arXiv subjects

Tangrui Liao

Publications and source records attributed to Tangrui Liao.

2 recordsLinked to original sources

arXiv2026

Dirichlet Eigenvalues for the Logarithmic-Hardy operator

In this paper, we study the Dirichlet eigenvalue problem for the logarithmic Hardy operator, defined as the logarithmic Laplacian with a critical logarithmic potential, in a bounded Lipschitz domain containing the origin. We first establish a logarithmic Hardy inequality and use it to identify the associated energy space, showing that the embedding into $L^2$ is compact when the perturbation parameter exceeds the endpoint value $-1$, but fails to be compact at that endpoint. For parameters above $-1$, we develop a complete variational spectral theory, prove that the problem admits a discrete sequence of eigenvalues tending to infinity, characterized by successive minimizations over orthogonal complements, whose eigenfunctions form a complete orthonormal basis of $L^2$. We further establish a uniform lower bound for the first eigenvalue, a scaling property under domain dilation that determines a critical radius for the sign of the first eigenvalue and leaves the eigenvalue gaps invariant.

math.AP↗

arXiv2026

Quantum coherence of mixed states under noisy channels in noninertial frames

We focus our attention on tripartite mixed states as initial states, and apply coherence concurrence to investigate quantum coherence properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytic complementary relationships based on coherence concurrence for tripartite subsystems are proposed. In the case of the bit flip channel, the behavior of the coherence concurrence is similar to the one of the phase damping channel, the accessible coherence concurrence always degrades as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible coherence increases from zero monotonically. Interestingly, the coherence concurrence is decreasing at first and then increasing as the decay probability rising under phase flip channel. Unlike the case of tripartite pure states, the coherence concurrence of mixed state with X shape is equal to $l_1$ -norm of coherence.

quant-ph↗