Results 11 to 20 of about 19,967,816 (378)
Nonlocal solitons supported by non-parity-time-symmetric complex potentials
New Journal of Physics, 2020 We report on the existence and stability of fundamental and out-of-phase dipole solitons in nonlocal focusing Kerr media supported by one-dimensional non-parity-time (PT)-symmetric complex potentials.
Xing Zhu +4 more
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Perturbation Theory for Time-Dependent Quantum Systems Involving Complex Potentials
Frontiers in Physics, 2020 We explore how to apply perturbation theory to complicated time-dependent Hamiltonian systems that involve complex potentials. To do this, we introduce a generalized time-dependent oscillator to which the complex potentials are connected through a weak ...
Jeong Ryeol Choi
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Pseudomodes for Schrödinger operators with complex potentials [PDF]
Journal of Functional Analysis, 2019 For one-dimensional Schroedinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. Our (non-semi-classical) approach results in substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including discontinuous
Krejčiřík, David, Siegl, Petr
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A universal form of localized complex potentials with spectral singularities [PDF]
New Journal of Physics, 2020 We establish necessary and sufficient conditions for localized complex potentials in the Schrödinger equation to enable spectral singularities (SSs) and show that such potentials have the universal form $U(x)=-{w}^{2}(x)-{{\rm{i}}{w}}_{x}(x)+{k}_{0}^{2}$
Dmitry A Zezyulin, Vladimir V Konotop
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Fluids, 2019 A long overdue distinction between so-called variant and invariant complex potentials is proposed here for the first time. Invariant complex potentials describe physical flows where a switch of the real and imaginary parts of the function will still ...
Aadi Khanal, Ruud Weijermars
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Reconstruction techniques for complex potentials [PDF]
Journal of Mathematical Physics, 2023 An approach for solving a variety of inverse coefficient problems for the Sturm–Liouville equation −y″ + q(x)y = ρ2y with a complex valued potential q(x) is presented. It is based on Neumann series of Bessel functions representations for solutions. With their aid the problem is reduced to a system of linear algebraic equations for the coefficients of ...
V. Kravchenko
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Complex potentials: bound states, quantum dynamics and wave operators [PDF]
, 2014 Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated.
Stepin, S. A.
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Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schrödinger equations [PDF]
Physica A: Statistical Mechanics and its Applications, 2023 In this paper, we firstly extend the physics-informed neural networks (PINNs) to learn data-driven stationary and non-stationary solitons of 1D and 2D saturable nonlinear Schr\"odinger equations (SNLSEs) with two fundamental PT-symmetric Scarf-II and ...
Jin Song, Zhenya Yan
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Resolvent estimates for one-dimensional Schrödinger operators with complex potentials [PDF]
Journal of Functional Analysis, 2022 We study one-dimensional Schr\"odinger operators $\operatorname{H} = -\partial_x^2 + V$ with unbounded complex potentials $V$ and derive asymptotic estimates for the norm of the resolvent, $\Psi(\lambda) := \| (\operatorname{H} - \lambda)^{-1} \|$, as $|\
A. Arnal, P. Siegl
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Diverging Eigenvalues in Domain Truncations of Schrödinger Operators with Complex Potentials [PDF]
SIAM Journal on Mathematical Analysis, 2021 Diverging eigenvalues in domain truncations of Schrödinger operators with complex potentials are analyzed and their asymptotic formulas are obtained. Our approach also yields asymptotic formulas for diverging eigenvalues in the strong coupling regime for
Iveta Semor'adov'a, P. Siegl
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