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We survey the basic notions of scattering theory in Hamiltonian mechanics with a particular attention to the analogies with scattering theory in quantum mechanics. We discuss the scattering symplectomorphism, which is analogous to the…
A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M x M and the role of the corresponding antisymmetry conditions in the construction of the causal ladder is stressed. The…
I explain how the Lax-Phillips theory can be applied to a purely innovating time series and compute the corresponding scattering function. I then associate such a time series to an algebraic curve (of genus at least 1) over a finite field…
We review the random matrix theory describing elastic scattering through zero-dimensional ballistic cavities (having chaotic classical dynamics) and quasi-one dimensional disordered systems. In zero dimension, general symmetry…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling…
Modern machine learning (ML) methods typically fail to adequately capture causal information. Consequently, such models do not handle data distributional shifts, are vulnerable to adversarial examples, and often learn spurious correlations.…
We consider the classical map proposed previously to be the exact classical analogue of Rydberg Molecules calculated with the approximations relevant to the multi-channel quantum defect theory. The resulting classical map is analyzed at…
We consider two type of systems, a linear singular discrete time system and a linear singular fractional discrete time system whose coefficients are square constant matrices. By assuming that the input vector changes only at equally space…
A scattering event in a quantum field theory is a coherent superposition of all processes consistent with its symmetries and kinematics. While real-time simulations have progressed toward resolving individual channels, existing approaches…
A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying $\mathcal{PT}$-symmetry. It is illustrated that unlike in…
It is shown how initial conditions can be appropriately defined for the integration of Lorentz-Dirac equations of motion. The integration is performed \QTR{it}{forward} in time. The theory is applied to the case of the motion of an electron…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
Scattering methods are widely used in many research areas to analyze and resolve material structures. Given the importance, a large number of full textbooks are devoted to this topic. However, technical details in experiments and…
This paper introduces Whittemore, a language for causal programming. Causal programming is based on the theory of structural causal models and consists of two primary operations: identification, which finds formulas that compute causal…
While the standard formulation of quantum theory assumes a fixed background causal structure, one can relax this assumption within the so-called process matrix framework. Remarkably, some processes, termed causally nonseparable, are…
Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
The probability of a quantum particle being detected in a given solid angle is determined by the $S$-matrix. The explanation of this fact in time dependent scattering theory is often linked to the quantum flux, since the quantum flux…
It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, due to quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal…