Search results for "Schrödinger equation"

Discrete spectral incoherent solitons in nonlinear media with noninstantaneous response

2011

International audience; We show theoretically that nonlinear optical media characterized by a finite response time may support the existence of discrete spectral incoherent solitons. The structure of the soliton consists of three incoherent spectral bands that propagate in frequency space toward the low-frequency components in a discrete fashion and with a constant velocity. Discrete spectral incoherent solitons do not exhibit a confinement in the space-time domain, but exclusively in the frequency domain. The kinetic theory describes in detail all the essential properties of discrete spectral incoherent solitons: A quantitative agreement has been obtained between simulations of the kinetic…

Application of a Novel Refinement Method for Accurate Determination of Chemical Diffusion Coefficients in Electroactive Materials by Potential Step T…

2005

We describe application of a novel refinement method for an accurate determination of the chemical diffusion coefficient, D, and the generalized kinetic parameter, A, from experimental potentiostatic intermittent titration technique (PITT) data suited for a variety of electrochemically doped electroactive polymers and inorganic intercalation host materials. The proposed, simple, two-step refinement procedure, based on earlier derived analytical expressions for the PITT response, is exemplified by the analysis of chronoamperometric responses to small-amplitude potential perturbation for p- and n-doped poly(fluorenone-bithiophene) (PFDOBT-HH) thin film electrode. The initial p-doping and the …

Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media

2009

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we…

2020

Abstract This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint subsets of the exterior. Both the cases of infinitely many measurements and a single measurement are addressed. The results are based on a reduction from the fractional conductivity equation to the fractional Schrodinger equation, and as such represent extensions of previous works. Moreover, a simple application is shown in which the fractional conductivity equation is put into relation with a long jump random walk with weights.

Normalized solutions to the mixed dispersion nonlinear Schr��dinger equation in the mass critical and supercritical regime

2019

In this paper, we study the existence of solutions to the mixed dispersion nonlinear Schrödinger equation γΔ2u − Δu + αu =

Monotonicity-based inversion of the fractional Schr\"odinger equation II. General potentials and stability

2019

In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness results for the fractional Calder\'on problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Sch…

The Calderón problem for the fractional Schrödinger equation

2020

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where the measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension $\geq 2$ and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calder\'on problem.

High-order harmonic generation via bound-bound transitions in an elliptically polarized laser field

2016

We use a simplified five-level system to investigate the high-order harmonic generation (HHG) spectrum emitted by an atom driven by a linearly or elliptically polarized laser field. For this model, the Schrödinger equation is exactly analytically reduced to the system of ordinary differential equations, which is solved numerically. Studying the intensity and polarization of the emitted radiation, we find that under high laser ellipticity the harmonic emission is suppressed. However, the harmonic intensity typically depends nonmonotonously on the laser ellipticity. Such anomalous behavior is very pronounced for the resonant harmonic. We offer an explanation of this behavior based on the incr…

Spatially limited diffusion coupled with ohmic potential drop and/or slow interfacial exchange: a new method to determine the diffusion time constant…

2004

Abstract We have analyzed chronoamperometric curves, I ( t ), after small-amplitude potential steps Δ E (PITT technique) for the model of linear diffusion of a species inside an electroactive film, taking into account ohmic effects in the external media (solution and electrode) as well as a finite rate of the interfacial exchange. For its short-time interval, t ≪ τ d ( τ d is the diffusion time constant, corresponding to unlimited diffusion from the interface), three approximate analytical expressions have been proposed. One of these represents an interpolation formula between the value of the current at the start of the diffusion process, I (0)=Δ E / R ext (after the end of the EDL chargin…

Musical pitch quantization as an eigenvalue problem

2020

How can discrete pitches and chords emerge from the continuum of sound? Using a quantum cognition model of tonal music, we prove that the associated Schrödinger equation in Fourier space is invariant under continuous pitch transpositions. However, this symmetry is broken in the case of transpositions of chords, entailing a discrete cyclic group as transposition symmetry. Our research relates quantum mechanics with music and is consistent with music theory and seminal insights by Hermann von Helmholtz.