arXiv subjects

Lei-Hua Liu

Publications and source records attributed to Lei-Hua Liu.

At least 19 recordsLinked to original sources

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

Non-minimally Coupled Running Curvaton for DESI-motivated Dynamical Dark Energy

Recent DESI BAO data combined with CMB and supernova measurements suggest a dynamical dark energy that can cross the phantom divide. We show that introducing a non-minimal coupling $ξχ^2R$ to the running-curvaton framework allows a single field to drive early-universe curvature perturbations and late-time phantom-crossing cosmic acceleration without ghost instabilities. Using MCMC background likelihoods with DESI DR2 BAO, Pantheon+ SNe, and a reduced CMB prior, we constrain the cosmological parameters: $H_0 = 67.88^{+0.53}_{-0.61}\,{\rm km\,s^{-1}\,Mpc^{-1}}$, $Ω_m = 0.3072^{+0.0059}_{-0.0054}$, $w_0 = -0.922^{+0.055}_{-0.063}$, and $w_a = -0.205^{+0.173}_{-0.182}$. Parameter degeneracies leave the coupling constants weakly constrained, highlighting the need for full perturbation-level analysis using CMB spectra and lensing.

astro-ph.CO↗

arXiv2026

Geometric-phase control of Krylov complexity in adiabatic dynamics

We show that geometric phases accumulated during adiabatic evolution can be converted into observable interference in Krylov space, leading to a geometric-phase-dependent Krylov oscillation. Adiabatic dynamics force Krylov complexity to vanish if the initial Krylov basis is an instantaneous eigenstate of the Hamiltonian; Nevertheless, we demonstrate that the Krylov complexity will be non-vanishing if the initial Krylov basis is a superposition state rather than an eigenstate. Consequently, Krylov complexity is found to depend on the difference of dynamical phases in the Krylov space, which is deeply related to the Berry connections in the original Hilbert space. In particular, for a single qubit system with constant Lanczos coefficients, Krylov complexity oscillates harmonically at a frequency given by the strength of the external field and the geometric Berry phase. Therefore, our work may provide a novel avenue to probe the geometric phase from the Krylov complexity.

quant-ph↗

arXiv2026

QCD sum rule analysis of hidden strange $1^{++}$ tetraquark masses and radial excitations

We revisit the light tetraquark states with quantum numbers $J^{PC}=1^{++}$ using QCD sum rules, focusing on a complete set of derivative-free diquark-antidiquark interpolating currents. By calculating the operator product expansion up to dimension-eight condensates, we extract the ground-state mass of the hidden-strange $us\bar{u}\bar{s}$ tetraquark from both Laplace sum rules (LSR) and finite-energy sum rules (FESR). Our combined analysis yields $M_{us\bar{u}\bar{s}} = 1.45\pm0.11$~GeV, which agrees well with the mass of the $a_1(1420)$ resonance and supports its tetraquark interpretation. Furthermore, we perform Gaussian sum rule (GSR) analyses to probe radial excitations, adopting a two-resonance narrow-width model. The GSR fit reveals a heavier state with mass $m_2 = 1.86\pm0.12$~GeV and a relative coupling $r = 0.15\pm0.03$ for the lighter state, indicating that the $a_1(1930)$ is a promising candidate for a compact $1^{++}$ tetraquark. We also discuss the dominant decay modes of these tetraquark candidates, emphasizing hidden-strange channels such as $K^*K$ and $f_0(980)π$, which can be tested in future experiments.

hep-ph↗

arXiv2026

Inflationary thermal Krylov complexity

This work explores thermal Krylov complexity and thermal K-entropy of primordial perturbations under three comoving momentum correction frameworks, including canonical scalar field inflation (standard inflation), non-trivial sound speed, and the modified dispersion relations. Adopting the thermal field double state purification, we derive the thermal wave function and obtain the evolutions of effective temperature and squeezed angle, and further compare the quantum information dynamics of closed and open thermal quantum systems. The numerical results indicate that comoving momentum suppresses the growth of Krylov observables in standard inflation. In the non-trivial sound speed model, larger correction strength enhances their oscillatory behaviors, while the ultraviolet correction in the modified dispersion relation model induces stage-dependent oscillations. By analyzing the Lanczos coefficient and dissipation strength, we find that system dissipation suppresses quantum coherent oscillations. Continuous oscillations only emerge for larger non-trivial sound speed, whereas modified dispersion relations yield monotonic evolution. These distinct signatures provide effective quantum information probes for discriminating quantum gravity corrections in inflationary cosmology.

