In this paper, the excitation of modulation instability (MI) and oscillation structures evolved from initial localized perturbations occuring in the nonlinear stage of MI for two typical discrete models, namely the nonlocal discrete nonlinear Schrödinger equation with $PT$ symmetric potential and the discrete Manakov model, are studied. We obtain the different conditions for MI to be excited in the focusing and defocusing cases, respectively. We investigate the linear stage of MI analytically to obtain specific conditions on the wavenumber and constant amplitude for MI occurring. When the small perturbation becomes close to the background amplitude, this stage is no longer valid and the nonlinear stage happens, which is investigated numerically with three initial localized perturbations of the nonzero constant background. Next, the dynamics of oscillation structures are analyzed.
The asymptotic stability of Takagi–Sugeno (T-S) fuzzy systems is investigated by using multi-rate sampled-data control and a refined fuzzy Lyapunov function. Firstly, a multi-rate sampling mechanism is introduced, to accommodate system variables with differing dynamic rates. It enables sensors to acquire dataat rates aligned with variable characteristics and performance requirements. Secondly, to mitigate conservativeness in stability analysis, a refined fuzzy Lyapunov function is constructed to fully exploit state information at multi-rate sampling instants. Based on this function, a corresponding stability analysis method is developed and a control gain design algorithm is designed. Finally, simulation examples of a spring system and a truck-trailer system validate the effectiveness of the proposed method.
In this paper, we investigate a $(2+1)$-dimensional noncommutative coupled dispersionless (CD) system with variable coefficients. The proposed model extends the classical CD equations by incorporating matrix-valued dependent variables, spatially varying coefficients, and an additional spatial dimension, allowing the study of transverse modulation effects in a noncommutative setting. We show that the resulting system remains integrable by constructing an associated Lax pair and establishing a zero-curvature condition. A Darboux transformation formulated in terms of quasideterminants is developed to generate exact solutions. Using this approach, general quasi-Wronskian expressions for multi-soliton solutions are obtained. Explicit one-soliton and two-soliton solutions are derived and analyzed in both the scalar (commutative) limit and the fully noncommutative case. The influence of variable coefficients and noncommutativity on soliton dynamics is illustrated through representative examples and graphical visualizations. Our results demonstrate that the combined effects of spatial inhomogeneity and noncommutativity lead to richer nonlinear wave structures while preserving integrability.
We investigate spin squeezing and optimal phase sensing in parity-conserving one-axis twisting (OAT) and two-axis twisting (TAT) spin systems. For the OAT model, we analytically identify a plateau regime where the quantum Fisher information (QFI) reaches $0.5N^2$ with a fixed $y$-axis sensing direction—a configuration well-suited for standard interferometry. For an even number of particles $N$, it is essential to switch the sensing direction from the $y$-axis to the $z$-axis to further enhance the QFI to $ N^2$. In contrast, for odd $N$, the $y$-axis remains nearly optimal without such a directional transition. We analytically demonstrate that this transition in the optimal sensing direction is exclusive to the even-$N$ case. For the TAT model, we demonstrate a discontinuous jump in the optimal sensing direction from the anti-squeezing direction to the $z$-axis, enabling the QFI to reach a peak value $\sim 0.93N^2$, thereby exceeding the earlier benchmark of $0.64N^2$. Our results reveal the important role of the sensing direction transition in achieving a high-precision quantum phase estimation.
Based on a coupled resonator array, we theoretically construct and numerically simulate a nonlinear quantum optics platform to dynamically control the Bloch wavevector. By scanning the modulation parameters ($\alpha, k_y$), we reproduce the Hofstadter's butterfly structure in the biphoton energy spectrum and reveal clear correspondences among the eigenenergy spectrum, transmission spectrum, and biphoton joint spectral intensity (JSI). Further research demonstrates that screening the pump wavelength can effectively tailor the JSI profile and the Schmidt number of the quantum state, enabling flexible manipulation of frequency entanglement characteristics. This work provides a theoretical framework for exploring quantum state generation and manipulation in nonlinear topological photonic systems and demonstrates the potential for realizing programmable quantum light sources in integrated quantum photonic circuits.
