For two bilinearly coupled harmonic oscillators, whose exact solution is known analytically, the linear transformation from physical to normal-mode coordinates is obtained explicitly. This transformation belongs to GL(2,ℝ) and admits a unique (Iwasawa) factorization into an orthogonal component describing symmetric mixing and an upper-triangular component encoding a hierarchical dependence of fast on slow coordinates. The Born–Oppenheimer approximation is identified with this triangular factor. In the adiabatic limit of small frequency ratio, the orthogonal contribution becomes negligible, and the exact transformation reduces to the Born–Oppenheimer map. This identification is supported by numerical comparisons of energies and wavefunctions across different coupling regimes.
The modified Chaplygin gas scenario is explored in the context of f(T,L_m) gravity by employing the linear functional expression f(T,L_m)=δ T+β L_m . From the conservation equation, we derive the corresponding form of the Hubble parameter and place constraints on the model parameters using the joint datasets of cosmic chronometers (CC), BAO observations and Type Ia supernova compilations (Pantheon+, DES-SN5Y and Union 3). The obtained value of the Hubble constant, H_0 ≈ 67-68,km s^-1 Mpc^-1 , is consistent with early-Universe determinations, while the MCG parameters satisfy all physical constraints and indicate a cosmology that nearly follows the Λ CDM scenario with slight departures. Model selection diagnostics show that, although the proposed f(T,L_m) model successfully reproduces the observed expansion history, the information criteria ( Δ AIC≈ 4 , Δ BIC≈ 15 ) favor the simpler Λ CDM model because of its lower parameter complexity. Nevertheless, the proposed framework remains observationally viable and provides a consistent description of the late-time accelerated expansion of the Universe. A change from a decelerating expansion to an accelerating phase occurs at z_tr∼ 0.57 -0.60 , as reflected by the deceleration parameter and supported by observations. The positivity of energy density together with negative pressure guarantees the occurrence of accelerated expansion. The EoS parameter begins in a matter-like state, later transitioning into a quintessence-dominated phase and asymptotically tending toward ω =-1 . The satisfaction of energy conditions and the corresponding statefinder results provide additional evidence for the model’s physical reliability and its tendency toward the Λ CDM limit. The model predicts a cosmic age of t_0 ∼ 13.3-13.5 Gyr, in agreement with observations, which confirms its robustness.
In the present analysis, we investigate the effect of self-gravitating parameters on the internal structure of a shock-front in a self-gravitating gaseous medium. Using continuum hydrodynamics model, the exact solution and analytical expression of the different flow variables are obtained, and thereafter, the width of the shock front is calculated. In addition, the variation in the thickness due to various parameters, namely the shock strength M, the density parameter w, and the gravitational parameter D, is analysed within the shock transition region. The asymptotic variations in the thickness of the shock-front due to these flow parameters have been discussed and analysed numerically and graphically. The findings confirm that the shock-front thickness is significantly affected not only by various physical parameters but also by the properties of the gaseous medium across the shock-front. The present outcomes show that gravitational parameters should be included for more reliable predictions about the nature of shock wave fronts in various geophysical and astrophysical atmospheres.
Recently, quantum-state texture has attracted increasing attention as a quantum resource with potential applications in quantum information processing. We derive tight lower and upper bounds relating the geometric texture of a superposition of n≥ 2 mutually orthogonal pure states to the textures of its constituent states and characterize the corresponding equality conditions. As an application, we determine the temperature-dependent attainable texture range of phase-generalized coherent Gibbs states in arbitrary dimensions. The coherent Gibbs state attains the lower bound at every positive temperature, whereas the upper bound is attained by appropriately choosing the relative phases of the energy-eigenbasis expansion coefficients of the phase-generalized coherent Gibbs state. For equally spaced energy levels, increasing the dimension lowers the scaled temperature at which the upper bound reaches unity, while the lower bound approaches its high-temperature limit of zero more slowly. These results provide a quantitative characterization of geometric texture under superposition and reveal how temperature, dimension and relative phases jointly determine the attainable texture range.
