Results 11 to 20 of about 17,519,874 (311)
Bounds on eigenvalues of perturbed Lamé operators with complex potentials [PDF]
Mathematics in Engineering, 2022 Several recent papers have focused their attention in proving the correct analogue to the Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the distribution of their eigenvalues in the complex plane.
Lucrezia Cossetti
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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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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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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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Schrödinger Operators with Complex Sparse Potentials [PDF]
Communications in Mathematical Physics, 2022 AbstractWe establish quantitative upper and lower bounds for Schrödinger operators with complex potentials that satisfy some weak form of sparsity. Our first result is a quantitative version of an example, due to S. Bögli (Commun Math Phys 352:629–639, 2017), of a Schrödinger operator with eigenvalues accumulating to every point of the essential ...
Jean-Claude Cuenin
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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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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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Reconstruction techniques for complex potentials [PDF]
Journal of Mathematics and 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.
V. Kravchenko
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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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