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Extensions of dissipative operators with closable imaginary part [PDF]
Opuscula Mathematica, 2021 Given a dissipative operator \(A\) on a complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) is closable, we give a necessary and sufficient condition for an extension of \(A\) to still be ...
Christoph Fischbacher
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Completeness Theorem for Eigenparameter Dependent Dissipative Dirac Operator with General Transfer Conditions [PDF]
Journal of Function Spaces, 2020 This paper deals with a singular (Weyl’s limit circle case) non-self-adjoint (dissipative) Dirac operator with eigenparameter dependent boundary condition and finite general transfer conditions.
Kun Li +3 more
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Dissipative operators and operator Lipschitz functions [PDF]
Proceedings of the American Mathematical Society, 2019 The purpose of this paper is to obtain an integral representation for the difference f ( L 1
Aleksandrov A.B. +2 more
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Coordinate-Free Approach for the Model Operator Associated With a Third-Order Dissipative Operator
Frontiers in Physics, 2019 In this paper we investigate the spectral properties of a third-order differential operator generated by a formally-symmetric differential expression and maximal dissipative boundary conditions.
Ekin Uğurlu +2 more
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Dilatations of Linear Operators
Современная математика: Фундаментальные направления, 2020 The article is devoted to building various dilatations of linear operators. The explicit construction of a unitary dilation of a compression operator is considered.
Yu. L. Kudryashov
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On Krylov complexity in open systems: an approach via bi-Lanczos algorithm
Journal of High Energy Physics, 2023 Continuing the previous initiatives [1, 2], we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm generating two bi-orthogonal Krylov spaces, which ...
Aranya Bhattacharya +3 more
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Nonunitary gate operations by dissipation engineering
Quantum Science and Technology, 2022 Abstract Irreversible logic is at odds with unitary quantum evolution. Emulating such operations by classical measurements can result in disturbances and high resource demands. To overcome these limitations, we propose protocols that harness dissipation to realize the nonunitary evolution required for irreversible gate operations.
Elias Zapusek +2 more
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Criterion for the functional dissipativity of the Lamé operator [PDF]
European Journal of Mechanics - A/Solids, 2023 After introducing the concept of functional dissipativity of the Dirichlet problem in a domain $Ω\subset {\mathbb R}^N$ for systems of partial differential operators of the form $\partial_{h}({\mathscr A}^{hk}(x)\partial_{k})$ (${\mathscr A}^{hk}(x)$ being $m \times m$ matrices with complex valued $L^\infty$ entries), we find necessary and sufficient ...
A. Cialdea, V. Maz’ya
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Stable iPEPO Tensor-Network Algorithm for Dynamics of Two-Dimensional Open Quantum Lattice Models
Physical Review X, 2021 Being able to accurately describe the dynamics steady states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology.
C. Mc Keever, M. H. Szymańska
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Nonself-Adjoint Second-Order Difference Operators in Limit-Circle Cases
Abstract and Applied Analysis, 2012 We consider the maximal dissipative second-order difference (or discrete Sturm-Liouville) operators acting in the Hilbert space ℓ2𝑤(ℤ) (ℤ:={0,±1,±2,…}), that is, the extensions of a minimal symmetric operator with defect index (2,2) (in the Weyl ...
Bilender P. Allahverdiev
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