In this paper, we consider the vacuum free boundary problem of compressible Navier-Stokes-Korteweg equations with spherical symmetry. The capillary coefficient is assumed to be a positive constant and the bulk and shear viscosities are assumed to be power functions of density. By using some ansatzes, we construct a self-similar analytical solution to the problem when both the adiabatic exponent and the power of the functions of viscosities are equal to 3/2. Moreover, we show that the free boundary spreads outward at least sub-linearly in time with the rate of 𝒪((1+t)^2/3) and not more than linearly in time for the constructed solution, by using the averaged quantities method. Particularly, with the aid of some inequality techniques, we prove that the free boundary can spreads outward almost linearly in time provided that the capillary coefficient is sufficiently large. This may indicate that the capillary effect can stimulus the expansion of free boundary.
We investigate the entanglement of bipartite states arising from the Barut-Girardello coherent states of the 𝒜_κ Weyl-Heisenberg algebra. The geometric aspects of entanglement of our bipartite quantum system were investigated into account by calculating the Berry connection, the Berry phase and the Berry curvature in addition to determining the roots of the Majorana polynomial.
The scattering of a quantum particle by a two or three-dimensional Dirac delta potential leads to divergent integrals, rendering the cross section ill-defined and requiring an ad hoc regularization scheme. We demonstrate that this problem is naturally resolved by invoking a minimal length scale, as predicted by models of quantum gravity and encoded in a generalized uncertainty principle (GUP). This cutoff regularizes the theory and yields finite s-wave scattering amplitudes and cross sections without the introduction of any external regulator or additional parameters. Moreover, we derive an upper bound on the minimal length based on the resonance energy in proton–proton scattering.
The Schrödinger–Newton (SN) equation is the foundational model of semiclassical gravity. In this work, we develop a Gaussian variational reduction that makes the intrinsic scale-invariant structure of the SN equation analytically explicit, yielding a compact and accurate one-dimensional effective Hamiltonian. This framework maps the phase-space geometry of the SN dynamics and reveals that the dimensionally required m^11 stiffness scaling produces a strongly mass-dependent restoring force against wave-packet deformation. Applying this self-gravitational stiffness to levitated optomechanics, we identify a concrete and falsifiable laboratory signature: a mass-dependent, nonlinear upward shift in the mechanical frequency of a trapped nanoparticle.
In this manuscript, based on the Clarkson-Kruskal (CK) direct method, we study the well-known (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KPBBM) equation, which describes the propagation of small-amplitude long waves in a nonlinear dispersive medium. By employing a “decoupling approach”, we modified the common CK method. Together with proving the equivalence between two reduction forms, we greatly reduced computational complexity and successfully overcame the lengthy, intricate calculations inherent in the common CK method. Hence, we obtain new exact solutions and new similarity reductions of the KPBBM equation. Compared with the existing relevant work, the feature of this manuscript lies in that, firstly, we obtain a variety of new exact solutions for the KPBBM equation, including soliton–lump collision solutions, lump–lump collision solutions, mixed Airy-lump wave solutions, Airy function solutions, and Weber–Hermite function solutions, etc. To the best of our knowledge, these solutions have not been reported by other researchers. These new analytical solutions and reduced equations are great significance for the physical understanding of the KPBBM equation and the natural phenomena it describes; Secondly, in particular, for the KPBBM equation, two new types of solutions, i.e., the Airy function solutions and the Weber–Hermite function solutions, are reported here for the first time. They have important applications in ocean water dynamics and wave propagation with Gaussian decay in the distance region, respectively; Thirdly, we find the “independence condition” for the KPBBM equation. The independence condition enables us to observe, for the first time, that complex solutions can be approximately decomposed into two independently interacting waves. In nonlinear systems, the phenomenon of approximately independent collision of multiple waves resembling linear superposition effects is commonly seen among soliton solutions, such as in two-soliton solutions. Here, unlike common multi-soliton collisions, the nonlinear KPBBM system exhibits approximately independent collision phenomena among waves of different types, such as between a soliton and a lump. This condition thus provides a more comprehensive understanding of the nonlinear dynamics of complex solutions. In summary, our results provide a more thorough understanding of the integrable structure of the KPBBM nonlinear system and the dynamics of its collision wave propagation phenomena, which enhance understanding of shallow-water wave evolution and nonlinear wave interactions.
