Related papers: Wave Equations with Point Interactions in Finite E…
A comparative study between the L\"uscher's finite volume method and the time-dependent HAL QCD method is given for the $\Xi\Xi$($^1\mathrm{S}_0$) interaction as an illustrative example. By employing the smeared source and the wall source…
Very recently the Wood-Saxon (WS) type interaction in the single-folding potential approach are constructed to simulate the $ \phi{\text -}\alpha $ potentials. One set of the $ \phi{\text -}\alpha $ potentials are based on the first…
We propose a simple model of an interacting, fully spin--polarized Fermi gas in dimensions $d=2$ and $d=3$, and derive the approximate expression for the energy spectrum and the corresponding formula for the Helmholtz free energy. We…
We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…
For $N$-body Schr\"o\-dinger operators with time-periodic short-range pair-potentials we show by a time-dependent commutator method that all channel wave operators exist. For $N=2$ we prove asymptotic completeness by a simplified version of…
The cosmological history and evolution are examined for gravitational models with interaction in the dark sector of the universe. In particular, we consider the dark energy to be described by a phantom scalar field and the dark matter $\rho…
First order phase transitions are well-motivated and extensively studied sources of gravitational waves (GWs) from the early Universe. The vacuum energy released during such transitions is assumed to be transferred primarily either to the…
A pointlike electric charge at rest is considered in the spacetime which is a wormhole connecting two otherwise Minkowskian spaces. The potential (i. e. a solution of the Maxwell equations) is split into two parts: one of them depends only…
We present a continuum theory of self-propelled particles, without alignment interactions, in a momentum-conserving solvent. To address phase separation we introduce a scalar concentration field $\phi$ with advective-diffusive dynamics.…
Re-analyzing the old phase shift data of I=0, \pi\pi (I=1/2, K\pi) scattering, we show an evidence for existence of the \sigma-particle (\kappa-particle) with a comparatively light mass, which has been missing for a long time: In the…
We consider interactions between surface and interfacial waves in the two layer system. Our approach is based on the Hamiltonian structure of the equations of motion, and includes the general procedure for diagonalization of the quadratic…
We construct a microscopic model of electron interactions which gives rise to both superconductivity and antiferromagnetism, and which admits an approximate SO(5) symmetry that relates these two phases. The symmetry can be exact, or it may…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
The equation of state and phase diagram of strongly interacting matter composed of $\alpha$ particles are studied in the mean-field approximation. The particle interactions are included via a Skyrme-like mean field, containing both…
The spectrum of excited states observed in the finite volume of lattice QCD is governed by the discrete symmetries of the cubic group. This finite group permits the mixing of orbital angular momentum quanta in the finite volume. As…
A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a "walker." Previous works have demonstrated that the dynamics of a single walker is driven by its global…
The effective potential for the local composite operator $\phi^{2}(x)$ in $\lambda \phi^{4}$-theory is investigated at finite temperature in an approach based on path-integral linearisation of the $\phi^4 $-interaction. At zero temperature,…
In the Quantum theory the wave functions form a full and orthonormalized functional space. For this reason we can use the equation on eigenfunctions and eigenstates and find the eigenenergies $E_n$ and eigenfunctions $\Psi_n$ to determine…
In this work we consider the wave equation with a repulsive potential, either on the half line ${\mathbb R}^+$ or the Euclidean space ${\mathbb R}^d$ with $d\geq 3$. We combine the operator theory and the inward/outward energy theory to…
A mathematical model for unidirectional wave generation explained in this study. The model consists of Laplace's equation in the semi-infinite two-dimensional water interior, dynamic and kinematic boundary conditions at the free surface,…