Search Results (154)

We investigated an exact solution in a conformal invariant Randall-Sundrum 5D warped brane world model on a time dependent Kerr-like spacetime. The singular points are determined by a quintic polynomial in the complex plane and fulfills Cauchy’s theorem on holomorphic functions. The solution, which is determined by a first-degree differential equation, shows many similarities with an instanton. In order to describe the quantum mechanical aspects of the black hole solution, we apply the antipodal boundary condition. The solution is invariant under time reversal and also valid in Riemannian space. Moreover, CPT invariance in maintained. The vacuum instanton solution follows from the 5D as well as the effective 4D brane equations, only when we allow the contribution of the projected 5D Weyl tensor on the brane (the KK-‘particles’). The topology of the effective 4D space of the brane is the projective $\mathbb{R}{P}^3$ (elliptic space) by identifying antipodal points on $S^3$. The 5D is completed by applying the Klein bottle embedding and the ${\mathbb{Z}}_2$ symmetry of the RS model. This model fits very well with the description of the Hawking radiation, which remains pure. We have also indicated a possible way to include fermions. Our 5D space admits a double cover of $S^3$ and after fibering to the $S^2$, we obtain the effective black hole horizon. The connection with the icosahedron discrete symmetry group is investigated. It seem that Bekenstein’s conjecture that the area of a black hole is quantized, could be applied to our model. Full article

This paper investigates the reverse space-time nonlocal nonlinear Schrödinger (NNLS) equation, which arises in nonlinear optics, Bose–Einstein condensation, integrable systems, and plasma physics. Several classes of exact solutions are constructed using multiple analytical techniques. First, traveling wave solutions of Jacobi elliptic, hyperbolic, and trigonometric function types are ultimately obtained by employing a traveling wave transformation combined with a Weierstrass-type Riccati equation expansion method. Second, Lie symmetry analysis is applied to the NNLS equation, and the corresponding infinitesimal generators are determined. Using these generators, the original equation is reduced to local and nonlocal ordinary differential equations (ODEs), whose invariant solutions are subsequently obtained through integration. Finally, the NNLS equation is generalized to a multi-component system, for which the general form of the infinitesimal symmetries is derived. Symmetry reductions of the extended system yield further classes of reduced ODEs. In particular, the general form of the multi-component solutions is derived. Full article

This paper introduces the UG-EM (Unconditional Gamma-Exponential Model) as a new compound lifetime model designed to enhance flexibility in tail behavior compared to traditional distributions. The UG-EM model provides a unified framework for analyzing deviations from symmetry in survival data, effectively capturing right-skewed patterns, which are commonly observed in real-world lifetime phenomena. The main analytical properties are derived, including the probability density, cumulative distribution, hazard and reversed-hazard functions, mean residual life, and several measures of dispersion and uncertainty. The effects of the UG-EM parameters (α and λ) are examined, showing that increasing either parameter can cause a temporary reduction in entropy H(T) at early times followed by a long-term increase; in some cases, the influence of α is stronger than that of λ. Parameter estimation is carried out using the maximum likelihood method and assessed through Monte Carlo simulations to evaluate estimator bias and variability, highlighting the significant role of sample size in estimation accuracy. The proposed model is applied to three survival datasets (Lung, Veteran, and Kidney) and compared with classical alternatives such as Exponential, Weibull, and Log-normal distributions using standard goodness-of-fit criteria. Results indicate that the UG-EM model offers superior flexibility and can capture patterns that simpler models fail to represent, although the empirical results do not demonstrate a clear, consistent superiority over standard competitors across all tested datasets. The paper also discusses identifiability issues, estimation challenges, and practical implications for reliability and medical survival analysis. Recommendations for further theoretical development and broader model comparison are provided. Full article

