Norm estimates of complex symmetric operators applied to quantum systems

Abstract

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schrödinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schrödinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schrödinger operators appearing in the complex scaling theory of resonances.

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Cited by in corpus (9)

• Robustness of the Spin-Chern number
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Mathematical and physical aspects of complex symmetric operators
• Non-Commutative Tools for Topological Insulators
• Anti- (Conjugate) Linearity
• The edge spectrum of Chern insulators with rough boundaries
• $PT$ symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
• Topological quantization of ensemble averages
• On complex symmetric weighted shifts