arXiv subjects

Peng-Zhang He

Publications and source records attributed to Peng-Zhang He.

16 recordsLinked to original sources

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

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 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↗

arXiv2025

Krylov Complexity in the Schrödinger Field Theory

We investigate the Krylov complexity of Schrödinger field theories, focusing on both bosonic and fermionic systems within the grand canonical ensemble that includes a chemical potential. Krylov complexity measures operator growth in quantum systems by analyzing how operators spread within the Krylov space, a subspace of the Hilbert space spanned by successive applications of the superoperator $[H,\cdot]$ on an initial operator. Using the Lanczos algorithm, we construct an orthonormal Krylov basis and derive the Lanczos coefficients, which govern the operator connectivity and thus characterize the complexity. Our study reveals that the Lanczos coefficients $\{b_{n}\}$ are independent of the chemical potential, while $\{a_{n}\}$ exhibits a dependence on it. Both $\{a_{n}\}$ and $\{b_{n}\}$ show linear relationships with respect to $n$. For both bosonic and fermionic systems, the Krylov complexities behave similarly over time, especially at late times, due to the analogous profiles of the squared absolute values of their autocorrelation functions $\abs{φ_{0}(t)}^{2}$. The Krylov complexity grows exponentially with time, but its asymptotic scaling factor $λ_{K}$ is significantly smaller than the twice of the slope of the $\{b_{n}\}$ coefficients, contrasting to the relativistic field theories where the scaling aligns more closely with the twice of the slope of $\{b_{n}\}$.

hep-th↗

arXiv2024

Revisit the relationship between spread complexity rate and radial momentum

This article discusses the relationship between the boundary spread complexity rate and the radial momentum in the bulk within the framework of AdS/CFT. We demonstrate that the radial momentum of a freely falling particle, as measured by a stationary observer in the bulk, is equal to the spread complexity rate of the boundary conformal field theory. For a massive particle (no matter what the specific mass is), the particle is located at the asymptotic boundary with zero velocity at $t=0$. Additionally, we provide a simple method for obtaining spread complexity from radial momentum using optical geometry.

hep-th↗

arXiv2024

Probing Krylov Complexity in Scalar Field Theory with General Temperatures

Krylov complexity characterizes the operator growth in the quantum many-body systems or quantum field theories. The existing literatures have studied the Krylov complexity in the low temperature limit in the quantum field theories. In this paper, we extend and systematically study the Krylov complexity and Krylov entropy in a scalar field theory with general temperatures. To this end, we propose a new method to calculate the Wightman power spectrum which allows us to compute the Lanczos coefficients and subsequently to study the Krylov complexity (entropy) in general temperatures. We find that the Lanczos coefficients and Krylov complexity (entropy) in the high temperature limit will behave somewhat differently from those studies in the low temperature limit. We give an explanation of why the Krylov complexity does not oscillate in the high-temperature region. Moreover, we uncover the transition temperature that separates the oscillating and monotonic increasing behavior of Krylov complexity.

hep-th↗

arXiv2024

A Study of Decay Rate of Bound Negative Muons

A number of experiments show that the decay lifetimes of muons bound to atomic nuclei are longer than the decay lifetimes of free muons. In this paper, a scheme of extending quantum mechanics (EQM) is proposed to resolve this problem. The Schr$\ddot{\text{o}}$dinger's equation is obtained to prove the validation of this attempt. The decay ratio of bound muons is also calculated in EQM, and the result is in good agreement with the experimental data.

hep-ph↗

arXiv2024

Holographic Timelike Entanglement Entropy from Rindler Method

For a Lorentzian invariant theory, the entanglement entropy should be a function of the domain of dependence of the subregion under consideration. More precisely, it should be a function of the domain of dependence and the appropriate cut-off. In this paper, we refine the concept of cut-off to make it applicable to timelike regions and assume that the usual entanglement entropy formula also applies to timelike intervals. Using the Rindler method, the timelike entanglement entropy can be regarded as the thermal entropy of the CFT after the Rindler transformation plus a constant $icπ/6$ with $c$ the central charge. The gravitational dual of the `covariant' timelike entanglement entropy is finally presented following this method.

hep-th↗

arXiv2023

Revisit the entanglement entropy with gravitational anomaly

In this paper we study the entanglement entropy in the CFT$_2$, whose gravity dual is AdS$_3$ spacetime with a Chern-Simons term. Using the generalized Rindler method, we obtain the Rindler transformation in the two-dimensional planar CFT and compute the entanglement entropy of the CFT with gravitational anomalies. The conditions under which the entanglement entropy may have anomalous contributions is also discussed. In addition, we present a relatively general form of the Rindler AdS metric and compute its thermal entropy, which agrees with the entanglement entropy in the field theory. Moreover, we utilize the conformal transformation, which maps a cylinder to a plane, to compute the entanglement entropy of the CFT residing on a cylinder, as well as the entanglement entropy of the CFT at finite temperature on a plane. The corresponding contribution of the Chern-Simons term in gravity to the black hole thermal entropy is also obtained from this approach. These results are important for further understandings of the two-dimensional CFT with gravitational anomalies.

