arXiv subjects

Zhiqiang Huang

Publications and source records attributed to Zhiqiang Huang.

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

Exact replica-sector hierarchy of multi-resolvent correlations in random free fermions

The spectral weight with which a many-body eigenstate contributes to a given channel is not fixed by the smooth one-point ETH envelope, and its higher-order correlations---the connected cumulants of three and more channel-resolved spectral functions---have lacked a systematic organization. We construct one. In random free fermions, where every channel overlap is a squared Slater minor of a Haar-orthogonal one-body eigenvector matrix, the $r$-resolvent moment admits an exact replica-sector decomposition: a sum over the double-coset sectors of the orthogonal Weingarten algebra, in which the permutation sectors are the replica contraction classes and each sector value is determined by the overlap pattern of the channels and of the eigenstates. The sector coefficients follow from an exact occupancy-matrix assembly---a signed convolution over the slot permutations, a decomposition into connected blocks, and a finite-state chain transfer matrix whose local transition rules are independent of $r$ and $k$---so the sector theorem holds at arbitrary finite multiplicity, realized exactly at $r=3$ ($k=2,3,4$), $r=4$ and $r=5$ ($k=2$). The structure carries the physical hierarchy: the fully coincident sector is the projection that yields the Selberg moment ratios $q_r$, the levels are nested by exact marginalization, and the sectors are the multi-energy spectral cumulants behind the resolvent cumulants, with the irreducible self-energy vertices of the Feshbach ladder as the connected kernel. The multi-resolvent correlations of random free fermions are therefore organized, level by level, by one replica-sector algebra---an exact microscopic benchmark for the higher-order fluctuation sector of eigenstate thermalization, with its microscopic sector geometry made explicit.

quant-ph↗

arXiv2026

Beyond the ETH envelope: exact two-resolvent fluctuation structure, projected microscopic closure, and rigid versus nonperturbative sectors

Eigenstate thermalization fixes the smooth energy-resolved envelope of few-body observables but not the microscopic overlap statistics that realize it. In the multi-resolvent hierarchy, this missing information appears in a two-resolvent fluctuation sector. We solve that sector exactly in a tractable benchmark, random free fermions, obtaining a non-Porter-Thomas intensity hierarchy, a structured channel-distance covariance, and an exact overlap kernel that closes the two-resolvent covariance. We then reconstruct the same sector without using its exact solution: a projected self-consistency scheme fixes the irreducible vertex through independently computable projections, while unconstrained residuals identify the sectors missed by a minimal ansatz and are completed exactly by a finite-size Weingarten evaluation, without fitting. For interacting deformations, we prove a model-independent moment identity showing that the deep-plane coefficients are fixed by Hamiltonian-moment covariances. This yields an exact rigidity law: pair-hopping interactions freeze the sector, dense perturbations add only an isotropic layer, and density-density interactions produce an explicit polynomial deformation in channel geometry. By contrast, the bulk sector requires the interacting eigenstate-overlap kernel and exhibits a logarithmically divergent perturbative response. The fluctuation sector therefore splits into a rigid moment-determined part and an intrinsically nonperturbative eigenstate-resolved part.

quant-ph↗

arXiv2026

On the generic increase of entropy in isolated systems

We investigate the generic emergence of entropy in isolated quantum systems from the spectral structure of their long-time dephased states. Using a resolvent-based hierarchy, we separate the smooth energy-shell envelope of eigenstate intensities from their intra-shell fluctuations. The single-resolvent sector determines the coarse-grained intensity envelope and yields an entropy contribution that is quantitatively captured by a Lorentzian-Gaussian form. We then show that the difference between this envelope entropy and the von Neumann entropy is governed exactly by the conditional statistics of the residual intensity fluctuations. The two-resolvent covariance sector identifies their leading variance, while higher correlation sectors control the full non-Gaussian correction. A Gaussian-amplitude closure provides a benchmark entropy deficit, whereas exact diagonalization of an interacting Ising chain exhibits substantial finite-size deviations from this benchmark. These results establish a hierarchical spectral framework in which entropy beyond the smooth envelope is directly tied to multi-resolvent correlations, providing a systematic route toward its microscopic characterization.

quant-ph↗

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 Multi-Resolvent Hierarchy for the ETH Smooth Function