We theoretically investigate the control of the Goos–Hänchen shift (GHS) of a reflected weak probe field in both parity–time ($\mathcal{PT}$)-symmetric and conventional optomechanical systems. The proposed scheme consists of a single optomechanical platform where a passive optical cavity is coupled to an active mechanical resonator, in contrast to standard passive–passive configurations. Analysis of the eigenfrequency spectrum reveals the emergence of an exceptional point under balanced gain–loss conditions at a tunable effective optomechanical coupling strength. Using the transfer-matrix method combined with stationary-phase analysis, we examine the GHS across broken and unbroken $\mathcal{PT}$ phases and compare it with that in the conventional system. The lateral shift exhibits strong phase dependence: it is markedly enhanced in the unbroken regime relative to both the broken phase and the passive configuration. We further show that the GHS can be actively tuned through the cavity detuning and the intracavity medium length. These results provide a controlled means for manipulating beam shifts in optomechanical systems and suggest pathways toward tunable photonic components and precision optical sensing.
We suggest an investigation of the photonic spin Hall effect (PSHE) in a mid-infrared probe field by employing an asymmetric double AlGaAs/GaAs quantum well as the intracavity medium. The system is designed such that an external control beam together with tunable tunneling barriers regulates the quantum interference of the probe tunneling process. This configuration enables precise manipulation of the PSHE for both horizontally and vertically polarized components of light. Our analysis reveals the emergence of a giant horizontal PSHE in the quantum well-based cavity system. Moreover, by incorporating absorptive and gain-assisted cavity slabs, the horizontal PSHE is further amplified, leading to an even more pronounced photonic spin separation. The results provide novel insights into light–matter interactions in semiconductor quantum wells and suggest an effective route for enhancing and controlling the PSHE in mid-infrared photonic devices.
The direct detection of gravitational waves (GWs) by LIGO has confirmed general relativity (GR), but testing GR via GWs requires estimating parameterized post-Einsteinian (ppE) deviation parameters in waveform models. Traditional Bayesian inference methods like Markov chain Monte Carlo (MCMC) provide reliable estimates but suffer from prohibitive computational costs, failing to meet the real-time demands and surging data volume of future GW detectors. Here, we propose a factorized neural posterior estimation framework: we construct independent normalizing flow models for each of the nine ppE deviation parameters, and effectively integrate prior information from other source parameters via a conditional embedding network. Leveraging a hybrid neural network with a convolutional neural network and a residual neural network for feature extraction, our method performs rapid and statistically reliable posterior inference directly from binary black hole signals. Compared to conventional MCMC, our approach achieves millisecond-scale inference time with a speedup factor of $9 \times 10^4$. Comprehensive validations show that the posterior estimates pass the Kolmogorov–Smirnov test and achieve empirical coverage probabilities close to theoretical targets. We apply this method to the GW150914 event and find that the resulting posterior distributions are in good agreement with existing results. This work demonstrates the great potential of deep learning for GW parameter estimation and provides a viable technical solution for real-time GR tests with next-generation detectors.
Recent critiques have addressed certain aspects of the generalized uncertainty principle (GUP) effective metric (Ong 2023 Eur. Phys. J. C 83 209). This study presents a scale-dependent quadratic GUP effective metric, constructed through analyses of the gravity-induced phase shift (Collela, Overhauser, and Werner experiment) and the Einstein–Bohr photon box Gedanken experiment. In contrast to the procedure outlined in Xiang (2018 Ann. Phys. 396 334–50), the momentum-dependent metric is improved by introducing an interpolating function $\Delta p (r)$, which employs the effective distance concept to accurately capture the distinct behavior of $\Delta p (r)$ in both short and long distance regimes. The resulting effective metric exhibits the same structure as that derived from the renormalization group (RG) theory. However, the RG parameter $\hat{\gamma}$ can now be related to the dimensionless GUP parameter $\beta_0$, thereby distinguishing this metric from the RG-based approach. The corresponding effective metric prediction demonstrates internal consistency of the model, and phenomenologically the predictions are in agreement with some quantum black hole (BH) models in some limits. The effective metric improved BH thermodynamics and shadow predictions compared to the heuristic approach and other proposed GUP effective metrics. Furthermore, the relationship between GUP and $f(R)$ gravity (D'Agostino 2024 Phys. Lett. 878 140519) may provide a possible future route toward a more fundamental description of GUP.
