Related papers: Radiationless energy exchange in three-soliton col…
We find the exact quasiparticle spectrum for the continuum Kondo problem of $k$ species of electrons coupled to an impurity of spin $S$. In this description, the impurity becomes an immobile quasiparticle sitting on the boundary. The…
We investigate the spin of the ground state of a geometrically confined many-electron system. For atoms, shell structure simplifies this problem-- the spin is prescribed by the well-known Hund's rule. In contrast, quantum dots provide a…
In these proceedings, I will discuss collisions of poles in the complex plane as a signature of phase transitions for theories relevant to the quark gluon plasma. I will begin with an illustrative example, namely the chiral phase…
We derive a closed-form expression for the phase shift experienced by 1+1 dimensional kinks colliding at ultra-relativistic velocities (gamma v >> 1), valid for arbitrary periodic potentials. Our closed-form expression is the leading order…
It has recently become possible to form molecules in ultracold gases of trapped alkali metal atoms. Once formed, the molecules may undergo elastic, inelastic and reactive collisions. Inelastic and reactive collisions are particularly…
We study the excitation, decay and interactions of novel, velocity locked three-wave parametric solitons in a medium with quadratic nonlinearity and dispersion. We analytically describe the particle-like scattering between stable or…
Energy partition between ions and electrons in collisionless shocks has long been an unsolved fundamental physical problem. We show that kinetic simulations of moderate Alfv\'enic Mach number, magnetized, collisionless shocks reveal rapid,…
Applications of the integrable system techniques to the non-equilibrium transport problems are discussed. We describe one-dimensional electrons tunneling through a point-like defect either by the s-d exchange (Kondo) mechanism, or via the…
We consider radial sine-Gordon kinks in two, three and higher dimensions. A full two dimensional simulation showing that azimuthal perturbations remain small allows to reduce the problem to the one dimensional radial sine-Gordon equation.…
The outflows from gamma ray bursts, active galactic nuclei and relativistic jets in general interact with the surrounding media through collisionless shocks. With three dimensional relativistic particle-in-cell simulations we investigate…
The (2+1)-dimension Klein-Gordon generalised equation is numerically solved through the finite differences method. Only the sine-Gordon case is focused: kink and antikink solutions are obtained in cartesian coordinates and evidence of…
In this paper, we study the single kink and the kink-antikink collisions of a nonlinear beam equation bearing a fourth-derivative term. We numerically explore some of the key characteristics of the single kink both in its standing wave and…
The aim of this work is to establish a instability study for stationary kink and antikink/kink profiles solutions for the sine-Gordon equation on a metric graph with a structure represented by a Y-junction so-called a Josephson tricrystal…
In this thesis, we study interactions between topological defects in two-dimensional spacetimes. These defects are called kinks. They are solutions of scalar field theories with localized energy which propagate without losing its shape. In…
We theoretically investigate the nonlinearity of trion-polaritons in a two-dimensional material that arises from Coulomb interaction between quasiparticles. To evaluate the interaction constant, we solve a three-body Wannier equation…
Nonlinear space-time dynamics, defined in terms of celebrated 'solitonic' equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. In this paper, we review…
Elastic collisions in the transplanckian region, where the center-of-mass energy is much larger than the fundamental gravity mass scale, can be described by linearized general relativity and known quantum-mechanical effects as long as the…
We examine the significance of $2 \rightarrow 2$ partonic collisions as the suppression mechanism of high-energy partons in the strongly interacting medium formed in ultrarelativistic heavy ion collisions. For this purpose, we have…
We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two polarization directions, described by a coupled pair of nonlinear Schroedinger equations. We study a low-dimensional…
We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $\phi$ and $\chi$ whose scalar potential $V(\phi,\chi)$ has a standard $\chi^4$ sector and a sine-Gordon one for $\phi$. These fields are coupled through a…