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Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and give rise to a variety of…
We derive universal properties of nonlinear response functions of nonequilibrium steady states. In particular, sum rules and asymptotic behaviors are derived. Their consequences are illustrated for nonlinear optical materials and nonlinear…
Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of…
We show that the entropy of entanglement is sensitive to the coherent quantum phase transition between normal and super-radiant regions of a system of a finite number of three-level atoms interacting in a dipolar approximation with a…
Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states in…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
The coherent superposition of orthogonal modes can result in transverse offsets, variations of the Rayleigh length and a reduction of the beam quality factor of the coherent sum of modes in comparison to the incoherent sum. Relations for…
Exciton effects on conjugated polymers and the resulting optical nonlinearities are investigated in soliton lattice states. We use the Su-Schrieffer-Heeger model with long-range Coulomb interactions for electrons. The third-harmonic…
We present a formalism for modelling parametric amplification by resonators subject to rate-limited nonlinearity of mixed reactive/dissipative character, with particular relevance to superconducting devices. The non-linearity is assumed to…
The overlap integrals of scattering states in potentials of finite widths are expressed with their asymptotic behaviors and those of energies $E_1$ and $E_2$ consist of diagonal terms that are proportional to $\delta(E_1-E_2)$ and…
It has been shown, in the case of meson photoproduction, that the power-law falloff of these reactions can be described by lowest order (real) sum rules, at moderate momentum transfer. The phases of these processes, in this regime, are…
$N$-body non efimovian bound or quasi-bound states for particles with short range interactions are considered in arbitrary dimensions. The different resonance regimes near the threshold are depicted by using a generalization of the…
We show how analogues of a large number of well-known nonlinear-optics phenomena can be realized with one or more two-level atoms coupled to one or more resonator modes. Through higher-order processes, where virtual photons are created and…
We present in this talk a series of new results on the nature of a bound state or resonance based on the calculation of the expectation values of the number operators of the free particles in the state of interest. In this way, a new…
The problem of detecting non-classical correlations of states of many qudits is incomparably more involved than in a case of qubits. The reason is that for qubits we have a convenient description of the system by the means of the…
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…
We investigate nonlinear effects on the dynamics of entanglement and other quantum observables in a system of two harmonic modes coupled through angular momentum. The nonlinearity arises from a quartic anharmonic term in each mode. The…
We present a model for molecular materials made up of polar and polarizable molecular units. A simple two state model is adopted for each molecular site and only classical intermolecular interactions are accounted for, neglecting any…
Interaction of intense laser beam with an inversion symmetric third order nonlinear medium is modeled as a quartic anharmonic oscillator. A first order operator solution of the model Hamiltonian is used to study the possibilities of…
Plasmonic metasurfaces are promising as enablers of nanoscale nonlinear optics and flat nonlinear optical components. Nonlinear optical responses of such metasurfaces are determined by the nonlinear optical properties of individual…