In this work, the magnetic properties and blocking temperature of an antiferromagnetic MnPS _3 monolayer are investigated using the mean field approximation combined with the Ising model. The influence of key system parameters, such as the exchange interactions (J _1 and J _2 ) and the external magnetic field h, on the magnetization, susceptibility, specific heat and internal energy are systematically analyzed and discussed. Notably, the study reveals that the blocking temperature decreases with increasing external magnetic field, while its behavior is also influenced by the exchange interactions.. In the second part, a specific set of exchange parameters yields a Néel temperature T _N =113.45 K which is consistent with values reported in previous studies for MnPS _3 .
We propose a probabilistic controlled quantum teleportation (CQT) protocol for an arbitrary single-qubit state using a non-symmetric B1.1-class four-qubit entangled channel. An auxiliary qubit and a non-unitary positive operator-valued measure (POVM) filter compensate the channel-induced coefficient distortion on accepted branches. The physical success probability is analytically P_succ=1/3 , whereas 12.5% is a per-attempt resource index and not a success probability. For a Haar-uniform input ensemble conditioned on Alice’s |Φ ^+⟩ outcome, the receiver’s optimal average fidelity without Charlie’s record is 8/9; thus, the controller’s record is necessary for deterministic, input-independent recovery of a generic unknown qubit, but no claim of absolute controller authority is made. We simulate the protocol with Qiskit Aer using six representative input states, including complex relative phases. For each noise setting, we report conditional fidelity, acceptance probability, and their product from 10,000 shots. The simulations provide a reproducible characterization of the trade-off between postselected fidelity and accepted-output rate under amplitude- and phase-damping noise.
Single-mode quartic fermionic Hamiltonians are often used as pedagogical examples, but their interaction terms are algebraically reducible through the identity n^2=n and therefore do not represent genuine many-body interactions. In this work, we identify a minimal genuinely interacting extension in the form of a two-mode fermionic dimer with intermode density coupling. Working in the grand-canonical ensemble, we derive the exact finite-temperature partition function, many-body spectrum, average filling, double occupancy, entropy, thermal response functions, and single-particle Green’s functions. The exact solution shows explicitly how the chemical potential controls the filling, while the interaction selectively modifies the doubly occupied sector and generates interaction-dependent spectral branches beyond a simple one-body level shift. We also construct the coherent-state Grassmann path-integral representation and formulate a two-channel Hubbard–Stratonovich decomposition based on charge and imbalance fields. This representation makes explicit the sign-dependent role of real and imaginary auxiliary-field couplings, with an imaginary coupling appearing in the charge channel for repulsive interaction. It also provides a channel-complete starting point for comparison with the exact grand-canonical solution. Although the Hubbard dimer has been studied extensively, the channel dependence of static auxiliary-field approximations and its quantitative finite-temperature consequences have not, to our knowledge, been presented in this compact grand-canonical form. A numerical comparison shows that the static two-field approximation captures the qualitative filling-controlled behavior and avoids the unphysical negative double occupancy produced by the scalar one-field approximation, although quantitative deviations remain because of the static restriction. The scalar density-channel static approximation considered here is therefore interpreted only as a diagnostic example, since it effectively assigns the wrong sign to the interaction contribution in the doubly occupied sector. The analysis establishes a sharp distinction between algebraically reducible quartic fermion terms and genuine density-density interactions, and provides a compact exact benchmark for analytical, numerical, and pedagogical studies of interacting fermionic systems.