A classically scale-invariant quadratic phase admits a homogeneous Einstein regime only after a finite Planck mass has been generated dynamically. On spatially flat Friedmann–Robertson–Walker backgrounds, this reduction is exact: $C^2$ vanishes identically, a constant Gauss–Bonnet coupling is topological, and the background equations retain only the scalar mode carried by $R^2$. A minimal Coleman–Weinberg order parameter with nonminimal coupling $\xi$ induces $M_\textrm{Pl}^2 = \xi v^2$ and gives the infrared curvature coefficient $\alpha_\textrm{eff} = \alpha+\xi^2/(2\beta_{\sigma})$ after the heavy radial mode is integrated out. If the CMB pivot exists after this transmutation, the measured scalar amplitude fixes $\alpha_\textrm{eff}\sim10^9$, which defines a narrow CMB compatible band in $\beta_{\sigma}\xi^{-2}$ and determines the scalaron mass $m_\phi\sim3\times10^{13}\,\mathrm{GeV}$, reheating temperature $T_\textrm{reh}\sim10^9\,\mathrm{GeV}$, and heavy-threshold hierarchy $m_\sigma^2/H_*^2\simeq24\xi$ for a subdominant bare $R^2$ term. The homogeneous exit of quadratic gravity is therefore a quantitative sequence of Planck-mass transmutation, infrared threshold matching, and scalaron reheating, not a freely adjustable interpolation.
Exploring quantum effects from black hole thermodynamics has always been a pivotal topic. In recent years, the free energy landscape and ensemble-averaged theory based on the Euclidean path integral approach have provided further understanding of the statistical aspects of the black hole system. We investigate the quantum-corrected thermodynamics of the Reissner–Nordström Anti-de Sitter black hole by including off-shell geometries in a reduced gravitational path integral. Within this collective-variable approximation, we derive an effective action by considering the subleading-order terms in the ensemble-averaged theory and show that the corresponding thermodynamic quantities define consistent thermodynamics. Furthermore, the phase diagram is modified by the off-shell effects, resulting in a more abundant phase structure. We show that traditional black hole thermodynamics can be recovered in the semi-classical limit. The region of first-order phase transitions shrinks and zero-order phase transitions emerge when off-shell effects are included. These results provide a tractable framework for understanding how off-shell black hole geometries generate quantum corrections to black hole phase structures.
Several hundred of gravitational wave (GW) events have been detected: they are good tools to investigate various fundamental problems, including tests of general relativity (GR) theory. Among the GR test schemes based on GW data, the parameterized scheme has been extensively studied by many groups including the LIGO–VIRGO–KAGRA collaboration (LVK). Existing results indicate that the deviation parameters from GR are small. In the current paper, we would like to estimate whether these deviation parameters are small enough to confirm GR. We transform the deviation parameters into mass–mass relations and, by comparing the resulting mass–mass relations from different parameters, we can estimate the probabilities that the data favor the GR theory. Applying our null test scheme to five O1/O2 binary black hole events, we found some GR deviation signatures, however, they are not conclusive yet. We also found no monotonic correlation between the network SNR and the strength of GR deviation, suggesting that the observed tensions are not simply driven by signal strength. Our null test scheme can be easily generalized and applied to all GW observation data.
Ultralight vector dark matter (DM) is an important class of DM candidates. In this work, we investigate the detection of ultralight vector DM using spatially separated atom interferometers (AIs). In particular, we focus on models where the ultralight vector DM could couple to standard-model particles via baryon number or baryon-minus-lepton number and exert a force on them. First, we calculate the phase shift of AIs caused by ultralight vector DM. Then, we propose a method to detect ultralight vector DM using spatially separated AIs. Finally, we estimate the sensitivity of spatially separated AIs for ultralight vector DM. The results indicate that spatially separated AIs could improve current constraints by several orders of magnitude.
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical distribution and invariance under a uniform shift of the energy zero. These conditions uniquely yield the Boltzmann factor, whose parameter is fixed by the mean energy per particle. For separable Hamiltonians, the equilibrium weight factorizes into kinetic and configurational contributions sharing the same parameter, identified from the kinetic part as the inverse kinetic temperature. The principle extends to any physical quantity with a stationary distribution and translational invariance. It is illustrated in a one-dimensional diatomic hard-core gas and a nonlinear lattice chain, where it predicts velocity, energy, spacing, collision-time, and pressure-dependent displacement distributions in agreement with simulations. The lattice model further shows how harmonic elasticity, anharmonic corrections, internal pressure, and thermal expansion emerge from the same exponential equilibrium weights. Finally, the relationships among different ensembles are briefly discussed.
