Related papers: Particle creation and annihilation at interior bou…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…
We study the following one-dimensional model of annihilating particles. Beginning with all sites of $\mathbb{Z}$ uncolored, a blue particle performs simple random walk from $0$ until it reaches a nonzero red or uncolored site, and turns…
For indefinite (Pontryagin space) canonical systems that contain an inner singularity we prove the existence of generalised boundary values at the singularity, which are used to formulate interface conditions. With the help of such…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
Isolated and Dynamical horizons are used to generate boundary conditions upon the lapse and shift vectors. Numerous results involving the Hamiltonian of General relativity are derived, including a self-contained derivation of the…
A spectral approach to building the exterior calculus in manifold learning problems is developed. The spectral approach is shown to converge to the true exterior calculus in the limit of large data. Simultaneously, the spectral approach…
We present quantization of particle dynamics on one-sheet hyperboloid embedded in three dimensional Minkowski space. Taking account of all global symmetries enables unique quantization. Making use of topology of canonical variables not only…
We find exact conditions for the enhancement or suppression of internal and/or scattered fields and the determination of their spatial distribution or angular momentum through the combination of simple fields. The incident fields can be…
For itinerant fermionic and bosonic systems, we study `particle entanglement', defined as the entanglement between two subsets of particles making up the system. We formulate the general structure of particle entanglement in many-fermion…
The article describes Boltzmann equations for a potential case of multi-particle dark matter with symmetric and asymmetric dark matter components in a model-independent approach. We focus on the specific scenario where one of the DM…
Birth of objective properties from subjective quantum world has been one of the key questions in the quantum-to-classical transition. Basing on recent results in the field, we study it in a quantum mechanical model of a boson-boson…
We consider a macroscopic model describing a system of self-gravitating particles. We study the existence and uniqueness of non-negative stationary solutions and allude the differences to results obtained from classical gravitational…
Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well…
The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a…
The problem of ballistic annihilation for a spatially homogeneous system is revisited within Boltzmann's kinetic theory in two and three dimensions. Exact analytical results are derived for the time evolution of the particle density for…
Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces…
The correspondence between cosmological models powered by a decaying vacuum energy density and gravitationally induced particle production is investigated. Although being physically different in the physics behind them we show that both…
Filtration of real gases described by Peng-Robinson equations of state in 3-dimensional space is studied. Thermodynamic states are considered as either Legendrian submanifolds in contact space, or Lagrangian submanifolds in symplectic…
We explain the origin of bound states in the continuum (BICs) in a planar grating waveguide, in particular, a mechanism for formation of degenerate BICs, via the analytical theory of the infinite-grating eigenmodes. Conventional…
Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…