We present a comprehensive theoretical study of thermal quantum correlations in a two-qubit Heisenberg XYZ spin-1/2 chain under the combined influence of an external magnetic field, Dzyaloshinskii-Moriya (DM) antisymmetric and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) symmetric spin-orbit interactions, and Zeeman splitting. We derive closed-form analytical expressions for two complementary discord-type quantifiers – the trace distance discord (TDD) and the local quantum uncertainty (LQU) – as functions of temperature, magnetic field, spin-orbit coupling parameters, and Zeeman energy. Our analysis reveals that the DM interaction provides robust thermal protection for quantum correlations, while the KSEA interaction produces asymmetric effects on the two correlation measures. The magnetic field and Zeeman interaction offer effective control knobs for modulating correlations, exhibiting non-monotonic behavior that arises from the competition between Zeeman polarization and exchange interactions. We extend our analysis to both ferromagnetic and antiferromagnetic exchange regimes, demonstrating that the qualitative behavior of quantum correlations is preserved across both phases. Finally, we connect our theoretical findings to realistic solid-state platforms, including semiconductor quantum dots and molecular magnets, providing experimental benchmarks for current quantum information technologies.
Quantum field theory allows local violations of the classical energy conditions, such as regions of negative energy density. The Ford–Roman quantum inequalities quantify how negative these regions can be and for how long. We present a derivation of these inequalities from the second law of thermodynamics, in an operational framework that couples the field to a small thermal detector. The detector acts as a physical probe of the field’s energy density and, by the non-negativity of the entanglement entropy between the two systems, one can show that its heat loss is bounded from below by a state-independent quantity.
Atomic localization with sub-wavelength precision has attracted considerable attention due to its applications in atom lithography, laser cooling, and quantum technologies. In this work, we theoretically investigate the role of spontaneously generated coherence (SGC) in controlling atomic localization using super-Gaussian laser beams. Localization can be effectively manipulated in both one- and two-dimensional configurations by varying the beam exponent. The presence of SGC significantly improves the probability of localization while reducing spatial uncertainty, with the localization increasing from approximately 20 % to nearly 100 % as the SGC parameter increases. The superposition of orthogonal standing-wave fields enables precise two-dimensional localization, while the coherent driving field reduces peak width without affecting amplitude. These results demonstrate that the combined effects of super-Gaussian beam shaping and SGC provide a tunable mechanism for achieving enhanced localization beyond conventional Gaussian-field limits. The proposed scheme offers promising applications in atom nano-lithography, laser cooling and trapping, and Bose-Einstein condensation.
We review two recent applications of operator-algebraic methods to the analysis of homogeneous Bose gases at finite temperature. The first part concerns the semiclassical description of Bose–Einstein condensation in the framework of Weyl C^* -algebras. In this setting, the semiclassical parameter is naturally linked to the density of the system, and the classical weak KMS condition emerges as the limit of quantum equilibrium states. We show in particular that the condensate structure is preserved in a suitable large-density regime. The second part discusses a joint work with Prof. Jan Dereziński which the Araki–Woods representation is used to formulate a systematic perturbative theory for interacting Bose gases at positive temperature. Within this representation, thermal effects are encoded directly in the field operators, allowing for a transparent implementation of Wick’s theorem and the computation of damping coefficients via the Fermi Golden Rule. The review synthesizes results obtained in two recent works presented at IQSA2025, emphasizing the conceptual role of algebraic methods in connecting semiclassical analysis, equilibrium states, and finite-temperature perturbation theory.
