Search Results (182)

Landau–Zener–Stückelberg–Majorana (LZSM) interference describes the coherent superposition of nonadiabatic transitions when a quantum system is driven through an avoided crossing, but its classical optical analog remains largely unexplored. This work establishes an optical-resonator-based platform for exploring LZSM interference in atomic polarization dynamics using temporal coupled-mode theory. By exploiting the formal correspondence between the cavity mode and atomic polarization in a weakly driven two-level system (TLS), exact analytical solutions are derived for linear frequency sweeps and sinusoidal modulation. The results reveal that the Landau–Zener transition of atomic polarization occurs even when the input frequency transiently sweeps across resonance. The finite temporal memory inherent in the cavity response gives rise to Stückelberg interference, manifesting as oscillations in transmission and cavity energy. The dependence of the interference pattern on sweep rate, linewidth, and modulation is systematically analyzed, and a non-monotonic behavior of oscillation amplitude versus the cavity linewidth is identified. Furthermore, the conventional critical coupling concept is reexamined in the nonadiabatic regime, where counterintuitively the deepest transmission dip occurs under over-coupling rather than critical coupling. Finally, an inverse-design approach engineering both the amplitude and frequency of the input frequency is introduced to tailor the LZSM interference pattern. Our results provide a new platform to all-optical simulation of complex quantum interference. Full article

Quantum mechanics is among the most successful physical theories, yet its formulation and empirical testing rely on classical structures. Following Lev Landau and Niels Bohr, this reliance is not merely pragmatic: quantum observables acquire empirical meaning only relative to classical reference frames, and, in practice, quantization starts from classical models. At the same time, the two domains display forms of mutual irreducibility: intrinsically quantum features (that is, spin and exchange statistics) have no counterpart in the phase-space ontology of classical point-particle mechanics, while classical trajectory chaos does not arise straightforwardly from unitary quantum evolution in closed systems. A hierarchy is commonly established between classical and quantum theories, namely, a claim of ontological and explanatory priority according to which quantum mechanics is fundamental and classical mechanics is only a limiting case. This claim is less secure than is often assumed; therefore, the traditional hierarchy deserves to be examined. In this paper, we argue that a quantum–classical framework provides an effective and structurally faithful representation of empirically accessible physical systems in regimes where quantum and classical degrees of freedom coexist within a single, consistent effective dynamical description. To give this point of view a firm theoretical basis, we discuss the quasi-Lie formal structure underlying quantum–classical hybrid dynamics, with applications ranging from gravity and condensed matter to open, driven systems in biology and complex media. Full article

The $XY$ model is one of the basic models of statistical mechanics. It is often used for the description of important physical systems like ⁴He films and liquid crystals. In the present work, we consider the Ginzburg–Landau mean-field approximation of the 3D $XY$ model. We study the Lie-point symmetries of the corresponding Ginzburg–Landau Hamiltonian and the associated Euler–Lagrange equations for finite systems with film geometry and establish the variational symmetries among them in the presence of an external ordering field. Then, using the Noether theorem, we find conservation laws that allow us to obtain and present in analytic form, by means of Weierstrass elliptic, zeta, and sigma functions, the general solution of the so-called twisted boundary value problem in the absence of an external ordering field. It should be remarked that exact solutions in the absence of an external ordering field are only known within the so-called $\mathsf{\Psi }$-theory and some other mean-field-like theories. Full article

High-temperature superconductivity in strongly correlated materials is often accompanied by pseudogap behavior, strange-metal transport, strong phase fluctuations, and reduced superfluid stiffness, particularly in quasi-two-dimensional systems. These features suggest that pairing alone may not determine the onset of global superconductivity. We develop a coordination-based framework in which superconductivity is promoted by the collective organization of internal electronic degrees of freedom coupled to a carrier phase. A minimal lattice model is introduced, combining a U(1) phase sector, an internal coordination field, and an inter-sector coupling. A Landau analysis shows that internal coordination enhances the effective phase stiffness and can destabilize the incoherent state once the coordination amplitude becomes sufficiently large. Monte Carlo simulations of the model confirm that increasing coordination strength enhances phase stiffness and shifts the onset of global coherence to higher temperature. The framework provides a possible organizing interpretation of the separation between pseudogap onset and superconducting coherence, as well as the sensitivity of layered superconductors to reduced dimensionality, competing orders, and vortex-core structure. It is not intended to replace BCS theory, but to extend phase-stiffness-based descriptions to regimes where pairing, local coordination, and global phase coherence are distinct. Full article

