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In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…
Within the framework of mode-coupling theory, the glass-transition scenario is investigated for a system of particles interacting with a hard-core repulsion and an additional square-shoulder soft core at larger distances. The static…
We study various acyclicity conditions on higher-categorical pasting diagrams in the combinatorial framework of regular directed complexes. We present an apparently weakest acyclicity condition under which the $\omega$-category presented by…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
The 2020 Nobel prize in Physics has revived the interest in the singularity theorems and, in particular, in the Penrose theorem published in 1965. In this short paper I briefly review the main ideas behind the theorems and then proceed to…
We study the spatial decoherence dynamics for the relative position of two atoms in a singlemode ring cavity. We find that the spatial decoherence of the two atoms depends strongly on their relative position. Taking into account the spatial…
We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities.
We study the time evolution of a supercurrent imprinted on a one-dimensional ring of interacting bosons in the presence of a defect created by a localized barrier. Depending on interaction strength and temperature, we identify various…
We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture,…
We study condensation transitions in the steady state of a zero-range process with two species of particles. The steady state is exactly soluble -- it is given by a factorised form provided the dynamics satisfy certain constraints -- and we…
The conditions under which an open quantum mechanical system may be described by mixed quantum-classical dynamics are investigated. Decoherence is studied using influence functional methods in a model composite quantum system comprising two…
Landau's work on the singularities of Feynman diagrams suggests that they can only be of three types: either poles, logarithmic divergences, or the roots of quadratic polynomials. On the other hand, many Feynman integrals exist whose…
In this article, we investigate a multispecies generalization of the single-species asymmetric simple exclusion process defined on an open one-dimensional lattice. We devise an exact projection scheme to find the phase diagram in terms of…
We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV -> VV. In this formalism, the…
Coupling a system to a nonthermal environment can profoundly affect the phase diagram of the closed system, giving rise to a special class of dissipation-induced phase transitions. Such transitions take the system out of its ground state…
In this work we study the Brusselator - a prototypical model for chemical oscillations - under the assumption that the bifurcation parameter is of order $O(1/\epsilon)$ for positive $\epsilon\ll 1$. The dynamics of this mathematical model…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
The behavior of a class of solutions of the shallow water Airy system originating from initial data with discontinuous derivatives is considered. Initial data are obtained by splicing together self-similar parabolae with a constant…
We study the topological and differentiable singularities of the configuration space C(\Gamma) of a mechanical linkage \Gamma in d-dimensional Euclidean space, defining an inductive sufficient condition to determine when a configuration is…