We present a comprehensive investigation of thermal quantum correlations in a two-qubit Heisenberg XXZ spin-1/2 chain subject to Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions oriented along the z-axis. The study focuses on the characterization of non-classical correlations at thermal equilibrium using two complementary discord-type quantifiers: trace distance discord (TDD) and local quantum uncertainty (LQU). We derive explicit analytical expressions for these quantifiers in the thermal state regime and systematically analyze their dependence on temperature, exchange coupling, spin-orbit interactions, and anisotropy parameters. A central contribution of this work is the identification and characterization of quantum phase transitions induced by the competition between different interaction terms. Our results demonstrate that both the antisymmetric DM and symmetric KSEA contributions from spin-orbit coupling significantly enhance thermal quantum correlations, while temperature acts as a decoherence mechanism that degrades these correlations. Furthermore, we establish clear connections between the critical behavior of quantum correlations and the underlying phase structure of the system. The interplay between different interaction parameters reveals fascinating quantum phase transitions characterized by non-analytic behaviors in the correlation measures. Our findings provide valuable insights into the manipulation and control of quantum correlations in spin-based quantum information processing architectures.
The present study investigates static anisotropic hybrid-star configurations containing hadronic matter and strange quark matter in the framework of f(ℚ,𝒯) gravity, where ℚ is the non-metricity scalar and 𝒯 denotes the trace of the energy-momentum tensor. The Finch-Skea spacetime geometry is adopted to construct exact solutions of the modified field equations. The physical viability of the resulting stellar model is examined through a detailed graphical analysis of the metric potentials, matter variables, radial and tangential pressures, anisotropic contribution, radial gradients, quark-sector density and pressure components, equation of state parameter, mass profile, and energy conditions. In addition, the stability of the configuration is tested by considering the compactness factor, gravitational redshift, sound-speed constraints, Herrera cracking condition, and adiabatic index. The analysis is carried out for the compact object EXO 1785-248, whose observed mass and radius are taken as 1.3^+0.2_-0.2M_⊙ and 8.849^+0.4_-0.4 km , respectively. The obtained results indicate that the considered f(ℚ,𝒯) model can provide a consistent theoretical setting for describing the internal structure and stability behavior of hybrid stars.
In this paper, we introduce and investigate a new class of strongly multiplicative convex functions ( ... s) within the framework of multiplicative calculus. By employing multiplicative k-Riemann-Liouville ( ℛ_ie - ℒ_io ) fractional integrals ( ℱ_r - ℐs ), we establish several new fractional Hermite-Hadamard ( ℋ_er - ℋ_ad ) type inequalities for ( ... s). The obtained results are further extended to product and quotients involving .. and strongly multiplicative concave functions. In addition, new Milne-type inequalities are derived in the setting of multiplicative fractional calculus. By suitable selections of the involved parameters, a variety of known inequalities from the literature can be derived as special cases of obtained results. The validity and effectiveness of the proposed inequalities are illustrated through suitable examples and graphical interpretations. Furthermore, applications to special means and related special functions are provided to demonstrate the applicability of the developed theory. The presented results generalize and unify a number of earlier contributions in fractional integral inequalities and provide new perspectives in the study of multiplicative fractional calculus and convex analysis.
We implement axio-dilaton fields from spin geometry and indicate potential links between these structures and conformal spacetimes. Our approach is based on the complex generalization Ωε _AB of the metric spinor ε _AB , which simultaneously converts Maxwell electrodynamics in vacuum into axio-dilaton electrodynamics with modular coupling τ̃=iΩ ^-2 and the spacetime metric into a conformally related metric rescaled by (Ω ^*Ω ) . By applying this complex rescaling to the Maxwell-Euler-Heisenberg theory, we demonstrate that this approach not only reproduces established axio-dilaton structures in the linear regime but also uncovers new mathematical structures within the nonlinear sector. Subsequently, by focusing on the duality group of τ̃ , a set of SL (2,ℤ) -dual metrics for the conformally equivalent spacetime is obtained through the Infeld-van der Waerden map. As a formal application of these dualities, we adapt our formulation to conformal cyclic cosmology and show how the pre- and post-conformal metrics can be mapped to each other via 𝒮 -duality.