Serpentine group minerals, including lizardite, antigorite, and chrysotile, are common gangue minerals in nickel sulfide ores, and exhibit complex and often unexpected wettability that adversely affects flotation efficiency. However, how these serpentine polymorphs differ in surface hydrophobicity is still not well known, making it difficult to explain their distinct flotation behaviors. In this work, molecular dynamics (MD) simulations and experimental contact angle measurements are used to investigate the wettability of the three main serpentine polymorphs. MD simulation results reveal that the contact angles of the lizardite Si–(00$\overline{1}$) surface and Mg–(001) are 78.6° and 71.1°, respectively. Chrysotile exposes the Mg–(001) surface, with a contact angle of 74.9°. The water droplet on the antigorite surface is spread along the SiOH region. Even the Mg–OH-terminated octahedral surfaces of the three serpentine polymorphs can exhibit hydrophobicity, depending on hydroxyl orientation and oxygen bonding configuration. Contact angle measurements show that antigorite (001) is moderately hydrophobic at about 40°, while (020) is highly hydrophilic at about 10°. The combination of Derjaguin–Landau–Verwey–Overbeek (DLVO) theory and hydrophobic interactions between antigorite and air bubbles produces a net attractive force, enabling particle–bubble adhesion. This work provides new insights for controlling serpentine behavior during flotation of copper–nickel ores hosted in ultramafic rocks. Full article

We develop a theoretical model for the flexoelectric instability in bent-core nematic liquid crystals, focusing on the coupling between elastic distortions and an external electric field through flexoelectric polarization. The analysis is carried out in the nematic phase close to the twist-bend transition, where both the flexoelectric coefficients and the effective bend elastic constant exhibit strong temperature dependence. Within a Landau–de Gennes framework, we derive analytical expressions for the threshold electric field and the corresponding wave vector of the emerging periodic modulation by minimizing the total free energy and assuming $K_1=K_2$. Numerical simulations illustrate the temperature dependence of the threshold parameters and the role of dielectric anisotropy and elastic constants. The results indicate that the flexoelectric instability may occur only within a finite temperature interval above the transition into the twist-bend phase and that both the threshold electric field and the periodic structure’s wave vector decrease as the temperature decreases. Full article

Alumina is a commonly used ceramic material known for high permittivity, low dielectric loss, good thermal conductivity, and low cost. In the development of electronic devices, the size effect of powdery materials is crucial, particularly in applications involving composite materials. This study introduces the field-enhancement method (FEM) to measure the resonant frequency ($f_0$) and the quality factor (Q) of alumina powders packed in a Teflon container and placed on top of the central rod in the proposed cavity. The measured resonant condition ($f_0$ and Q) is mapped to a contour plot and simulated using a high-frequency structure simulator (HFSS). The contour mapping technique allows the researchers to obtain the effective complex permittivity of alumina–air composites. The complex permittivity of the alumina powder is retrieved using a hybrid model and the effective medium theories (EMTs), respectively. The Landau–Lifshitz–Looyenga (LLL) model is compared with the results using the hybrid model for its applicability. The dielectric constant and the loss tangent of the alumina powder are found to increase as the powder size reduces. A power relation is found to fit the obtained permittivity, covering sizes ranging from nanometers to micrometers, and a surface-charge scaling argument is proposed to explain the observed trend. This finding opens a new avenue for manipulation of permittivity in composite materials and has potential applications in stealth/absorber technology and as a self-limiter for grain growth during sintering. Full article

Stringent cleanliness standards govern process fluid transport in integrated circuit (IC) manufacturing. Cavitation-induced surface defects on flow control components promote bacterial adhesion, thereby compromising wafer fabrication. To elucidate the coupling mechanisms among surface topography, hydrodynamics, and bacterial retention, this study utilizes a one-way coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) approach integrated with extended Derjaguin–Landau–Verwey–Overbeek (XDLVO) theory. We constructed a numerical model of rod-shaped Pseudomonas aeruginosa, integrated with a customized API-based coupling scheme to resolve temporal scale disparities, and systematically simulated flow evolution and adhesion behaviors across varying groove geometries (quadrilateral, triangular, and semicircular) and inlet velocities (1–3 m/s). The results indicate that groove-induced flow separation and recirculation vortices drive bacterial accumulation at the trailing edge. Triangular profiles exhibited superior flow stability, yielding significantly lower adhesion than quadrilateral and semicircular shapes. Bacterial retention scaled inversely with flow velocity due to enhanced hydrodynamic shear. These findings provide theoretical and engineering insights for the anti-contamination design of ultra-clean flow control components in IC manufacturing. Full article