hep-th↗

arXiv2026

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

We present a compact and unified framework for quantum-information diagnostics of time-dependent two-mode bosonic systems based on the Bogoliubov ratio $λ_k(η) \equiv β_k(η)/α_k(η)$. For a general time-dependent quadratic two-mode Hamiltonian, the state dynamics is exactly reduced to a single complex Riccati equation for $λ_k$. Upon tracing out one partner mode, the spectrum of the one-mode reduced density matrix is determined entirely by the squared magnitude $q_k(η) = \vert{}λ_k(η)\vert{}^2$. Consequently, we could construct the explicit, model-independent formula for the reduced-state purity, linear entropy, Rényi-2 entropy, and von Neumann entropy without reconstructing and diagonalizing the reduced density matrix on a model-by-model basis using coupled squeezing parameters ($r_k, ϕ_k$). We demonstrate the utility of this framework in two distinct non-stationary setups: primordial cosmological perturbations and a chirped-pulse nondegenerate optical parametric amplifier. In the cosmological context, our formulation clarifies how background-induced phase rotation and frequency softening regulate squeezing growth and state mixedness; in the optical domain, it captures the delayed onset, suppression of squeezing accumulation, and late-time entropy saturation induced by finite pump duration and frequency chirp. By cleanly factorizing model-dependent driving protocols from universal information-theoretic metrics, this framework offers an efficient, standardized diagnostic tool for a broad class of parametrically driven quadratic bosonic systems.

quant-ph↗

arXiv2026

Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry

We extend the CV conjecture to quantum states of two-mode Hermitian systems using the framework of information geometry. Specifically, we conjecture that the Krylov complexity of a quantum state equals the volume of the Fubini-Study metric. To test this conjecture, we construct the wave functions for both closed and open two-mode systems. For the closed system, the wave function corresponds to the well-known two-mode squeezed state, while for the open system, we employ the second kind of Meixner polynomials to generate an open two-mode squeezed state. Remarkably, in both cases, the calculated Fubini-Study volume matches the Krylov complexity, providing analytic evidence for the generalized CV relation in this controlled two-mode setting. Our results establish a direct link between operator growth in Krylov space and geometric properties of quantum states, highlighting the potential applications of this framework in quantum information and quantum optics.

hep-th↗

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

Krylov complexity of thermal state in early universe

Thermal interactions are ubiquitous in the cosmos, driving systems toward equilibrium. In this work, we investigate the evolution of thermal states across the early universe, encompassing the inflationary, radiation-dominated (RD), and matter-dominated (MD) eras, through the lens of Krylov complexity. Utilizing a purification scheme, we map the thermal state to a two-mode pure state, facilitating an open-system analysis of Krylov complexity in contrast to closed-system methodologies. Our numerical results demonstrate that Krylov complexity grows exponentially during inflation, indicating chaotic behavior, before saturating at nearly constant values in the RD and MD eras due to particle production via preheating. Furthermore, we analyze the Krylov entropy, which exhibits an evolutionary trend analogous to that of complexity. Crucially, our analysis reveals a dynamical transition in the universe's dissipative nature: with the universe acting as a strongly dissipative system during inflation and transitioning to a weakly dissipative regime in the subsequent eras. These findings provide a novel quantum information perspective on early universe dynamics.

