相关论文: Nonlocal PDEs and Quantum Optics: Bound States and…

Nonlinear eigenvalue equations arise naturally in quantum information theory, particularly in the variational quantification of entanglement. In this work, we present a hybrid analytical and numerical framework for evaluating the geometric…

Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed.

We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…

In this article, the interaction of an arbitrary number of quantum dots, behaving as artificial molecules, with different energy levels and multi-mode electromagnetic field is studied. We make the assumption that each quantum dot can be…

We present a model to find analytically the electronic states in self-assembled quantum dots with a truncated spherical cap (`lens') geometry. A conformal analytical image is designed to map the quantum dot boundary into a dot with…

We prove the existence of time-periodic, small amplitude solutions of autonomous quasilinear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class. The result holds for frequencies in a Cantor set that has…

The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…

We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] \times \Sigma$, where $\Sigma$ is a compact manifold with smooth boundaries $\partial\Sigma$. By using an appropriate…

We consider the relativistic quantum mechanics of a two interacting fermions system. We first present a covariant formulation of the kinematics of the problem and give a short outline of the classical results. We then quantize the system…

We address the problem of the persistence of entanglement of quantum light under mode transformations, where orthogonal modes define the parties between which quantum correlations can occur. Since the representation of a fixed photonic…

Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved…

The boundary integral equation method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of…

A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…

We present a theoretical study of the collective optical effects which can occur in groups of three and four quantum dots. We define conditions for stable subradiant (dark) states, rapidly decaying superradiant states,and spontaneous…

We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the…

In this paper we study an interacting two-particle system on the positive half-line. We focus on spectral properties of the Hamiltonian for a large class of two-particle potentials. We characterize the essential spectrum and prove, as a…

In this paper, we give the quantum wave equations of single photon when it is in the free or medium space. With these equations, we can study light interference and diffraction with quantum approach. Otherwise, they can be applied in…

We comprehensively investigate the nontrivial states of interacting Bose system in one-dimensional optical superlattices under the open boundary condition. Our results show that there exists a kind of stable localized states: edge gap…

Quantum dots (QDs) are one of the promising candidates of interconnection between electromagnetic field and electrons in solid-state devices. Dark states appear as a result of coherence between the electromagnetic fields and the discrete…

The relativistic two-body system in (1+1)-dimensional quantum electrodynamics is studied. It is proved that the eigenvalue problem for the two-body Hamiltonian without the self-interaction terms reduces to the problem of solving an…