Homeostasis, which supports and maintains brain function, results from the continuous regulation of thermodynamics within tissue: the balance of heat production, redox oscillations, and vascular convection regulates coherent energy flow within the organ. Neuroinflammation disturbs this balance, creating measurable entropy gradients that precede structural damage to its tissue components. This paper proposes that a thermodynamic unity can be devised that incorporates nanoscale physics, energetic neurophysiology, and systems neuroscience, and can be used to understand and treat neuroinflammatory processes. Using multifactorial modalities such as quantum thermometry, nanoscale calorimetry, and redox oscillometry we define how local entropy production (s_t), relaxation time (τ^R), and coherence lengths (λc) allow quantification of the progressive loss of energetic symmetry within neural tissues. It is these variables that provide the basis for the etiology of thermodynamic biomarkers which on a molecular-redox-to-network scale characterize the transitions governing the onset of the neuroinflammatory process as well as the recovery potential of the organism. The entropic probing of systems (PEP) further allows the translation of these parameters into dynamic patient-specific trajectories that model the behavior of individuals by predicting recurrent bouts of instability through the application of machine learning algorithms to the vectors of entropy flux. The parallel development of the nanothermodynamic intervention, which includes thermoplasmonic heat rebalancing, catalytic redox nanoreacting systems, and adaptive field-oscillation synchronicity, shows by example how the corrections that can be applied to the entropy balance of the cell and system as a whole offer a feasible form of restoration of energy coherence. Such closed loop therapy would not function by the suppression of inflammatory signaling, but rather by the re-establishment of reversible energy relations between mitochondrial, glial, and vascular territories. The combination of these factors allows for correction of neuroinflammation, which can now be viewed from a fresh perspective as a dynamic phase disorder that is diagnosable, predictable, and curable through the physics of coherence rather than the molecular suppression of inflammatory signaling. The significance of this set of ideas is considerable as it introduces a feasible and verifiable structure to what must ultimately become the basis of a new branch of science: predictive energetic medicine. It is anticipated that entropy, as a measurable and modifiable variable in therapeutic “inscription”, will be found to be one of the most significant parameters determining the neurorestoration potential in future medical science. Full article

Motivated by the seminal discoveries in graphene, the exploration of novel physical phenomena in alternative two-dimensional (2D) materials has attracted tremendous attention. In this work, through theoretical investigation using first-principles calculations, we reveal that Mo-intercalated ${\mathrm{CrI}}_3$ bilayer exhibits ferromagnetic semiconductor behavior with a small easy-plane magnetocrystalline anisotropy energy (MAE) of 0.618 meV/Cr(Mo) between (100) and (001) magnetizations. The spin–orbit coupling (SOC) opens a narrow band gap at the Fermi level for both magnetization orientations with nonzero Chern number for realizing the quantum anomalous Hall effect (QAHE) in the former and with trivial topology in the latter. The small MAE implies the efficient experimental manipulation of magnetization between distinct topologies through an external magnetic field. Our findings provide compelling evidence that the QAHE in this system originates from the quantum spin Hall effect (QSHE), driven by intrinsic magnetism under broken time-reversal symmetry. These unique properties position Mo-intercalated ${\mathrm{CrI}}_3$ as a promising candidate for tunable spintronic applications. Full article

We theoretically investigate the supercurrent and superconducting diode effect (SDE) in an Aharonov–Bohm (AB) interferometer sandwiched between two aluminium-based superconducting leads. The interferometer features a quantum dot (QD), which is created in an indium arsenide (InAs) semiconductor nanowire by local electrostatic gating, inserted in one of its arms and a magnetic flux threading through the ring structure. The magnetic flux breaks the system time-reversal symmetry by modulating the quantum phase difference between electronic transport through the QD path and the direct arm, which enhances constructive interference in one direction and destructive interference in the other. This leads to a discrepancy between the magnitudes of the forward and reverse critical supercurrents and is the core mechanism that induces the SDE. We demonstrate that the critical supercurrents exhibit Fano line shapes arising from the interference between discrete Andreev bound states in the QD and continuous states in the direct arm. It is found that when electron transport is dominated by the QD-containing path as compared to the direct arm path of the interferometer, the diode efficiency reaches a maximum, with values as high as 80%. In contrast, when the direct arm path dominates transport, the diode efficiency becomes weak. This attenuation is attributed to the participation of higher-order quantum interference processes, which disrupt the nonreciprocal supercurrent balance. Importantly, the proposed AB interferometer system has a relatively simple structure, and the realization of the SDE within it is feasible using current nano-fabrication technologies. Full article

Exploiting inherent symmetries in data and models is crucial for accurate renewable energy forecasting. To address limited accuracy improvements under complex temporal dependencies, this study proposes a hybrid Bi-xLSTM-Informer model that incorporates temporal symmetry via bidirectional processing of time-flipped sequences. First, key features are screened using the Boruta algorithm, followed by PCA dimensionality reduction to construct an optimal feature subset with orthogonal transformation properties. Second, a Bi-xLSTM-Informer hybrid forecasting model is constructed. In the xLSTM model, the mLSTM is modified into a bidirectional network structure to capture short-term fluctuation patterns via forward and time-reversed propagation; Informer then analyzes global dependencies via ProbSparse attention. Validated on data from the photovoltaic (PV) Power Plant AI Competition, the experimental results demonstrate that the Bi-xLSTM-Informer model achieves the best prediction performance and the lowest error among all compared models, with an R² of 98.76% and an RMSE of 0.3776. This work proves that explicitly modeling temporal symmetry and feature orthogonality significantly enhances PV forecasting, providing an effective solution for renewable energy utilization. Full article

