This paper presents a geometric perspective that connects reciprocal transformations with multidimensional integrable deformations. By interpreting conservation laws as closed 1-forms, we formalize reciprocal transformations as induced local diffeomorphisms on the jet bundle. This allows us to characterize higher-dimensional deformations as systematic fiber bundle extensions, where fiber coordinates are generated by potential functions of the conservation laws. This perspective provides an interpretation for the covariant lifting of Lax pairs to higher dimensions and reveals that auto-Bäcklund transformations are composite diffeomorphisms. These results are applied to several classical integrable models.
In this paper, we investigate the convex roof measures of quantum coherence, with a focus on their superadditive properties. We propose sufficient conditions and establish a framework for coherence superadditivity in tripartite and multipartite systems. Through theoretical derivation, the relevant theorems are given. These results not only expand our understanding of the superadditivity of pure and mixed states but also characterize the conditions under which the superadditivity relations reach equality. Finally, the proposed methods and conclusions are verified through representative examples, providing new theoretical insights into the distribution of quantum coherence in multipartite systems.
We propose a scheme to achieve nonreciprocal single-photon transmission in a system consisting of a spinning whispering-gallery-mode resonator and a stationary resonator containing a scatterer, both coupled to a one-dimensional waveguide. By tuning the Sagnac−Fizeau shift induced by the spinning resonator, high-contrast nonreciprocal transmission in both forward and backward directions can be realized. Furthermore, we investigate the influences of system parameters including waveguide-resonator coupling strength, inter-mode coupling strengths within two resonators, and inter-cavity coupling strength on nonreciprocal transmissions. The results indicate that the synergistic regulation of these parameters can adjust the position of the nonreciprocal transmission peak and achieve high-contrast nonreciprocal transmission.
Multi-valued quantum adder circuits, based on multi-valued logic, are significant components in numerous quantum algorithms. Their low-cost implementations can enhance the efficiency of these algorithms. In this paper, innovative universal architectures for d(d>3)-level quantum half-adder, full-adder, parallel adder, and parallel adder/subtractor circuits are designed using d-level 1-qudit (quantum digit) and M–S gates. To demonstrate the effectiveness of these architectures, quaternary adder circuits derived from them are displayed and compared with several existing counterparts. Judging by the results, these circuits exhibit reductions in quantum cost (QC), hardware complexity (HC), number of constant inputs (NCIs), and number of garbage outputs (NGOs).
Methods of quantum information processing often appear in terms of specially selected states. For example, mutually unbiased bases (MUBs) and symmetric informationally complete measurements are widely applied. Finite frames have found use in many areas including quantum information. Due to its specific inner structure, a single equiangular tight frame (ETF) allows one to formulate criteria to detect non-classical correlations. This study aims to approach entanglement detection with the use of mutually unbiased ETFs. Such frames are an interesting generalization of widely recognized MUBs. It still uses rank-one operators, but the number of outcomes can exceed the dimensionality. Several approaches are considered including separability criteria and entanglement witnesses. Separability criteria for multipartite systems are finally obtained.
The study of nuclear isomers can deepen our understanding of nuclear structure and astrophysics. In this work, we have performed the ab initio calculations of isomers in the N = 49 isotones. With a chiral two- plus three-nucleon force, the valence-space effective Hamiltonian was derived using the ab initio many-body perturbation theory named $\hat{Q}$-box folded diagrams. The effective operators of electromagnetic operators and β-decay were obtained using $\hat{{\rm{\Theta }}}$-box folded diagrams. With the effective Hamiltonian and operators, we studied the properties of the isomers, gaining a microscopic understanding of the single-particle behaviour of the isomers which we are interested in, showing the reliability of the ab initio calculations.