The eigenstate thermalization hypothesis (ETH) parametrizes off-diagonal matrix elements by a smooth function whose microscopic origin remains largely phenomenological. We develop a multi-resolvent hierarchy that derives this smooth structure from the microscopic Hamiltonian. Starting from exact projection identities, we express the ETH variance as $f_{ji}^2=D_{ji}+g_{ji}$, where $D_{ji}$ is the diagonal-overlap baseline and $g_{ji}=\sum_{r\ge2}g_{ji}^{(r)}$ is a systematically improvable hierarchy of multi-channel interference processes. The leading $r=3$ sector generates an odd-parity component in the energy difference, inaccessible to parity-preserving single-resolvent closures. The same resolvent construction yields an exact covariance representation of eigenstate fluctuations. Under amplitude isotropy, decorrelation, and regularity, it reduces to the Gaussian limit, with $q-3=κ_4/\langle c^2\rangle^2$; normalization further fixes the cross-channel covariance $\bar C_i$, including its energy-resolved form. Exact diagonalization verifies these relations in random-matrix and structured systems, while the latter exhibit controlled breakdown of the isotropic Gaussian closure. The framework thus provides a microscopic hierarchy for both the smooth and fluctuation sectors of subsystem ETH.

quant-ph↗

arXiv2026

Multi-site Radar Systems for High-Precision Indoor Positioning and Tracking

This paper introduces a high-precision indoor positioning and tracking method that utilizes multi-site single-input single-output (SISO) radar systems. We propose a novel velocity synthesis-assisted (VSA) localization algorithm that iteratively refines target position estimates within range bins by fusing radial velocity measurements from multiple radars. This approach ensures enhanced accuracy in both velocity and position estimation. Moreover, the inherent geometric constraints introduced by velocity synthesis enable the proposed algorithm to remain robust under low signal-to-noise ratio (SNR), severe multipath propagation, and large synchronization latency. Notably, our method eliminates the use of multiple-input-multiple-output (MIMO) configurations and stringent phase synchronization requirements, substantially reducing hardware complexity while maintaining high positioning accuracy. We define standardized reference trajectories to facilitate a comprehensive and reproducible performance evaluation. Extensive simulations and experimental validations demonstrate that our multi-site radar systems achieve centimeter-level tracking accuracy for human subjects, outperforming existing methods in complex trajectory tracking.

eess.SP↗

arXiv2026

Unified Error Analysis of Multi-site Radar via Equivalent Angular Resolution

High-precision indoor sensing using monostatic multiple-input multiple-output (MIMO) radar typically relies on increasing the physical aperture size of antennas, leading to high hardware complexity and cost. To overcome this bottleneck, this paper establishes a unified framework for multi-site radar sensing based on equivalent angular resolution, together with a design methodology that uses this metric to optimize distributed Single-Input Single-Output (SISO) configurations. By mapping spatial diversity into the angular domain, the proposed metric enables a direct and physically interpretable comparison with monostatic MIMO beamwidth. The associated methodology provides a principled way to select node placement and geometry to synthesize an effective virtual aperture that suppresses angular glint and multipath. Experiments with commercial 60-GHz radars in cluttered indoor environments validate the superiority of the multi-site SISO configuration over monostatic MIMO, demonstrating a reduction in maximum localization error from 0.58 m to 0.20 m and mean error from 0.35 m to 0.12 m.

eess.SP↗

arXiv2026

Respiration Monitoring of Multiple People using Multi-site FMCW SISO Radar Systems

Continuous contactless respiration monitoring of co-sleeping subjects faces a dilemma: conventional single-site multiple-input multiple-output (MIMO) radars struggle with limited angular resolution for closely spaced individuals, while distributed radar networks typically require complex hardware synchronization. To address these limitations, this paper proposes non-coherent multi-site single-input-single-output (SISO) radar systems that completely eliminate the need for physical synchronization cables or common reference clocks. The fundamental challenge of ghost target ambiguity in such non-coherent multilateration is resolved through a novel physiological-feature-assisted suppression technique. By exploiting the inherent statistical independence of individual respiratory rhythms, true target locations are robustly distinguished from ghosts via cross-correlation analysis. Experimental validation demonstrates that the proposed system can accurately resolve two subjects spaced less than 20 cm apart, surpassing the resolution limits of traditional compact MIMO arrays, while achieving a respiration rate estimation accuracy of 0.7 bpm root mean square error (RMSE) compared to contact-based ground truth.

eess.SP↗

arXiv2025

Broadband tunable microwave photonic radar for simultaneous detection of human respiration, heartbeat, and speech with deep learning-based speech recognition