hep-th↗

arXiv2026

Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory

We study Krylov complexity in Schrödinger field theory in the grand canonical ensemble with chemical potential $μ$, with an emphasis on the qualitatively new features that arise for $μ>0$. In this regime the fermionic Wightman power spectrum is effectively single-sided and sharply truncated at $ω=μ$, which induces a crossover in the Lanczos coefficients {and signals a dynamical transition from a bulk-dominated regime to a spectral-edge-dominated regime}: $b_n$ displays a two-stage linear growth (from an early-time slope $π/β$ to an asymptotic slope $2/β$), while $a_n$ bends from near-zero values to a linear descent with slope $-4/β$. We provide analytic support for the resulting complexity growth from three complementary viewpoints: (i) using an $SL(2,\mathbb{R})$ algebraic construction matched to the asymptotic Lanczos data, we show that the late-time Krylov complexity must grow quadratically, $K(t)\propto t^{2}$; (ii) by analyzing engineered Wightman spectra with controlled decay and truncation, we identify single-sided exponential decay as the key spectral feature responsible for the quadratic asymptotics, while an approximately even two-sided exponential spectrum explains the early-time $K(t)\sim\sinh^{2}(πt/β)$ behavior at large $μ$; (iii) we formulate the problem in terms of orthogonal polynomials and estimate the crossover scale separating the early- and late-stage regimes. Overall, our results help clarify the role of chemical potential and spectral truncation in shaping operator growth and Krylov complexity in this non-relativistic quantum field theory setting.

hep-th↗

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↗

arXiv2026

Krylov Complexity in early universe

The Lanczos algorithm offers a framework for constructing wave functions in closed and open quantum systems from their Hamiltonians. Since the early universe is inherently an open system, we employ this algorithm to investigate Krylov complexity across various cosmological phases: inflation, radiation domination (RD), and matter domination (MD). Our results highlight a clear distinction in Krylov complexity between the closed- and open-system methodologies. To accurately capture the influence of potentials during RD and MD, we examine a set of inflationary potentials, including the Higgs potential, $R^2$ inflation, and chaotic inflation, while incorporating violations of slow-roll conditions. This study is conducted in conformal time through the preheating stage. Numerically, we find that the evolution of Krylov complexity and Krylov entropy shows remarkable similarity across different potentials during RD and MD. Furthermore, we rigorously construct an open two-mode squeezed state using the second kind of Meixner polynomial. Based on this construction, we derive for the first time the evolution equations for the squeezing parameter $r_k$ and phase $ϕ_k$ in terms of the scale factor. Our analysis indicates that dissipative effects lead to rapid decoherence-like behavior. In addition, we observe that the inflationary universe behaves as a strongly dissipative system, whereas during the RD and MD epochs the universe exhibits weak dissipative characteristics. This work opens new perspectives for studying the universe from a quantum-informational viewpoint.

hep-th↗

arXiv2025

Microlensing of dark matter models in the Milky Way

We investigate constraints on the abundance of primordial black holes (PBHs) as dark matter (DM) candidates using five years of microlensing data from the OGLE survey. While the majority of OGLE's $\sim\!2000$ microlensing events are well-explained by stellar populations such as brown dwarfs, main-sequence stars, and compact remnants, a subset of six ultrashort-timescale events ($t_E \sim 0.1\text{--}0.3~\mathrm{days}$) may signal the presence of PBHs. Building upon prior work that adopted the Navarro-Frenk-White (NFW) DM profile, we examine how alternative DM halo models -- specifically the Einasto and Burkert profiles, affect microlensing predictions and the constraints on PBH abundance. In light of kinematic data of Milky Way, we could obtain the range of ($r_s, ρ_s$) for both profiles. We computed differential microlensing event rates for both profiles, using the main-sequence star rate as an observational benchmark. Our results show that neither the Einasto nor Burkert profiles reproduce the distribution of main-sequence star events, yet both allow for viable explanations of the ultrashort-timescale events with PBH masses $M_{\mathrm{PBH}} \sim 10^{-5} M_\odot$. Using a Poisson likelihood analysis under the null hypothesis that no PBH is observed in OGLE dataset, we derive $95\%~\text{C.L.}$ upper and lower bounds on $f_{\mathrm{PBH}}$ for both profiles, finding that the constraints are significantly relaxed under Burkert profiles compared to the NFW case. These results show the sensitivity of PBH constraints to the assumed DM halo structure and highlight the importance of accurately modeling the inner Galactic density profile to robustly assess PBH dark matter scenarios.