In this study, we present a comprehensive analysis of a modified Frolov black hole (BH) model that incorporates two types of topological defects, a global monopole (GM) and a cloud of strings (CS). This composite BH solution is examined from multiple theoretical perspectives to explore the impact of these modifications on the BH’s geometric, thermodynamic and dynamical properties. We begin by studying the geometrical optics of the spacetime, focusing on the motion of null geodesics. Key features, such as the effective potential, photon sphere, the force acting on photons and the stability of circular photon orbits, are analyzed in detail. Our results show that the presence of GM and CS significantly affects the spacetime geometry and photon dynamics. In addition, the thermodynamic behavior of the modified BH is also investigated. We derive essential quantities such as the Hawking temperature and entropy, demonstrating how the inclusion of GM and CS leads to deviations from the standard thermodynamic relations observed in classical BH solutions. These deviations may offer valuable insights into quantum gravity and the role of topological defects in BH physics. Furthermore, we examine the BH shadow as an observational signature of the underlying geometry. Our analysis shows that the Frolov parameter tends to reduce the apparent size of the shadow, while the presence of topological defects, particularly GM and CS, enlarges it. In addition, we investigate the perturbative dynamics of the BH by studying both scalar (spin-0), fermionic (spin-1/2) and electromagnetic (spin-1) fields through the massless Klein–Gordon and Maxwell equations, respectively. Using the Wentzel–Kramers–Brillouin approximation, we compute the quasinormal modes (QNMs) for scalar and electromagnetic field perturbations. The results confirm the stability of the BH under small perturbations and show that the QNM frequencies and damping rates are strongly influenced by the Frolov parameter, electric charge, GM and CS.
We show that in Schwarzschild equivalent mediums, the massless spin particles obey the same dynamical equation, from which we obtain remarkably simple formulae for the frequencies of the quasibound states. We find that the quasibound frequencies of different bosons can be identical at the same quantum number l, and the same is true of different fermions, but a quasibound frequency for bosons can never equal a quasibound frequency for fermions. These results mean that in Schwarzschild equivalent mediums with the quasibound-state boundary conditions, characteristics of electromagnetic waves are the same as those for all the massless bosonic waves, thereby allowing electromagnetic waves to simulate gravitational waves. Our predictions can be tested in future experiments, building upon the successful preparation of Schwarzschild equivalent mediums.
This study explores asymptotically flat wormhole solutions within the framework of f(R, T) gravity. We analyze f(R, T) expressed as f(R, T) = R + λT + λ1T2. A linear equation of state (EoS) is employed for both radial and lateral pressures, resulting in a power-law shape function. The investigation encompasses solutions characterized by both negative and positive energy densities. It has been determined that solutions with positive energy density comply with all energy conditions, specifically the null, weak, strong, and dominant energy conditions. Additionally, we identify constraints on the parameters λ, λ1, and the parameters associated with the EoS and shape function.
In this study, we explore a spherically symmetric charged black hole (BH) with a negative cosmological constant under the influence of a Kalb–Ramond field background. We compute the photon sphere and shadow radii, validating our findings using observational data from the Event Horizon Telescope, with a particular emphasis on the shadow images of Sagittarius A*. Furthermore, we investigate the greybody factors, emission rate, and partial absorption cross section. It is shown that the Lorentz-violating parameter $\bar{l}$ has an important effect on the absorption cross section. Our analysis also includes an examination of the topological charge, temperature-dependent topology, and generalized free energy. In particular, we regard the AdS charged BH with an antisymmetric tensor background as a topological defect in the thermodynamic space, then the system has the same topological classification to the charged Reissner–Nordström–AdS BH.
We perform the manifestly covariant quantization of f(R) gravity in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance. We explicitly calculate various equal-time commutation relations (ETCRs), in particular the ETCR between the metric and its time derivative, and show that it has a nonvanishing and nontrivial expression, whose situation should be contrasted to the previous result in higher-derivative or quadratic gravity where the ETCR was found to be identically vanishing. We also clarify global symmetries, the physical content of f(R) gravity, and clearly show that this theory is manifestly unitary and has a massive scalar and massless graviton as physical modes.
This study examines the effect of charge on physical features of a gravastar model in the framework of Rastall gravity. A gravastar is an alternative model to a black hole consisting of three separate regions: the inner sector, the intermediate shell and the outer sector. Different values of the barotropic equation of state (EoS) parameter provide the mathematical basis for these regions. Field equations (FEs) are initially developed for a spherically symmetric spacetime coupled with charged matter distribution. We then use the temporal component of Tolman IV spacetime to formulate the radial metric potential for both the inner region and intermediate shell. We also apply the matching criteria to ensure smooth matching of exterior and interior spacetimes so that the constants resulting from integrations can be determined. Afterwards, we explore various physical properties of the developed gravastar model such as the proper length, entropy, energy, and others to analyze how shell thickness and charge affect them. It is concluded that, in the background of Rastall theory, a gravastar model exists and serves as a viable alternative to the black hole.
