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We study three distinct types of planar, spherically symmetric and localized structures, one of them having non-topological behavior and the two others being of topological nature. The non-topological structures have energy density…
In recent years there have been significant advances in the study of many-body interactions between atoms and light confined to optical cavities. One model which has received widespread attention of late is the Dicke model, which under…
We study the $1+1$ flat spacetime dynamics of a classical field configuration corresponding to an ensemble of sine-Gordon kinks and antikinks, semi-classically coupled to a quantum field. This coupling breaks the integrability of the…
We analyze non-integrable deformations of two-dimensional N=1 supersymmetric quantum field theories with kink excitations. As example, we consider the multi-frequency Super Sine Gordon model. At weak coupling, this model is robust with…
This study theoretically considers the motion of N identical inelastic particles between two oscillating walls. The particles' average energy increases abruptly at certain critical filling fractions, wherein the system changes into a…
Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of $\phi^4$ kinks. Three different reduced models based on the kink position, width and…
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…
Scattering from a scale invariant potential in two spatial dimensions leads to a class of novel identities involving the sinc function.
We obtain a microscopic description of the interaction between electron spins in bulk semiconductors and in pairs of semiconductor quantum dots. Treating the k.p band mixing and the Coulomb interaction on the same footing, we obtain in the…
We consider the motion of semiflexible polymers in double-well potentials. We calculate shape, energy, and effective diffusion constant of kink excitations, and in particular their dependence on the bending rigidity of the semiflexible…
We study the creation of solitons from particles, using the $\lambda \phi^4$ model as a prototype. We consider the scattering of small, identical, wave pulses, that are equivalent to a sequence of particles, and find that kink-antikink…
A model of soliton-defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for…
We study collisions of two, three, and four kinks of the double sine-Gordon model. The initial conditions are taken in a special form in order to provide collision of all kinks in one point. We obtain dependences of the maximal energy…
We consider the (1+1)-dimensional Lorentz-symmetric field-theoretic model with logarithmic potential having a Mexican-hat form with two local minima similar to that of the quartic Higgs potential in conventional electroweak theory with…
We quantitatively analyze the dynamics of the quantum phase distribution associated with the reduced density matrix of a system, as the system evolves under the influence of its environment with an energy-preserving quantum nondemolition…
Binary mixtures of hard-spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the…
A simple model coupling a one-dimensional beam particle to a one-dimensional harmonic oscillator is used to explore complementarity and entanglement. This model, well-known in the inelastic scattering literature, is presented under three…
In this thesis, we first review the linearized soliton perturbation theory developed in recent years, which is particularly simple in the one-kink sector. Using it, the amplitude and probability of kink-meson inelastic scattering can be…
We investigate the dynamics of the kinks that emerge in a one-dimensional scalar field theory with an octic potential containing a quartic minimum and two quadratic minima. We show analytically that kink-antikink and kink-kink pairs…
After a quantum phase transition the quantum vacuum can break up to form classical topological defects. We examine this process for scalar field models with $Z_2$ symmetry for different quench rates for the phase transition. We find that…