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On the physical origin of the quantum operator formalism
We offer a clear physical explanation for the emergence of the quantum operator formalism, by revisiting the role of the vacuum field in quantum...
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Data Assimilation: A Dynamic Homotopy-Based Coupling Approach
Homotopy approaches to Bayesian inference have found wide- spread use especially if the Kullback–Leibler divergence between the prior and the...
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Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise
We study the focusing stochastic nonlinear Schrödinger equation in one spatial dimension with multiplicative noise, driven by a Wiener process white...
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On the Variance of the Particle Number of a Supercritical Branching Random Walk on Periodic Graphs
We study the asymptotic behavior of the variance of the local particle number for a supercritical branching random walk with branching sources that...
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Asymptotics of Random Resonances Generated by a Point Process of Delta-Interactions
We introduce and study the following model for random resonances: we take a collection...
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Localisation for Delone operators via Bernoulli randomisation
Delone operators are Schrödinger operators in multi-dimensional Euclidean space with a potential given by the sum of all translates of a given...
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Representations of Pauli–Fierz Type Models by Path Measures
Functional integral representations of the semigroups generated by Pauli–Fierz type Hamiltonians in quantum field theory are reviewed. Firstly we...
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A Necessary and Sufficient Condition for the Solvability of the Nonlinear Schrödinger Equation on a Finite Interval
The admissibility of the initial-boundary data, which characterizes the existence of solution for the initial-boundary value problem, is important....
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Koopman Operator Spectrum for Random Dynamical Systems
In this paper, we consider the Koopman operator associated with the discrete and the continuous-time random dynamical system (RDS). We provide...
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Almost conservation laws for stochastic nonlinear Schrödinger equations
In this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I -method (= the...
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Mean random attractors of stochastic lattice fractional delay Gray–Scott equations in higher moment product sequence spaces
This paper is devoted to the study of mean attractors in some higher moment product sequence spaces for a three-component reversible lattice...
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Esca** Probabilities and Quasiballistic Dynamics
The so-called Laplace time average of dynamical quantities is introduced, which is technically convenient in various situations, particularly for the...
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Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions
In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix...
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The Probabilistic Scaling Paradigm
In this note we further discuss the probabilistic scaling introduced by the authors in (ar**v:1910.08492, 2019) and (Invent. Math. 228, 539–686,...
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A non-local quasi-linear ground state representation and criticality theory
We study energy functionals associated with quasi-linear Schrödinger operators on infinite weighted graphs, and develop a ground state...
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Asymptotic Behavior of Branching Random Walks on Some Two-Dimensional Lattices
A branching random walk on two-dimensional lattices corresponding to graphene and stanene is considered. It is assumed that sources of branching are...