We detail a procedure to transform the current empirical stage in the study of complex systems into a predictive phenomenological one. Our approach starts with the statistical-mechanical Landau-Ginzburg equation for dissipative processes, such as kinetics of phase change. Then, it imposes discrete time evolution to explicit back feeding, and adopts a power-law driving force to incorporate the onset of chaos, or, alternatively, criticality, the guiding principles of complexity. One obtains, in closed analytical form, a nonlinear renormalization-group (RG) fixed-point map descriptive of any of the three known (one-dimensional) transitions to or out of chaos. Furthermore, its Lyapunov function is shown to be the thermodynamic potential in q-statistics, because the regular or multifractal attractors at the transitions to chaos impose a severe impediment to access the system’s built-in configurations, leaving only a subset of vanishing measure available. To test the pertinence of our approach, we refer to the following complex systems issues: (i) Basic questions, such as demonstration of paradigms equivalence, illustration of self-organization, thermodynamic viewpoint of diversity, biological or other. (ii) Derivation of empirical laws, e.g., ranked data distributions (Zipf law), biological regularities (Kleiber law), river and cosmological structures (Hack law). (iii) Complex systems methods, for example, evolutionary game theory, self-similar networks, central-limit theorem questions. (iv) Condensed-matter physics complex problems (and their analogs in other disciplines), like, critical fluctuations (catastrophes), glass formation (traffic jams), localization transition (foraging, collective motion). Full article

Hydrophilic modification of polymeric membranes by employing TiO₂ nanoparticles has attracted much attention in enhancing antifouling performance. Micelles of PVPylated-TiO₂ nanoparticles were designed to alleviate the agglomeration of TiO₂ nanoparticles via steric hindrance and electrostatic stabilization effect. Herein, Poly(vinyl pyrrolidone) (PVP) was used as a surfactant to mitigate the thorny agglomeration of nanoparticles in the casting solution and simultaneously as a pore-forming additive during the membrane preparation process. The lowest backscattering (BS) peak and turbiscan stability index (TSI) of the composite casting solution indicated the effective dispersion and stabilization under the steric interaction of 4 wt.% PVP. Properties such as the fully developed finger-like structure of cross-sectional morphologies, water permeability, negative Zeta potential, and hydrophilicity were enhanced evidently by the optimal modification of PVPylated-TiO₂ materials. High interaction energy indicated by classic extended Derjaguin–Landau–Verwey–Overbeek (XDLVO) theory as well as the high relative flux during the filtration of various model foulants demonstrated the effective antifouling modification. The results of critical flux and fouling rate in 30 min also verified the enhancement of the antifouling performance of PVDF/PVPylated-TiO₂ composite membrane. This work provides a feasible strategy to construct composite membranes with high antifouling performance for wastewater treatment. Full article

Lithium batteries have emerged as the mainstream technology in the current energy storage field due to their advantages, such as high energy density and long cycle life. However, from a multi-physics coupling perspective, research remains relatively scarce regarding the analysis of dendrite nucleation and growth, as well as their influence on lithium dendrite growth. Based on the phase field theory, this study develops a mechanical-thermal-electrochemical coupling model to systematically investigate the evolution mechanisms and suppression strategies of lithium dendrites induced by relevant physical quantities through the coupled effects of mechanical, thermal, and electrochemical fields. The dynamic behavior of the solid-solid interface is characterized by introducing order parameters. The governing nonlinear partial differential equations are formulated by combining the Cahn-Hilliard and Ginzburg-Landau equations. The present numerical results and the previous results are compared to validate the present model in properly predicting lithium dendrite growth. Numerical simulations are performed to analyze the influence of various physical parameters, such as electric potential, anisotropic intensity and anisotropic modulus, on the morphological evolution of lithium dendrites. These findings provide critical insights for advancing strategies to suppress lithium dendrite growth and enhance battery performance in solid-state lithium batteries under multi-field coupling conditions. Full article