Multimodal vital sign monitoring and speech detection hold significant importance in medical health, public safety, and other fields. This study proposes a broadband tunable microwave photonic radar system that can simultaneously monitor respiration, heartbeat, and speech. The system works by generating broadband radar signals to detect subtle skin displacements caused by these physiological activities. It then utilizes phase variations in radar echo signals to extract and reconstruct the corresponding physiological signals. In order to enhance the processing capability for speech signals, a convolutional neural network with a dual-channel feature fusion model is incorporated, enabling high-precision speech recognition. In addition, the system's frequency-tunable characteristic allows it to flexibly switch frequency bands to adapt to different working environments, greatly improving its practicality and environmental adaptability. In concept-verification experiments, speech signals were reconstructed and recognized in the Ku, K, and Ka bands, achieving recognition accuracies of 97.20%, 98.07%, and 97.43%, respectively. The system's capability to detect multimodal vital signs was also thoroughly validated using a respiratory and heartbeat simulator. During a 20-second monitoring period, while accurately reconstructing speech, the maximum average error counts for respiratory and heartbeat monitoring were 0.39 and 0.87, respectively, proving its reliability and effectiveness in multimodal vital sign monitoring.

physics.optics↗

arXiv2025

Trade-off between diagonal and off-diagonal elements in the eigenstate thermalization hypothesis

To bypass the reliance on local observables in verifying the eigenstate thermalization hypothesis (ETH), we introduce an observable-independent measure of distinguishability based on the variance of a rescaled local operator. We establish a universal trade-off relation between the diagonal and off-diagonal elements of this measure, rigorously connecting it to eigenstate typicality and spatially averaged observables. This trade-off reveals that exponential growth in the number of off-diagonal terms enforces their suppression, indirectly constraining diagonal deviations. Numerical simulations on a one-dimensional Ising spin chain with tunable transverse and longitudinal fields demonstrate stark contrasts between integrable and non-integrable regimes: While off-diagonal elements are universally suppressed with system size, diagonal suppression fails in integrable systems due to the absence of chaotic dynamics. Our results unify subsystem ETH, weak ETH, and macroscopic observables under a single framework, offering new insights into thermalization mechanisms.

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↗

arXiv2024

Integral fluctuation theorems and trace-preserving map

The detailed fluctuation theorem implies symmetry in the generating function of entropy production probability. The integral fluctuation theorem directly follows from this symmetry and the normalization of the probability. In this paper, we rewrite the generating function by integrating measurements and evolution into a constructed mapping. This mapping is completely positive, and the original integral FT is determined by the trace-preserving property of these constructed maps. We illustrate the convenience of this method by discussing the eigenstate fluctuation theorem and heat exchange between two baths. This set of methods is also applicable to the generating functions of quasi-probability, where we observe the Petz recovery map arising naturally from this approach.

cond-mat.stat-mech↗

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

Multiple entropy production for multitime quantum processes

Entropy production and the detailed fluctuation theorem are of fundamental importance for thermodynamic processes. In this paper, we study the multiple entropy production for multitime quantum processes in a unified framework. For closed quantum systems and Markovian open quantum systems, the given entropy productions all satisfy the detailed fluctuation relation. This also shows that the entropy production rate under these processes is non-negative. For non-Markovian open quantum systems, the memory effect can lead to a negative entropy production rate. Thus, in general, the entropy production of the marginal distribution does not satisfy the detailed FT relation. Our framework can be applied to a wide range of physical systems and dynamics. It provides a systematic tool for studying entropy production and its rate under arbitrary quantum processes.

quant-ph↗

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↗

arXiv2022

Fluctuation Theorems for multitime processes

In this paper, we extend the fluctuation theorems used for quantum channels to multitime processes. The fluctuation theorems for quantum channels are less restrictive. We show that the given entropy production can be equal to the result of a closed system environment. The assumption that the system evolves under a completely positive and trace preserving map is quite general, but it is more specific for cases in which the system is initially correlated with the environment. System-environment correlations arise naturally in multitime processes, with which we can give clear and physical interpretations regarding the effects of correlations. Multitime processes can provide many-body channels. The Choi state of such a many-body channel is called a process tensor. One can derive channels by executing the process tensor on a set of operations. We establish a general quantum fluctuation theorem framework for a many-body channel and its derived channels. In this framework, the effects of correlations are reflected in a Markovian property. For Markovian processes, we can extend the two-point measurement to a three-point measurement and obtain that the fluctuation theorems contain complete information about the intermediate state. For non-Markovian processes, the complete measurement of the intermediate state leads to conflicts. Therefore, we use a general measurement, which only provides partial information, for the intermediate state. The corresponding fluctuation theorems show that memory effects can reduce these fluctuations. This is consistent with the fact that system states can be recovered under non-Markovian processes.

quant-ph↗