We develop a general framework for response theory in Markovian diffusion processes governed by Fokker–Planck equations. Our formalism, based on the notion of the dissipation function, is capable of handling dynamics that are driven by an external perturbation arbitrarily far from a given reference process. Using the analytically solvable Brownian oscillator model, we derive exact response formulae for both overdamped and underdamped dynamics of harmonically bound Brownian particles. We also demonstrate that for certain observables and under suitable time scaling, the operations of model reduction and response formula extraction commute, which highlights a relevant symmetry of the adopted mathematical formalism. Notably, the time reversal invariance symmetry, which is manifested as detailed balance in stochastic processes and is often required in statistical mechanics, is not necessary in our response framework. Full article

Recently, a new class of magnetic material, termed altermagnets, has caught the attention of the magnetism and spintronics community. The magnetic phenomenon arising from these materials differs from traditional ferromagnetism and antiferromagnetism. It generally lacks net magnetization and is characterized by unusual non-relativistic spin-splitting and broken time-reversal symmetry. This leads to novel transport properties, such as the anomalous Hall effect, the crystal Nernst effect, and spin-dependent phenomena. Spin-dependent phenomena such as spin currents, spin-splitter torques, and high-frequency dynamics emerge as key characteristics in altermagnets. This paper reviews the main aspects pertaining to altermagnets by providing an overview of theoretical investigations and experimental realizations. We discuss the most recent developments in altermagnetism and prospects for exploiting its unique properties in next-generation devices. Full article

Creep and stress sensitivity can lead to the long-term conductivity degradation of fractures, and this influences the accuracy of long-term productivity predictions in ultra-deep carbonate reservoirs (UDCRs). However, the current models do not consider these two factors. For the long-term conductivity degradation of acid-etched symmetry fractures in UDCRs, a new fracture permeability evolution model incorporating creep and stress sensitivity effects was established. Building upon this, a numerical simulation model for UDCRs was developed for the first time to quantitatively analyze the impacts of creep, stress sensitivity, and production strategies on well productivity. The research revealed that the creep and stress sensitivity characteristics of acid-etched fractures had a significant impact on the well productivity for UDCRs. The larger the creep coefficient and stress sensitivity coefficient, the lower the oil well productivity. The larger the initial reservoir pressure and drawdown pressure, the higher the daily production and cumulative production of the oil well, but the cumulative production growth rate decreased. The cumulative production in the early stage of the released-pressure production was significantly higher than that of the pressure-controlled production, but with the increase in the pressure-controlled time, the cumulative production reversed. When the pressure was controlled for three years, the cumulative production increased by 5952 m³ (38.8%); as the creep coefficient increased, the cumulative production increased by greater than the pressure-released production. This shows that the larger the creep coefficient, the better the effect of controlling pressure production. The research results can provide a theoretical basis and technical support for the efficient development of UDCRs. Full article

This study investigates the solution structure of the nonlinear Rayleigh oscillator equation through two widely used semi-analytical techniques: the Laplace–Adomian Decomposition Method (LADM) and the Homotopy Perturbation Method (HPM). The Rayleigh oscillator exhibits inherent asymmetry in its nonlinear damping term, which disrupts the time-reversal symmetry present in linear oscillatory systems. Applying the LADM and HPM, we derive approximate solutions for the Rayleigh oscillator. Due to the absence of exact analytical solutions in the literature, these approximations are benchmarked against high-precision numerical results obtained using Mathematica’s NDSolve function. We perform a detailed error analysis across different damping parameter values ε and time intervals. Our results reveal how the asymmetric damping influences the accuracy and convergence behavior of each method. This study highlights the role of nonlinear asymmetry in shaping the solution dynamics and provides insight into the suitability of the LADM and HPM under varying conditions. Full article

