arXiv subjects

Xiao-Kan Guo

Publications and source records attributed to Xiao-Kan Guo.

At least 19 recordsLinked to original sources

arXiv2026

On thermalization in random free fermions: Statistical origins and energy-dependent ETH structure

We study the thermalization in the random free fermion model by a detailed random-matrix analysis. By computing the ensemble average and fluctuations of $\operatorname{Tr}(Aρ(t))$ for a single-particle observable $A$, we derive the thermalization function $g^2(t/τ_λ)$ with $τ_λ= \hbar/(2η\sqrt{N})$, prove its $|t|^{-3}$ asymptotic decay, and show that the variance of the fluctuations vanishes as $O(1/N)$ in the thermodynamic limit.Particle number conservation is also incorporated into the model, by which we further study the energy-shell eigenstate statistics and prove a factorization theorem of the eigenstate statistics. We further show that under a controlled eigenvector-eigenvalue correlation deformation, the diagonal energy-resolved slope and the off-diagonal eigenstate thermalization hypothesis spectral function acquire an energy dependence.Finally, we compute the fluctuations of correlation functions and compare the fluctuation scales with those of a fully chaotic system, revealing quantitative differences rooted in the Gaussian nature of the eigenstates.Our work establishes the random free fermion model as an analytically solvable realization of weak eigenstate thermalization hypothesis type self-averaging, and as a controllable setting in which eigenbasis chaos can be separated from spectral chaos.

cond-mat.stat-mech↗

arXiv2026

Information-geometric bounds on nonequilibrium relaxation in quantum Markov dynamics

In this paper, we study the quantum information-geometric structure underlying short-time nonequilibrium relaxation in quantum Markov dynamics, and derive bounds on the nonequilibrium correction to the short-time relaxation curvature. These bounds generalize the information-geometric structure underlying Auconi's classical nonequilibrium relaxation inequality to quantum Markov dynamics. We consider the von Neumann relative entropy as quantum divergence, and parametrize perturbations through the Kubo-Mori map, which converts the second-order expansion of the relative entropy into the Bogoliubov-Kubo-Mori (BKM) inner product at all temperatures. For a quantum Markov semigroup with full-rank stationary state, the induced tangent-space generator admits a canonical decomposition into a BKM-symmetric and a BKM-antisymmetric part, and the leading nonequilibrium curvature correction takes the exact form of the expectation of the commutator between the dissipative and the transport part of the generator. This correction is bounded by the product of a BKM-symmetric dissipative activity and a transport-sector activity. The bound is verified on a noncommuting qubit model and a driven-dissipative qutrit, and the full chain is confirmed numerically on a two-dimensional Fokker-Planck steady state. In the high-temperature and overdamped limit the quantum formula reduces to the position-space Fokker-Planck expression and reproduces Auconi's entropy-production bound with the correct temperature factor.

quant-ph↗

arXiv2026

A no-go study on gravitational helicity in connection variables

We study the gravitational helicity using the covariant phase space method. Starting from the covariant phase space of general relativity expressed in terms of connection variables, we construct the symplectic form and identify a duality transformation based on the internal Hodge dual. In the complex self-dual Ashtekar variables the duality becomes a simple $U(1)$ phase rotation. We show, however, that this rotation is not a symmetry.We also show that the expression $\int_ΣΣ^{+AB}\wedge A^+_{AB}$ inspired by the electromagnetic helicity is neither a Noether charge nor a moment map.The duality of general relativity under a rotation of the curvature two-form is a symmetry of the equations of motion but not of the Lagrangian, and carries no Noether charge. An explicit computation shows that the mass and the NUT charge are not symplectically conjugate, so even in the reduced phase space of stationary solutions this duality has no moment map. This study therefore provides counter examples to the existence of a full-theory gravitational helicity in the covariant phase space approach.

gr-qc↗

arXiv2026

Duru-Kleinert Path Integral in Unimodular Quantum Cosmology

The Wheeler-DeWitt equation of a flat Friedmann-Lemaitre-Robertson-Walker universe filled with pressureless dust and a cosmological constant in the unimodular gravity is recently shown to be equivalent to the radial Schrödinger equation of a hydrogen atom. In this paper, we revisit this correspondence between the unimodular quantum cosmology and the hydrogen atom by using the Duru-Kleinert path integration technique. The Duru-Kleinert time reparametrization transforms the Euclidean path integral of the universe into that of a one-dimensional Coulomb system. Through a Mellin-Barnes integral representation, we extract the bound state poles of the Green's function, which give the quantized negative cosmological constant. We compute the quantum tunneling rate from ``nothing'' to a universe directly within the Coulomb model. Furthermore, for a positive cosmological constant, we compute the spectral density and the Krylov complexity for the unbounded state.

