Related papers: Wobbling kinks in $\phi^4$ theory
A strong-coupling expansion for the phase boundary of the (incompressible) Mott insulator is presented for the bose Hubbard model. Both the pure case and the disordered case are examined. Extrapolations of the series expansions provide…
In these lectures, we provide an introduction to the complex WKB method, using as a guiding example a class of anharmonic oscillators that appears in the ODE/IM correspondence. In the first three lectures, we introduce the main objects of…
We investigate the existence and propagation of solitons in a long-range extension of the quartic Fermi-Pasta-Ulam (FPU) chain of anharmonic oscillators. The coupling in the linear term decays as a power-law with an exponent greater than 1…
We obtain estimates on the rate of decay of a solution to the wave equation on a stationary spacetime that tends to Minkowski space at a rate $O(\lvert x \rvert^{-\kappa}),$ $\kappa \in (1,\infty) \backslash \mathbb{N}.$ Given suitably…
The transition from integrable to non-integrable highly-dispersive nonlinear models is investigated. The sine-Gordon and $\phi^4$-equations with the additional fourth-order spatial and spatio-temporal derivatives, describing the higher…
Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the…
We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which…
We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion…
We consider quantum plasmas of electrons and motionless ions. We describe separate evolution of spin-up and spin-down electrons. We present corresponding set of quantum hydrodynamic equations. We assume that plasmas are placed in an uniform…
A new type of instability resulting in oscillatory propagating kinks is presented. It is observed in periodically forced oscillatory media at 1:1 resonance, where phase kinks have close similarities to pulses in excitable media. Considering…
In the framework of the deformed quantum mechanics with minimal length, we consider the motion of a non-relativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function…
We study oscillons, extremely long-lived localized oscillations of a scalar field, with three different potentials: quartic, sine-Gordon model and in a new class of convex potentials. We use an absorbing boundary at the end of the lattice…
Decayless kink oscillations of plasma loops in the solar corona may contain an answer to the enigmatic problem of solar and stellar coronal heating. The polarisation of the oscillations gives us a unique information about their excitation…
Dynamical decoupling is a key method to mitigate errors in a quantum mechanical system, and we studied it in a series of papers dealing in particular with the problems arising from unbounded Hamiltonians. The standard bangbang model of…
We experimentally study the occurrence of spontaneous spinning (Quincke rotation) of an ellipsoid in a uniform DC electric field. For an ellipsoid suspended in an unbounded fluid, we find two stable states characterized by the orientation…
We give a detailed treatment of the back-reaction effects on the Hawking spectrum in the late-time expansion within the semiclassical approach to the Hawking radiation. We find that the boundary value problem defining the action of the…
Dynamics is studied of an electron in a quasi-one-dimensional ballistic ring under circularly polarized electromagnetic field propagating along the normal to the ring plane. The average emission intensity from the ring is calculated. The…
Compton scattering of low-frequency radiation by an isotropic distribution of (i) mildly and (ii) ultra relativistic electrons is considered. It is shown that the ensemble-averaged differential cross-section in this case is noticeably…
We study the sine-Gordon kink diffusion at finite temperature in the overdamped limit. By means of a general perturbative approach, we calculate the first- and second-order (in temperature) contributions to the diffusion coefficient. We…
The resonant interaction of the $\phi^4$ kink with a periodic $\mathcal{PT}$-symmetric perturbation is observed in the frame of the continuum model and with the help of a two degree of freedom collective variable model derived in PRA 89,…