arXiv subjects

Shi-Cheng Liu

Publications and source records attributed to Shi-Cheng Liu.

4 recordsLinked to original sources

arXiv2026

A Bogoliubov-ratio framework for quantum-information diagnostics of time-dependent two-mode Boson System

We formulate a compact dynamical representation of quantum-information diagnostics for time-dependent two-mode bosonic systems in terms of the Bogoliubov ratio $λ_k(η)=β_k(η)/α_k(η)$. For vacuum-evolved pure Gaussian pair states generated by a Hermitian quadratic Hamiltonian, $λ_k$ obeys a closed complex Riccati equation. After one partner mode is traced out, the reduced-state spectrum is determined by $q_k=|λ_k|^2$, from which the purity, linear entropy, Rényi-2 entropy, and von Neumann entropy follow directly. These Gaussian results are mathematically equivalent to those obtained from the standard density-matrix or covariance-matrix formalism; the advantage of the ratio representation is a compact separation between model-dependent dynamics and universal state diagnostics. Writing $λ_k=\sqrt{q_k}e^{iθ_k}$ further exposes how pair production drives radial growth, whereas frequency rotation and detuning act through the phase and can suppress coherent squeezing accumulation. We also establish an exact extension to non-Gaussian $SU(1,1)$ sectors. For a lowest-weight Fock seed with conserved number difference $d$, the same ratio equation governs the evolution, while the reduced spectrum becomes a negative-binomial distribution determined by $(q_k,d)$. The Gaussian formulas are recovered at $d=0$. Cosmological perturbations and a chirped-pulse optical parametric amplifier illustrate the common dynamical mechanism and its information-theoretic consequences.

quant-ph↗

arXiv2026

Krylov Complexity in Non-Inertial Quantum Systems

This study formulates observer-dependent Krylov spreading for non-inertial quantum systems driven by linear Bogoliubov transformations. Starting with the closed single Rindler-pair $SU(1,1)$ sector, we show that its Lanczos basis is identical to the Rindler pair-number basis. As a result, the Krylov spread complexity reduces exactly to the mean number of correlated Rindler pairs, $C_k=\vertβ_k\vert^2$. Within this framework, we demonstrate that Krylov spreading dynamics are governed by the competition between the detuning parameter and the coupling constant, naturally dividing the dynamics into three distinct regimes. Notably, Krylov complexity becomes localized in the detuning-dominated regime. By extending this to a multimode, strictly quadratic Bogoliubov Hamiltonian, we find that inequivalent Rindler wave-packet pairs violate the $C_k=\vertβ_k\vert^2$ correspondence, thereby highlighting the single-pair $SU(1,1)$ model as an exactly solvable, observer-adapted benchmark. In such multimode scenarios, the mean pair-number eigenstates no longer dictate Krylov complexity. Overall, our work provides a new perspective for analyzing Krylov complexity in non-inertial quantum systems.

quant-ph↗

arXiv2026

Quantum-information diagnostics of cosmological perturbations with nontrivial sound speed in inflation

In this work, we systematically investigate the quantum-information diagnostics of cosmological perturbations with a nontrivial sound speed, utilizing a normalized open two-mode squeezed-state framework. Rather than introducing new observables, our analysis focuses on how a modified sound speed dynamically reshapes the Schrödinger evolution of the squeezing parameters ($r_k$ and $ϕ_k$). We demonstrate how these dynamical changes are inherited by the reduced density matrix of the observable sector. By employing a sound-speed-resonance parametrization, we derive and evaluate the purity, von Neumann entropy, Rényi entropies, and logarithmic negativity. To overcome the intrinsic multiscale stiffness of the post-inflationary equations, we introduce a bounded variable $x = \tanh r_k$ as a partial regularization, which enables reliable numerical simulations exclusively within the inflationary regime. Our numerical results reveal that a nontrivial sound speed significantly suppresses the purity of the reduced state, indicating enhanced effective mixedness. Simultaneously, it strongly amplifies and modulates both the entropic and entanglement diagnostics. More precisely, a nontrivial sound speed postpones the onset of classicality by modulating the decoherence process. Ultimately, we show that a nontrivial sound speed leaves distinct and identifiable quantum-information signatures within the entanglement structure of the early universe.

gr-qc↗

arXiv2026

A quantum information method for early universe with non-trivial sound speed

Many quantum gravitational frameworks, such as DBI inflation, k-essence, and effective field theories obtained by integrating out heavy modes, can lead to a non-trivial sound speed. Meanwhile, our universe can be described as an open system. Under the non-trivial sound speed, we employ the method of open quantum systems combined with Arnoldi iterations to study the Krylov complexity throughout the early universe, including the inflationary, radiation-dominated, and matter-dominated epochs. A key ingredient in our analysis is the open two-mode squeezed state formalism and the generalized Lanczos algorithm. To numerically compute the Krylov complexity, we are the first time to derive the evolution equations for the parameters $r_k$ and $ϕ_k$ within an open two-mode squeezed state. Our results indicate that the Krylov complexity exhibits a similar trend in both the standard case and the case with non-trivial sound speed. To distinguish between these two scenarios, we also investigate the Krylov entropy for completeness. The evolution of the Krylov entropy shows a clear difference between the standard case and the non-trivial sound speed case. Furthermore, based on the behavior of the Lanczos coefficients, we find that the case of non-trivial sound speed behaves as a maximally chaotic system. However, our numerical results suggest that the Krylov complexity does not saturate to a constant value due to the huge expansion of spacetime background. This study offers a new perspective for exploring the early universe through the quantum information.

gr-qc↗