Formal verification has achieved remarkable outcomes in both theory advancement and engineering practice, with the formalization of mathematical theories serving as its foundational cornerstone—making this process particularly critical. Axiomatic set theory underpins modern mathematics, providing the rigorous basis for constructing almost all theories. Landau’s Foundations of Analysis starts with pure logical axioms from set theory, does not rely on geometric intuition, strictly constructs number systems, and is a benchmark for axiomatic analysis in modern mathematics. In this paper, we first develop a machine proof system for axiomatic set theory rooted in the Morse–Kelley(MK) system. This system encompasses effective proof automation, scale simplification, and specialized handling of the classification axiom for ordered pairs. We then prove the Transfinite Recursion Theorem, leveraging it to further prove the Recursion Theorem for natural numbers—the key result for defining natural number operations. Finally, we detail the implementation of a machine proof system for analysis, which adopts MK as its description language and adheres to Landau’s Foundations of Analysis. This formalization realized all the contents of the book from natural numbers to complex numbers. All formalization does not need to introduce the standard library and has undergone verification by Rocq(Coq) 8.16 to ensure reliability. Implemented using the Rocq proof assistant, the formalization has undergone verification to ensure reliability. This work holds broader applicability such as the formalization of point-set topology and abstract algebra, while also serving as a valuable resource for teaching axiomatic set theory and mathematical analysis. Full article

This study systematically investigated the electrorheological (ER) behavior of four aqueous smectite clay dispersions—fluorinated hectorite (Ht-F), stevensite (Stv), hectorite (Ht), and saponite (Sap)—with emphasis on transparency, rheological responses, and interparticle interactions. Optical observations revealed that the transparency of the aqueous dispersions followed the order Ht-F > Stv > Ht > Sap, which corresponded well to the finer network structures previously observed in Cryo-SEM images. Whereas micrometer-sized poly(methyl methacrylate) (PMMA) dispersions exhibited electrically induced rapid and reversible separation (ERS) due to sedimentation, the nanosized clays, which do not settle, developed ER effects through field-driven flocculation and subsequent network formation. Under low-frequency AC fields, Ht-F showed highly reversible responses similar to Stv, whereas Sap exhibited irreversible stress increases, accompanied by suspected ion release under the field. Dynamic rheological measurements showed that application of electric fields enhanced the loss modulus (G″) more prominently than the storage modulus (G′), clearly indicating a strengthening of viscous behavior. Derjaguin–Landau–Verwey–Overbeek theory (DLVO) potential analysis yielded a barrier-height sequence (Stv < Ht-F < Ht < Sap) that directly paralleled the order of ER responsiveness. These results demonstrate that the ER hierarchy of aqueous smectites can be rationalized by DLVO interactions and provide design guidelines for environmentally compatible ER fluids. Full article

We investigate the influence of Landau Levels (LLs) and Zeeman energy, induced by an applied magnetic field $\mathbf{B}$, on the critical temperature $T_c$ for two-dimensional (2D) ultraclean superconductors using a fully quantum mechanical approach within the Bardeen–Cooper–Schrieffer (BCS) theory. In contrast to standard BCS theory, it allows for Cooper pair formation between electrons with opposite spins and momenta along the $\mathbf{B}$ direction, both on the same or on neighboring LLs. Our quantum mechanical treatment of LLs reveals that the critical temperature $T_c$ for electrons paired on the same LL exhibits oscillations around the BCS critical temperature at low magnetic fields. The Zeeman energy leads to a decrease in $T_c(\mathbf{B})$ with increasing $\mathbf{B}$ for electrons paired both on the same and on neighboring LLs. Notably, as the g-factor increases, $T_c(\mathbf{B})$ decreases faster as the magnetic field increases for a larger g-factor than for a smaller one. Full article

We briefly review the early development of the mean-field dynamics for cooperatively interacting quantum many-body systems, mapped to pseudo-spin (Ising-like) systems. We start with (Anderson, 1958) pseudo-spin mapping the BCS (1957) Hamiltonian of superconductivity, reducing it to a mean-field Hamiltonian of the XY (or effectively Ising) model in a transverse field. Then, we obtain the mean-field estimate for the equilibrium gap in the ground-state energy at different temperatures (gap disappearing at the transition temperature), which fits Landau’s (1949) phenomenological theory of superfluidity. We then present in detail a general dynamical extension (for non-equilibrium cases) of the mean-field theory of quantum Ising systems (in a transverse field), following de Gennes’ (1963) decomposition of the mean field into the orthogonal classical cooperative (longitudinal) component and the quantum (transverse) component, with each of the component following Suzuki–Kubo (1968) mean-field dynamics. Next, we discuss its applications to quantum hysteresis in Ising magnets (in the presence of an oscillating transverse field), to quantum heat engines (employing the transverse Ising model as a working fluid), and to the quantum annealing of the Sherrington–Kirkpatrick (1975) spin glass by tuning down (to zero) the transverse field, which provides us with a very fast computational algorithm, leading to ground-state energy values converging to the best-known analytic estimate for the model. Finally, we summarize the main results obtained and draw conclusions about the effectiveness of the de Gennes–Suzuki–Kubo mean-field equations for the study of various dynamical aspects of quantum condensed matter systems. Full article