hep-th↗

arXiv2021

Shadow cast by a rotating and nonlinear magnetic-charged black hole in perfect fluid dark matter

We derived an exact solution of the spherically symmetric Hayward black hole surrounded by perfect fluid dark matter (PFDM). By applying the Newman-Janis algorithm, we generalized it to the corresponding rotating black hole. Then, we studied the shadows of rotating Hayward black hole in PFDM. The apparent shape of the shadow depends upon the black hole spin $a$, the magnetic charge $Q$ and the PFDM intensity parameter $k$ ($k<0$). The shadow is a perfect circle in the non-rotating case ($a=0$) and a deformed one in the rotating case ($a\neq{0}$). For a fixed value of $a$, the size of the shadow increases with the increasing $\vert{k}\vert$, but decreases with the increasing $Q$. We further investigated the black hole emission rate. We found that the emission rate decreases with the increasing $\vert{k}\vert$ (or $Q$) and the peak of the emission shifts to lower frequency. Finally, we discussed the observational prospects corresponding to the supermassive black hole $\mathrm{Sgr\ A^{*}}$ at the center of the Milky Way.

gr-qc↗

arXiv2021

Shadow of topologically charged rotating braneworld black hole

In this paper, we discuss optical properties of the topologically charged rotating black hole. We study the horizon, the photon region, the shadow of the black hole and other observables. The results show that in addition to the black hole spin parameter $a$, the other two parameters, tidal charge $β$ and electric charge $q$, are also found to affect the horizon, the photon region and the black hole shadow. In a certain range, with the increase of the three parameters, the horizon distance, shape of the photon region and the black hole shadow will all shrink. Moreover, with the increase of these three parameters, the distortion parameter $δ_{s}$ gradually increases, while the peak of the black hole energy emission rate decreases.

gr-qc↗

arXiv2021

Bardeen black hole surrounded by perfect fluid dark matter

We derive an exact solution of the spherically symmetric Bardeen black hole surrounded by perfect fluid dark matter (PFDM). By treating the magnetic charge $g$ and dark matter parameter $α$ as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. The thermodynamic stability of the black hole is also studied. The result show that, there exists a critical radius $r_{+}^{C}$, where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range $0<r_{+}<r_{+}^{C}$. In addition, the critical radius $r_{+}^{C}$ increases with the magnetic charge $g$ and decreases with the dark matter parameter $α$. Applying the Newman-Janis algorithm, we generalize the spherically symmetric solution to the corresponding rotating black hole. With the metric at hand, the horizons and ergospheres are studied. It turns out that for a fixed dark matter parameter $α$, in a certain range, with the increase of the rotation parameter $a$ and magnetic charge $g$, the Cauchy horizon radius increases while the event horizon radius decreases. Finally, we investigate the energy extraction by the Penrose process in rotating Bardeen black hole surrounded by PFDM.

gr-qc↗

arXiv2020

Shadows of rotating Hayward-de Sitter black holes with astrometric observables

Motivated by recent work on rotating black hole shadow [Phys. Rev. D101, 084029 (2020)], we investigate the shadow behaviors of rotating Hayward-de Sitter black hole for static observers at a finite distance in terms of astronomical observables. This paper uses the newly introduced distortion parameter in [arXiv:2006.00685] to describe the shadow's shape quantitatively. We show that the spin parameter would distort shadows and the magnetic monopole charge would increase the degree of deformation. At the same time, the distortion could be relieved because of the cosmological constant and the distortion would increase with the distance from the black hole. Besides, the spin parameter, magnetic monopole charge and cosmological constant increase will cause the shadow to shrink.

gr-qc↗

arXiv2020

The cosmological constant from space-time discreteness

We regard the background of space-time as a physical system composed of discrete volume elements at the Planck scale and get the internal energy of space-time by Debye model. A temperature-dependent minimum energy limit of the particles is proposed from the thermal motion part of the internal energy. As decreases of the temperature caused by the expansion of the universe, more and more particles would be"released" because of the change of the energy limit, we regard these new particles as a source of dark energy. The minimum energy limit also leads to a corrected number of particles in universe and a modified conservation equation. According to the modified conservation equation, an effective cosmological constant consistent with its observed value is obtained.

gr-qc↗

arXiv2020

Optical properties of a Brane-World black hole as photons couple to the Weyl tensor

In this article, we have investigated the equations of motion of the photons coupled to Weyl tensor by the geometric optics approximation and the corresponding shadow in a Brane-World black hole spacetime. It is shown that there exists a double shadow for a black hole since the coupling photons with different polarization directions propagate along different paths in the spacetime. Furthermore, we discuss the effects of the metric parameter $α$ related to the cosmological constant, X-cold dark matter parameter $β$ and the coupling parameter $λ$ on the umbra (the overlap region of the double shadow) and the penumbra. We also obtain the finite-distance corrections to the deflection angle of light in the Brane-World black hole spacetime as the photons coupled to Weyl tensor by using a recent geometric method.

gr-qc↗