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An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…

Quantum Physics · Physics 2007-05-23 C. Quesne

The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…

Pattern Formation and Solitons · Physics 2022-07-20 S. J. Chapman , M. E. Kavousanakis , E. G. Charalampidis , I. G. Kevrekidis , P. G. Kevrekidis

Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…

Numerical Analysis · Mathematics 2023-10-03 Samuel M. Greene , Robert J. Webber , Timothy C. Berkelbach , Jonathan Weare

We show that the study of the statistical properties of the scattering matrix S for quantum chaotic scattering in the presence of direct processes (charaterized by a nonzero average S matrix <S>) can be reduced to the simpler case where…

chao-dyn · Physics 2009-10-30 Victor A. Gopar , Pier A. Mello

The Schr\"odingerisation method combined with the autonomozation technique in \cite{cjL23} converts general non-autonomous linear differential equations with non-unitary dynamics into systems of autonomous Schr\"odinger-type equations, via…

Quantum Physics · Physics 2024-11-19 Chuwen Ma , Shi Jin , Nana Liu , Kezhen Wang , Lei Zhang

In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of…

We calculate two-body scattering phase shifts on a quantum computer using a leading order short-range effective field theory Hamiltonian. The algorithm combines the variational quantum eigensolver and the quantum subspace expansion. As an…

Nuclear Theory · Physics 2024-11-21 Sanket Sharma , Thomas Papenbrock , Lucas Platter

This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…

Analysis of PDEs · Mathematics 2018-12-26 Alexey Agaltsov , Thorsten Hohage , Roman Novikov

A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…

Atomic Physics · Physics 2007-05-23 Nark Nyul Choi , Min-Ho Lee , Sung Ho Suck Salk

We prove an error estimate for a Lie-Trotter splitting operator associated to the Schrodinger-Poisson equation in the semiclassical regime, when the WKB approximation is valid. In finite time, and so long as the solution to a compressible…

Numerical Analysis · Mathematics 2013-12-23 Rémi Carles

Compound resonances in nucleon-nucleus scattering are related to the discrete spectrum of the target. Such resonances can be studied in a unified and general framework by a scattering model that uses sturmian expansions of postulated…

Nuclear Theory · Physics 2015-06-26 K. Amos , L. Canton , G. Pisent , J. P. Svenne , D. van der Knijff

Coupled nonlinear Schr\"odinger equations model various physical phenomena, such as wave propagation in nonlinear optics, multi-component Bose-Einstein condensates, and shallow water waves. Despite their extensive applications, analytical…

Numerical Analysis · Mathematics 2024-07-29 Nate Lovett , Harish Bhatt

Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…

Analysis of PDEs · Mathematics 2022-02-28 Peter C. Gibson

We solve the two-particle s-wave scattering for an ultracold atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included in terms of Fermi's pseudopotential.…

Atomic Physics · Physics 2017-09-15 Vicente Leyton , Maryam Roghani , Vittorio Peano , Michael Thorwart

In this paper, we consider a sorting scheme for potentially spurious scattering resonant pairs in one- and two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a…

Mathematical Physics · Physics 2020-06-23 Juan Carlos Araujo Cabarcas , Christian Engström

This is the third part of a paper about non-relativistic Schroedinger theory on q-deformed quantum spaces like the braided line or the three-dimensional q-deformed Euclidean space. Propagators for the free q-deformed particle are derived…

Quantum Physics · Physics 2007-05-23 Hartmut Wachter

While providing a highly accurate framework for simulating laser-induced many-electron dynamics in atom and molecules, including linear and nonlinear steady-state and transient absorption spectra, time-dependent coupled-cluster theory does…

In this paper we study quantum simulation algorithms on the elastic wave equations using the Schr\"odingerisation method. The Schr\"odingerisation method transforms any linear PDEs into a system of Schr\"odinger-type PDEs -with unitary…

Quantum Physics · Physics 2025-05-27 Shi Jin , Chundan Zhang

We describe a parallel algorithm for solving the time-independent 3d Schrodinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between…

Quantum Physics · Physics 2014-11-18 Michael Strickland , David Yager-Elorriaga

Years ago S. Weinberg suggested the "Quasi-Particle" method (Q-P) for iteratively solving an integral equation, based on an expansion in terms of sturmian functions that are eigenfunctions of the integral kernel. An improvement of this…

Computational Physics · Physics 2015-05-27 George Rawitscher