Huifang Geng | Searcharxiv

arXiv2024

Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics

The spectral collocation method (SCM) exhibits a clear superiority in solving ordinary and partial differential equations compared to conventional techniques, such as finite difference and finite element methods. This makes SCM a powerful tool for addressing the Schrödinger-like equations with boundary conditions in physics. However, the Chebyshev differential matrix (CDM), commonly used in SCM to replace the differential operator, is not Hermitian but pseudo-Hermitian. This non-Hermiticity subtly affects the pseudospectra and leads to a loss of completeness in the eigenstates. Consequently, several issues arise with these eigenstates. In this paper, we revisit the non-Hermitian Liouville quantum mechanics by emphasizing the pseudo-Hermiticity of the CDM and explore its expanded models. Furthermore, we demonstrate that the spectral instability can be influenced by the compactification parameter.

quant-ph↗

arXiv2019

Dynamically Assisted Schwinger Effect at Strong Coupling with Its Holographic Extension

At strong-coupling and weak-field limit, the scalar Schwinger effect is studied by the field-theoretical method of worldline instantons for dynamic fields of single-pulse and sinusoidal types. By examining the Wilson loop along the closed instanton path, corrections to the results obtained from weak-coupling approximations are discovered. They show that this part of contribution for production rate becomes dominant as Keldysh parameter increases, it makes the consideration at strong coupling turn out to be indispensable for dynamic fields. Moreover a breaking of weak-field condition similar to constant field also happens around the critical field, defined as a point of vacuum cascade. In order to make certain whether the vacuum cascade occurs beyond the weak-field condition, following Semenoff and Zarembo's proposal, the Schwinger effects of dynamic fields are studied with an $\mathcal{N}=4$ supersymmetric Yang--Mills theory in the Coulomb phase. With the help of the gauge/gravity duality, the vacuum decay rate is evaluated by the string action with instanton worldline as boundary, which is located on a probe D3-brane. The corresponding classical worldsheets are estimated by perturbing the integrable case of a constant field.

hep-th↗