Longstanding anomalies in the Cosmic Microwave Background (CMB), including the low quadrupole moment and hemispherical power asymmetry, have recently been linked to an underlying parity asymmetry. We show here how this parity asymmetry naturally arises within a quantum framework that explicitly incorporates the construction of a geometric quantum vacuum based on parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) transformations. This framework restores unitarity in quantum field theory in curved spacetime (QFTCS). When applied to inflationary quantum fluctuations, this unitary QFTCS formalism predicts parity asymmetry as a natural consequence of cosmic expansion, which inherently breaks time-reversal symmetry. Observational data strongly favor this unitary QFTCS approach, with a Bayes factor, the ratio of marginal likelihoods associated with the model given the data $p\left(M|D\right)$, exceeding 650 times that of predictions from the standard inflationary framework. This Bayesian approach contrasts with the standard practice in the CMB community, which evaluates $p\left(D|M\right)$, the likelihood of the data under the model, which undermines the importance of low-ℓ physics. Our results, for the first time, provide compelling evidence for the quantum gravitational origins of CMB parity asymmetry on large scales. Full article

We investigate the bridge problem for stochastic processes, that is, we analyze the statistical properties of trajectories constrained to begin and terminate at a fixed position within a time interval $\tau$. Our primary focus is the time-reversal symmetry of these trajectories: under which conditions do the statistical properties remain invariant under the transformation $t\to \tau -t$? To address this question, we compare the stochastic differential equation describing the bridge, derived equivalently via Doob’s transform or stochastic optimal control, with the corresponding equation for the time-reversed bridge. We aim to provide a concise overview of these well-established derivation techniques and subsequently obtain a local condition for the time-reversal asymmetry that is specifically valid for the bridge. We are specifically interested in cases in which detailed balance is not satisfied and aim to eventually quantify the bridge asymmetry and understand how to use it to derive useful information about the underlying out-of-equilibrium dynamics. To this end, we derived a necessary condition for time-reversal symmetry, expressed in terms of the current velocity of the original stochastic process and a quantity linked to detailed balance. As expected, this formulation demonstrates that the bridge is symmetric when detailed balance holds, a sufficient condition that was already known. However, it also suggests that a bridge can exhibit symmetry even when the underlying process violates detailed balance. While we did not identify a specific instance of complete symmetry under broken detailed balance, we present an example of partial symmetry. In this case, some, but not all, components of the bridge display time-reversal symmetry. This example is drawn from a minimal non-equilibrium model, namely Brownian Gyrators, that are linear stochastic processes. We examined non-equilibrium systems driven by a "mechanical” force, specifically those in which the linear drift cannot be expressed as the gradient of a potential. While Gaussian processes like Brownian Gyrators offer valuable insights, it is known that they can be overly simplistic, even in their time-reversal properties. Therefore, we transformed the model into polar coordinates, obtaining a non-Gaussian process representing the squared modulus of the original process. Despite this increased complexity and the violation of detailed balance in the full process, we demonstrate through exact calculations that the bridge of the squared modulus in the isotropic case, constrained to start and end at the origin, exhibits perfect time-reversal symmetry. Full article

A magnetic toroidal monopole, which characterizes time-reversal-odd polar-charge quantity, manifests itself not only in antiferromagnetism but also in time-reversal switching physical responses. We theoretically investigate an atomic-scale description of the magnetic toroidal monopole based on multipole representation theory, which consists of four types of multipoles. We show that the magnetic toroidal monopole degree of freedom is activated as the off-diagonal imaginary hybridization between the single-site orbitals with the same orbital angular momentum but different principal quantum numbers. We demonstrate that the expectation value of the magnetic toroidal monopole becomes nonzero when both electric and magnetic fields are applied to the system. Full article

Magnetic toroidal multipoles have recently emerged as key descriptors of unconventional cross-correlation phenomena in antiferromagnetic systems. Among them, the rank-2 magnetic toroidal quadrupole, which is characterized as a time-reversal-odd polar tensor, has been theoretically associated with a variety of cross-correlation phenomena arising from the time-reversal symmetry breaking. In this study, we investigate the interplay between magnetic toroidal quadrupoles and electric toroidal dipoles in antiferromagnets, with a particular focus on magnetic field-induced ferroaxiality. Through symmetry analysis and microscopic model calculations, we demonstrate that ferroaxiality can be induced by an external magnetic field, depending on both the field direction and the type of the magnetic toroidal quadrupole. We classify all magnetic point groups that possess magnetic toroidal quadrupoles and identify various candidate materials based on the MAGNDATA database. Our findings reveal a route to coupling spin and lattice degrees of freedom via toroidal multipoles. Full article