Kubo formula for non-Hermitian systems and tachyon optical conductivity

Abstract

Linear response theory plays a prominent role in various fields of physics and provides us with extensive information about the thermodynamics and dynamics of quantum and classical systems. Here we develop a general theory for the linear response in non-Hermitian systems with non-unitary dynamics and derive a modified Kubo formula for the generalized susceptibility for arbitrary (Hermitian and non-Hermitian) system and perturbation. As an application, we evaluate the dynamical response of a non-Hermitian, one-dimensional Dirac model with imaginary and real masses, perturbed by a time-dependent electric field. The model has a rich phase diagram, and in particular, features a tachyon phase, where excitations travel faster than an effective speed of light. Surprisingly, we find that the dc conductivity of tachyons is finite, and the optical sum rule is exactly satisfied for all masses. Our results highlight the peculiar properties of the Kubo formula for non-Hermitian systems and are applicable for a large variety of settings.

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• $\mathcal{P}\mathcal{T}$ symmetry-protected exceptional cones and analogue Hawking radiation
• Correlation versus dissipation in a non-Hermitian Anderson impurity model
• Fractal Nodal Band Structures
• Electric conductivity in non-Hermitian holography
• Dissipation induced transition between delocalization and localization in the three-dimensional Anderson model
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits
• Nonlinear Hall effects with an exceptional ring
• Correlations at higher-order exceptional points in non-Hermitian models
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• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
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• Antiferromagnetism and spin excitations in a two-dimensional non-Hermitian Hatano-Nelson flux model
• Qudit-native measurement protocol for dynamical correlations using Hadamard tests
• Physical constraints on effective non-Hermitian systems