gr-qc↗

arXiv2026

Degenerate Limits of Scalar-Tensor Gravity

We study the degenerate limits of the scalar-tensor theory of gravity in its Hamiltonian connection dynamics formulation. The degenerate limit of the spatial triad is effectuated by a local scaling transformation of the triad, which leads to the degenerate limits of all other geometric quantities and relations in the connection dynamics. We derive the constraints for the degenerate scalar-tensor theory of gravity and discuss their physical implications.

gr-qc↗

arXiv2026

Semiclassical Ehrenfest paths in open quantum systems

We study the semiclassical Ehrenfest trajectories in open quantum systems. We first derive in explicit form the Fokker-Planck equation that governs the time evolution of the mixing measure for a Gaussian mixture. Then, we embed the generalized Ehrenfest theorem recently obtained for open quantum systems into this phase-space picture to study the time evolution of the expectations of observable with respect to the Gaussian mixture. We show how the coherent and irreversible contributions are microscopically separated. Our work provides a transparent phase-space interpretation of the emergence of classical trajectories in open quantum dynamics.

quant-ph↗

arXiv2025

Leggett-Garg inequalities for multitime processes

We study some aspects of the Leggett-Garg inequalities by using the operator-state formalism for multitime processes. The process tensor in its Choi-state form, which we call process state, is employed to investigate the Leggett-Garg inequalities and their violations. We find the sufficient conditions on process states for the Leggett-Garg inequalities to hold, based on which we find a new way of characterizing the influences on the violation of Leggett-Garg inequalities through the structure of process states.

quant-ph↗

arXiv2025

Thin Accretion Disk Around Rotating Hairy Black Hole: Radiative Property and Optical Appearance

The gravitational decoupling method systematically generates hairy modifications to the solutions in general relativity due to new gravitational sources. In view of the recent advances in astronomical observations, these hairy solutions are expected to be testable in the near-term observations. In this paper, we study the radiative property and optical appearance of the thin accretion disk around the rotating hairy black holes obtained by gravitational decoupling. We numerically compute the radiative flux, temperature, and differential luminosity of the thin accretion disk, and we also show its bolometric image by the ray-tracing method. By comparing with the results for the Kerr metric, we found that the deviations of the observational properties of the thin accretion disk from those of Kerr metric becomes significant in the rapid rotating case, or in the inner region of the disk. These results guide the observational investigations on the rotating hairy black hole.

gr-qc↗

arXiv2024

Subsystem eigenstate thermalization hypothesis for translation invariant systems

The eigenstate thermalization hypothesis for translation invariant quantum spin systems has been proved recently by using random matrices. In this paper, we study the subsystem version of eigenstate thermalization hypothesis for translation invariant quantum systems without referring to random matrices. We first find a relation between the quantum variance and the Belavkin-Staszewski relative entropy. Then, by showing the small upper bounds on the quantum variance and the Belavkin-Staszewski relative entropy, we prove the subsystem eigenstate thermalization hypothesis for translation invariant quantum systems with an algebraic speed of convergence in an elementary way. The proof holds for most of the translation invariant quantum lattice models with exponential or algebraic decays of correlations.

quant-ph↗

arXiv2023

On the relation between quantum Darwinism and approximate quantum Markovianity

There are strong evidences in the literature that quantum non-Markovianity would hinder the presence of Quantum Darwinism. In this Letter, we study the relation between quantum Darwinism and approximate quantum Markovianity for open quantum systems by exploiting the properties of quantum conditional mutual information. We show that for approximately Markovian quantum processes the conditional mutual information still has the scaling property for Quantum Darwinism. Then two general bounds on the backflow of information are obtained, with which we can show that the presence of Quantum Darwinism restricts the information backflow and the quantum non-Markovianity must be small.

quant-ph↗

arXiv2023

Energy extraction from rotating regular black hole via Comisso-Asenjo mechanism

Recently, it has been demonstrated by Comisso and Asenjo that magnetic reconnection processes in the ergosphere of a Kerr black hole can provide us with a promising mechanism for extracting the rotational energy from it. In this paper, we study the energy extraction from the the newly proposed rotating regular black holes via this Comisso-Asenjo mechanism. This novel rotating regular black hole has an exponential convergence factor $e^{-k/r}$ on the mass term characterized by the regular parameter $k$ in the exponent. We explore the effects of this regular parameter on the magnetic reconnection as well as other critical parameters determining the Comisso-Asenjo process. The parameter spaces allowing energy extraction to occur are investigated. The power, efficiency and the power ratio to the Blandford-Znajek mechanism are studied. The results show that the regularity of the rotating black hole has significant effects on the energy extraction via the Comisso-Asenjo mechanism.

gr-qc↗

arXiv2022

Classical and quantum parts of conditional mutual information for open quantum systems

We study the classical, classical-quantum, and quantum parts of conditional mutual information in the ``system-environment-ancilla'' setting of open quantum systems. We perform the separation of conditional mutual information by generalizing the classification of correlations of quantum states. The condition for identifying the classical part of conditional mutual information is given by adapting the no-local-broadcasting theorem to this setting, while the condition for classical-quantum part of conditional mutual information is obtained by considering the multipartite quantum discord and the no-unilocal-broadcasting theorem. For the quantum part of conditional mutual information, we further generalize the characterization of entanglement by quantum discord of state extensions to the multipatite setting, so as to derive a generalized Koashi-Winter-type monogamy equality for conditional mutual information. Our results have explicit dependence on the extensions of environment, which are useful for studying different environmental contributions to the quantum non-Markovianity of open quantum systems.

