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Quantum string, which was brought into discussion recently as a model for the stripe phase in doped cuprates, is simulated by means of the density-matrix-renormalization-group method. String collides with adjacent neighbors, as it wonders,…
We consider dephasing by interactions in a one-dimensional chiral fermion system (e.g. a Quantum Hall edge state). For finite-range interactions, we calculate the spatial decay of the Green's function at fixed energy, which sets the…
We prove quantitative scattering for the three-dimensional defocusing energy-critical quintic wave equation on a class of asymptotically flat, possibly non-stationary perturbations of Minkowski space, by establishing the first explicit…
In this paper, we present an accurate numerical method for the time-harmonic Maxwell's equations for bi-periodic multilayered media with quasi-periodic incident waves using the Method of Fundamental Solutions in conjunction with a…
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…
We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…
We consider the continuous-time Linear-Quadratic-Regulator (LQR) problem in terms of optimizing a real-valued matrix function over the set of feedback gains. The results developed are in parallel to those in Bu et al. [1] for discrete-time…
An exactly solvable time-dependent quantum mechanical problem is employed to study the convergence properties of transition amplitudes calculated by using the Schwinger variational principle. A detailed comparison between the amplitudes…
The quark-antiquark gauge invariant Green function is studied through its dependence on Wilson loops. The latter are saturated, in the large Nc limit and for large contours, by minimal surfaces. A covariant bound state equation is derived…
We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power wise interaction defined by a term proportional to 1/|n-m|^{\alpha+1}. Continuous medium equation for this system can be obtained in the…
This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second…
In the article, we discuss the conservation laws for the nonlinear Schr\"{o}dinger equation with wave operator under multisymplectic integrator (MI). First, the conservation laws of the continuous equation are presented and one of them is…
We derive expressions for the charge and spin response function for the Tomonaga model with quadratic dispersion and arbitrary (but finite for zero momentum) interaction. For constant interaction these expressions are analytic and for other…
Interaction of a charged particle in a static magnetic background, i.e., a Landau system with circularly polarised gravitational wave (GW) is studied quantum mechanically in the long wavelength and low velocity limit. We quantize the…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
With the advent of gravitational wave detectors employing squeezed light, quantum waveform estimation---estimating a time-dependent signal by means of a quantum-mechanical probe---is of increasing importance. As is well known, backaction of…
This thesis comprises two parts centered around the functional renormalization-group framework: in the first part, I study the role of symmetries and conservation laws in approximate solutions, while in the second part I analyze Friedel…
Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action…
Wind forcing of the ocean generates a spectrum of inertia-gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) are highly energetic and play a significant role in…
We discuss how one-dimensional interacting fermion systems, which in the low energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional charge and…