Our analysis is particularly motivated by its relevance to understanding compact object instabilities, gravitational collapse thresholds, and the formation of dense structures under the influence of modified gravity theories. The interplay of anisotropic pressures, perturbative dynamics, and modified gravity contributions offers insight into both the stable configuration of dense fluids and the mechanisms leading to dynamical instability. Such considerations directly contribute to the aims of high energy density profiles, particularly in modeling physical systems where extreme pressure, curvature, and matter interactions co-exist. We consider an axially symmetric, dense structure with anisotropic matter content and employ a specific equation of state (EoS) to examine the interplay between static and dynamic quantities via the adiabatic index. To address the complex dynamics of the collapse process, a perturbative scheme is utilized under Newtonian and post-Newtonian approximations, enabling a detailed examination of the stability and structural evolution of the system under the influence of the considered minimally coupled gravity. Our results demonstrate that hydrostatic equilibrium is maintained when effective pressure, gravitational, and anti-gravitational forces are balanced, while deviations from this balance initiate dynamical instability. Graphical representations of stable and unstable regimes are presented, revealing how the choice of gravity functions significantly affects the outcome. This work provides insight into the behavior of dense, self-gravitating configurations under modified gravity, offering broader implications for the modeling of compact astrophysical objects and contributing to the understanding of gravitational collapse in energy density regimes.
We search for the stochastic gravitational-wave background (SGWB) predicted by pre-Big-Bang (PBB) cosmology using data from the first three observing runs of Advanced LIGO and Advanced Virgo. PBB cosmology proposes an alternative to cosmic inflation where the Universe evolves from a weak-coupling, low-curvature state to the hot Big Bang through a high-curvature bounce phase, predicting a distinctive SGWB spectrum. We perform a Bayesian analysis of the cross-correlation data to constrain the model parameters characterizing the PBB spectrum. We find no evidence for a PBB-induced SGWB, with a Bayes factor of 0.03 between the PBB and noise-only model, strongly favoring the noise-only hypothesis. Our analysis establishes a lower bound β ≳ −0.19 at 95% confidence level, which is compatible with the theoretical requirement β ≥ 0 for a smooth bounce transition. While we do not detect a signal, our constraints remain consistent with the basic theoretical framework of PBB cosmology, demonstrating the potential of gravitational-wave observations to test early Universe theories.
Optical nonreciprocal transmission with unidirectional amplification in a gain-assisted cavity-QED system is investigated. The results demonstrate that unidirectional amplification of this system is induced by the phase difference between the atom–cavity coupling strengths associated with the optical gain and a phase-controlled unidirectional amplifier can be achieved. The optimal parameter conditions for the observation of ideal unidirectional amplification are obtained analytically, and are shown to be dependent on phase, atom–cavity and cavity–cavity coupling strength, and atomic dissipation. In particular, it is found that atomic dissipation is another essential condition for the realization of nonreciprocal amplification other than breaking of the time-reversal symmetry, and our unidirectional amplifier is robust against atom–cavity coupling mismatch. Such unidirectional amplifiers are crucial nonreciprocal devices for controlling photon transmission and may have potential applications in quantum information processing.
