota algebras that represent `gravitational quantum causal sets'.…
What does it mean for a causal structure to be `unknown'? Can we even talk about `repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary,…
We show that nonlinear transport responses in strange metals are strong, larger by a factor of $E_F/T$ than in Fermi liquids. Within the two-dimensional Yukawa-Sachdev-Ye-Kitaev model of a Fermi surface with a spatially random coupling to a…
We investigate the causal relations in the space of states of almost commutative Lorentzian geometries. We fully describe the causal structure of a simple model based on the algebra $\mathcal{S}(\mathbb{R}^{1,1}) \otimes M_2(\mathbb{C})$,…
We report NMR scattering circuit experiments that reveal causal structure. The scattering circuit involves interacting a probe qubit with the system of interest and finally measuring the probe qubit. The scattering circuit thereby…
Causal discovery, beyond the inference of a network as a collection of connected dots, offers a crucial functionality in scientific discovery using artificial intelligence. The questions that arise in multiple domains, such as physics,…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
Continuous-time dynamics models, such as neural ordinary differential equations, have enabled the modeling of underlying dynamics in time-series data and accurate forecasting. However, parameterization of dynamics using a neural network…