quant-ph↗

arXiv2021

Quantifying non-Markovianity via conditional mutual information

In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual information can be defined in this multipartite setup. The benefit of this approach is that the conditional mutual information is closely related to recovery maps and Markov chains; we also point out its relations with the change of distinguishability. We study along the way the properties of leaked information which is the conditional mutual information that can be back flowed, and we use this leaked information to show that the correlated environment is necessary for nonlocal memory effect.

quant-ph↗

arXiv2021

Contextual extensions of quantum gravity models

We present a simple way of incorporating the structure of contextual extensions into quantum gravity models. The contextual extensions of $C^*$-algebras, originally proposed for contextual hidden variables, are generalized to the cones indexed by the contexts and their limit in a category. By abstracting the quantum gravity models as functors, we study the contextual extensions as the categorical limits of these functors in several quantum gravity models. Such contextual extensions of quantum gravity models are useful for building topos-theoretic models of quantum gravity.

math-ph↗

arXiv2021

Thermofield Double States in Group Field Theory

Group field theories are higher-rank generalizations of matrix/tensor models, and encode the simplicial geometries of quantum gravity. In this paper, we study the thermofield double states in group field theories. The starting point is the equilibrium Gibbs states in group field theory recently found by Kotecha and Oriti, based on which we construct the thermofield double state as a "thermal" vacuum respecting the Kubo-Martin-Schwinger condition. We work with the Weyl $C^*$-algebra of group fields, and a particular type of thermofield double states with single type of symmetry are obtained from the squeezed states on this Weyl algebra. The thermofield double states, when viewed as states on the group field theory Fock vacuum, are condensate states at finite flow parameter $β$. We suggest that the equilibrium flow parameters $β$ of this type of thermofield double states in the group field theory condensate pictures of black hole horizon and quantum cosmology are related to the inverse temperatures in gravitational thermodynamics.

hep-th↗

arXiv2020

Weak cosmic censorship conjecture in higher-dimensional black holes with nonlinear electrodynamic sources

The new version of the gedanken experiments proposed by Sorce and Wald are designed to test the validity of the weak cosmic censorship conjecture (WCCC) by overspinning or overcharging the Kerr-Newman black hole in Einstein-Maxwell gravity. Following their setup, in this paper, we investigate the WCCC in the higher-dimensional charged black hole with a nonlinear electrodynamics source. We derive the first and seconder order perturbation inequalities of the charged collision matter based on the Iyer-Wald formalism as well as the null energy conditions, and show that they share the similar form as that in Einstein-Maxwell gravity. As a result, we find that the static higher-dimensional nonlinear electrodynamics (HDNL) black holes cannot be overcharged after considering these two inequalities. Our result might indicate the validity of WCCC for more general HNDL and related systems.

gr-qc↗

arXiv2020

Tensor networks for quantum causal histories

In this paper, we construct a tensor network representation of quantum causal histories, as a step towards directly representing states in quantum gravity via bulk tensor networks. Quantum causal histories are quantum extensions of causal sets in the sense that on each event in a causal set is assigned a Hilbert space of quantum states, and the local causal evolutions between events are modeled by completely positive and trace-preserving maps. Here we utilize the channel-state duality of completely positive and trace-preserving maps to transform the causal evolutions to bipartite entangled states. We construct the matrix product state for a single quantum causal history by projecting the obtained bipartite states onto the physical states on the events. We also construct the two dimensional tensor network states for entangled quantum causal histories in a restricted case with compatible causal orders. The possible holographic tensor networks are explored by mapping the quantum causal histories in a way analogous to the exact holographic mapping. The constructed tensor networks for quantum causal histories are exemplified by the non-unitary local time evolution moves in a quantum system on temporally varying discretizations, and these non-unitary evolution moves are shown to be necessary for defining a bulk causal structure and a quantum black hole. Finally, we comment on the limitations of the constructed tensor networks, and discuss some directions for further studies aiming at applications in quantum gravity.

quant-ph↗

arXiv2018

Lieb-Robinson Bound at Finite Temperature

The Lieb-Robinson bound shows that the speed of propagating information in a nonrelativistic quantum lattice system is bounded by a finite velocity, which entails the clustering of correlations. In this paper, we extend the Lieb-Robinson bound to quantum systems at finite temperature by calculating the dynamical correlation function at nonzero temperature for systems whose interactions are respectively short-range, exponentially-decaying and long-range. We introduce a simple way of counting the clusters in a cluster expansion by using the combinatoric generating functions of graphs. Limitations and possible applications of the obtained bound are also discussed.

cond-mat.stat-mech↗