Spin-density (charge) separation, marked by distinct propagation velocities of spin and density excitations, epitomizes strong correlations, historically confined to one-dimensional (1D) systems. The recent experimental work of Dhar et al (2025 Nature 642 53), using a weakly interacting 3D Bose–Einstein condensate of 133Cs atoms confined in a 2D optical lattice to realize spin-density separation and demonstrate boson anyonization, motivates a deeper exploration into how dimensionality and interactions govern quantum correlations. In this work, we investigate this in two-component bosonic mixtures with finite-range interactions, probing 1D and 3D dynamics. Using path integral effective field theory within the one-loop approximation, we derive analytical expressions for zero-temperature ground-state energy and quantum depletion, seamlessly recovering contact interaction results in the contact limit. By crafting an effective action for decoupled density and spin modes, we compute dynamic structure factors (DSFs), revealing how finite-range interactions sculpt spin-density separation. A pivotal finding is the dimensionality-driven divergence in DSF peak dynamics: in 1D, peaks ascend to higher frequencies with increasing interaction strength, yielding sharp responses; in 3D, peaks descend to lower frequencies, with broader density wave profiles. These insights highlight dimensionality’s critical role in collective excitations and provide a robust theoretical blueprint for probing interaction-driven quantum phenomena via Bragg spectroscopy, paving new pathways for the exploration of dimensionally tuned quantum correlations in ultracold quantum gases.
We introduce a minimal model consisting of a two-body system with stochastically broken reciprocity (i.e. random violation of Newton’s third law) and then investigate its statistical behaviors, including fluctuations of velocity and position, time evolution of probability distribution functions, energy gain, and entropy production. The effective temperature of this two-body system immersed in a thermal bath is also derived. Furthermore, we heuristically present an extremely minimal model where the relative motion adheres to the same rules as in classical mechanics, while the effect of stochastically broken reciprocity only manifests in the fluctuating motion of the center of mass.
We present a novel nonlinear state transition model for inositol 1,4,5-trisphosphate receptors (IP3Rs) that incorporates a pre-activated state, as suggested by electron microscopy observations. Our model provides a theoretical framework for the biphasic Ca2+ dependence of IP3Rs and accurately reproduces their experimentally observed state distribution under saturating IP3 conditions. By integrating receptor dynamics with cytoplasmic and endoplasmic reticulum (ER) calcium exchange, we simulate IP3R-mediated Ca2+ oscillations governed by six key conformational states. A pivotal finding is that IP3 regulates these oscillations in a switch-like manner: once a critical IP3 concentration is reached, the system abruptly transitions to sustained, constant-amplitude oscillations that quickly terminate when the concentration exceeds a secondary threshold. These results underscore the crucial role of the pre-activated state in modulating calcium signaling.
This study investigates the thermal and statistical properties of the Dirac oscillator within the framework of two prominent formulations of doubly special relativity (DSR): the Amelino-Camelia and Magueijo-Smolin models. DSR extends Einstein’s special relativity by introducing an additional invariant scale—the Planck energy—leading to modified energy-momentum relations that encode potential quantum-gravitational effects at ultra-high energies. In this context, we derive the modified Dirac equations for both DSR scenarios and analytically determine the corresponding energy spectra. These spectra are subsequently used to compute the partition function and key thermodynamic quantities, including specific heat, by employing the Euler–Maclaurin formula to facilitate an efficient approximation of the partition function. The analysis is restricted to the positive-energy sector, enabled by the exact Foldy–Wouthuysen transformation, which effectively decouples positive and negative energy states. The findings reveal that Planck-scale deformation parameters induce significant modifications in the energy spectrum and thermodynamic behavior of the Dirac oscillator in each DSR framework, thereby offering valuable insights into possible observable imprints of quantum gravitational phenomena in relativistic quantum systems.
The fractional quantum Hall effect remains a captivating area in condensed matter physics, characterized by strongly correlated topological order, which manifests as fractionalized excitations and anyonic statistics. Numerical simulations, such as exact diagonalization, density matrix renormalization groups, matrix product states, and Monte Carlo methods are essential for examining the properties of strongly correlated systems. Recently, density functional theory has been employed in this field within the framework of composite fermion theory. This paper systematically evaluates how density functional theory approaches have addressed fundamental challenges in fractional quantum Hall systems, including ground state and low-energy excitations. Special attention is given to the insights provided by density functional theory regarding composite fermion behavior, edge effects, and the nature of fractional charge and magnetoroton excitations. The discussion critically examines both the advantages and limitations of these approaches, while highlighting the productive interplay between numerical simulations and theoretical models. Future directions are explored, particularly the promising potential of time-dependent density functional theory for modeling non-equilibrium dynamics in quantum Hall systems.