The grand canonical catastrophe—characterized by order-unity relative fluctuations of the ground-state occupation in the grand canonical ensemble (GCE) at low temperatures—is a hallmark of ensemble inequivalence in ideal Bose gases and has been observed in photon Bose–Einstein condensates. In this work, we investigate an alternative class of observables defined via conditional ensemble averages, namely $\langle n_0/N \rangle$ and $\langle \delta n_0^2 / N^2 \rangle$, where the average excludes the empty-system sector ($N = 0$). Using the exactly solvable model of an ideal Bose gas in a one-dimensional harmonic trap, we show that these conditional averages reproduce microcanonical predictions even for modest particle numbers ($N \sim 10$) and exhibit vanishing relative fluctuations as temperature approaches zero. We stress that this does not contradict the standard GCE result $\langle \delta n_0^2 \rangle \to \langle N \rangle^2$, which remains thermodynamically valid for open systems. Instead, our framework provides a natural description for experimental scenarios involving post-selection or implicit conditioning on non-empty realizations—common in few-body quantum gas experiments. Thus, the absence of large fluctuations in these conditional averages reflects a change in the observable, not a failure of ensemble theory.
Isolated quantum systems follow a reversible unitary evolution, which seems inconsistent with the irreversibility of macroscopic thermodynamics. We notice that such a paradox can be reconciled when focusing on the local relaxation process. Here, we study the exact dynamics of an isolated system, which contains a finite number of three-level systems. When focusing on the dynamics of local states and local observables, irreversible behaviors naturally appear. Though the entropy of the full many-body state always remains unchanged, the total correlation entropy of this system exhibits an irreversibly increasing behavior. Moreover, our variation analysis shows that, the total correlation entropy would achieve its theoretical maximum if each site is in a generalized one-body Boltzmann state, which is not solely determined by the energy but also depends on the onsite pseudo-spins, and such a theoretical correlation maximum is highly coincidental with the exact time evolution. In this sense, the total correlation entropy serves well as a generalized indicator for the dynamical irreversibility of the nonequilibrium relaxation in this isolated system.
The longest increasing subsequence (LIS) problem—a classic combinatorial challenge with deep connections to statistical mechanics—exhibits a rich thermodynamic landscape. Introducing a temperature, we identify two distinct energy scales: a Schottky-like crossover at $T_{\text{cross}}$ and a condensation transition at $T_{\text{cond}}$, below which the number of maximum-length configurations becomes sub-exponential in system size. We also show that despite the existence of polynomial-time dynamic programming algorithms for the ground state, local Monte Carlo dynamics, after sudden quenches at low temperatures, become trapped in metastable state configuration displaying characteristic glassy signatures: two-step relaxation, persistent dynamical overlaps, and aging. On the other hand, logarithmic annealing tracks equilibrium down to the ground state. These results establish that thermodynamic sparsity—not energetic barriers—can render local search dynamically intractable, positioning the LIS problem as a bridge between exactly solvable optimization and glassy spin-glass phenomenology.
Majorana-bound states (MBSs) generated at the ends of a semiconductor nanowire in contact with an s-wave superconductor have been convincingly observed in various experiments. However, distinguishing MBSs from regular fermion-bound states (RFBSs) remains controversial and requires further investigation since there is no well-defined criterion. In this study, we investigate the average current, differential conductance, and finite-frequency shot noise of electron transport through a quantum dot (QD) coupled to two MBSs or RFBSs. We show that neither the number of steps in the average current nor the number of peaks in the differential conductance can be used to distinguish MBSs from RFBSs. In contrast, the number of dips in the finite-frequency shot noise of the source and drain electrodes, as well as the apparent variation in the dip value when the resonance level energy of the QD is tuned from a negative to a positive value, can be used to distinguish MBSs from RFBSs. In particular, the number and positions of the dips are independent of the applied bias voltage, the QD-electrode tunneling coupling strengths, and the temperature of the QD-MBS system. Consequently, the predicted properties of the finite-frequency shot noise dips in the source and drain electrodes suggest a well-defined criterion for distinguishing MBSs from RFBSs.
Quantum anomalous Hall insulator-superconductor heterostructures are predicted to host chiral Majorana fermions as edge modes, which is essential for topological quantum computing applications. Although the edge states have been extensively studied at zero chemical potential $\mu = 0$, the practically relevant regime with a shifted chemical potential ($\mu \neq 0$) remains less explored. Here, we present an analytical treatment of the edge states for $\mu \neq 0$, deriving an approximate but highly accurate solution applicable to realistic experimental parameters. Surprisingly, we find that the energy dispersion of the edge band exhibits nonlinearity and transforms into a twisted, braid-like structure within specific parameter ranges. This unique braid-like band leads to non-chirality of the edge modes, allowing propagation in both directions.