astro-ph.GA↗

arXiv2025

Inflationary power spectrum from the Lanczos algorithm

The generalized Lanczos algorithm can provide a universal method for constructing the wave function under the group structure of Hamiltonian. Based on this fact, we obtain an open two-mode squeezed state as the quantum origin for the curvature perturbation. In light of this wave function in the open system, we successfully develop a new method to calculate its corresponding power spectrum by using the Bogoliubov transformation. Unlike traditional approaches, we explicitly retain the Bogoliubov coefficients in terms of the squeezing amplitude $ r_k $ and the squeezing rotation angle $ ϕ_k $. As a result, the power spectrum of the open two-mode squeezed state will match that of the Bunch-Davies vacuum numerically. Furthermore, the derivation of the open two-mode squeezed state relies on the second kind Meixner polynomial (equivalent to the generalized Lanczos algorithm) and the symmetry of the Hamiltonian. Therefore, our research may offer a new insight into the calculation of the correlation functions through a group-theoretic perspective.

quant-ph↗

arXiv2025

Gravitational lensing of the wormhole in the Eddington-inspired Born-Infeld spacetime with a cosmic string

In this work we study gravitational lensing of the wormhole in the Eddington-inspired Born-Infeld (EiBI) spacetime that incorporates with a cosmic string. It was found that the presence of cosmic string can enhance the light deflection in strong field limit, compared to the case of the Eills-Bronnikov wormhole. The magnification effects of this composite structure could cause some substantial impacts on the angle separation between the first and the rest of the images, and their relative brightness. Furthermore, based on these observables, we model some observable aspects in the strong and the weak field limits. The presence of a cosmic string can affect some distinguishable observables compared to the wormhole without cosmic string. This work could deepen our understanding of the spacetime structure of the wormhole in EiBI spacetime with one-dimensional topological defects.

gr-qc↗

arXiv2024

Microlensing and event rate of static spherically symmetric wormhole

The study focuses on the impact of microlensing in modern cosmology and introduces a new framework for the static spherically symmetrical wormhole in terms of the radial equation of state. Following a standard procedure, the study calculates the lensing equation, magnification, and event rate based on the the radial equation of state. The analysis highlights that the image problem of the light source is complex. Furthermore, the study suggests that larger values for the throat radius of the wormhole and the radial equation of state lead to higher event rates. Additionally, it is proposed that the event rate of a wormhole will be larger compared to that of a black hole, provided their masses and distances from the light source and observer are comparable. This study offers the potential to distinguish between a wormhole and a black hole under similar conditions.

gr-qc↗

arXiv2024

Correlators for pseudo Hermitian systems

Pseudo-Hermitian system is a class of non-Hermitian system with Hamiltonian satisfying the condition $η^{-1}H^\daggerη=H$. We develop the in-in and Schwinger Keldysh formalism to calculate cosmological correlators for pseudo-Hermitian systems. We study a model consists of massive symplectic fermions coupled to the primordial curvature perturbation. The three-point function for the primordial curvature perturbation is computed up to one-loop and compared to earlier work where the loop correction comes from a massive scalar boson. The two results differ by a minus sign. Therefore, the one loop correction to the three-point function cannot be used to distinguished scalar bosons and symplectic fermions. To conclude, we discuss possibilities where the scalar bosons and symplectic fermions may be distinguished.

hep-th↗

arXiv2024

Inflationary Krylov complexity

In this work, we have systematically investigated the Krylov complexity of curvature perturbation for the modified dispersion relation in inflation, using the algorithm in closed system and open system. Our analysis could be applied to the most inflationary models. Following the Lanczos algorithm, we find the very early universe is an infinite, many-body, and maximal chaotic system. Our numerics shows that the Lanczos coefficient and Lyapunov index of the standard dispersion relation are mainly determined by the scale factor. As for the modified case, it is nearly determined by the momentum. In a method of the closed system, we discover that the Krylov complexity will show irregular oscillation before the horizon exits. The modified case will present faster growth after the horizon exists. Since the whole universe is an open system, the approach of an open system is more realistic and reliable. Then, we construct the exact wave function which is very robust only requiring the Lanczos coefficient proportional to $n$ (main quantum number). Based on it, we find the Krylov complexity and Krylov entropy could nicely recover in the case of a closed system under the weak dissipative approximation, in which our analysis shows that the evolution of Krylov complexity will not be the same with the original situation. We also find the inflationary period is a strong dissipative system. Meanwhile, our numerics clearly shows the Krylov complexity will grow during the whole inflationary period. But for the small scales, there will be a peak after the horizon exits. Our analysis reveals that the dramatic change in background (inflation) will significantly impact the evolution of Krylov complexity. Since the curvature perturbation will transit from the quantum level to the classical level.

hep-th↗