We investigate the long-time behavior of exact solutions and numerical approximations of linear stochastic evolution equations defined on the sphere. We focus on three classical models arising in mathematical physics: the stochastic wave equation, the stochastic Schrödinger equation, and the stochastic Maxwell's equations. For these SPDEs, we analyze several widely used time integrators with respect to trace formulas describing the evolution of physically relevant quantities such as energy, mass, and momentum dependent on the forcing term. In particular, we prove that the forward and backward Euler-Maruyama schemes fail to reproduce the correct long-time behavior of the exact solutions. In addition, we prove that the stochastic exponential integrator preserves the correct long-time behavior of the physical quantities of interest. Finally, several numerical experiments are provided to illustrate our theoretical findings.

Quantum circuit complexity quantifies the minimal number of gates needed to realize a unitary transformation and plays a central role in quantum computation. In this work, we investigate the complexity of quantum circuits through coherence and imaginarity resources. We establish a lower bound on the circuit cost by the Tsallis relative $α$ entropy of cohering power, which is shown to be tighter than the one presented by Bu et al.[\textit{Communications in Mathematical Physics} 405, no. 7 (2024):161] under restrictive conditions. As a consequence, we obtain the relationships between the circuit cost and the coherence generating power via probabilistic average in terms of skew information/relative entropy, and present explicit bounds of the circuit cost for typical quantum gates. Moreover, we derive lower bounds on the circuit cost via the imaginaring power of the circuit, induced by the Tsallis relative $α$ entropy and relative entropy. We demonstrate that imaginarity can yield nontrivial constraints on the circuit cost even when coherence-based lower bounds are zero (e.g., for the $T$ gate), which implies that imaginarity may provide advantages under certain circumstances compared with coherence. Our results may help better understand the connections between quantum resources and circuit complexity.

Water confined in low-dimensional materials exhibits structural and dynamical behaviors that diverge fundamentally from bulk liquid water. Nanoscale confinement reshapes the hydrogen-bond network, induces molecular ordering, and alters dielectric, vibrational, and transport properties through the interplay between geometry, surface chemistry, and electrostatics. This review presents a comparative synthesis of confined water in 0D–2D environments, from single-molecule encapsulation in molecular cages and single-file flow in carbon nanotubes to layered phases trapped between atomically flat van der Waals crystals. We outline how dimensionality and surface polarity dictate hydrogen-bond rearrangement, layering, and crystallization into low-dimensional ice polymorphs. Spectroscopically, Raman, infrared, terahertz, and nonlinear optical probes reveal distinct vibrational fingerprints reflecting modified hydrogen-bond strength, dipole alignment, and collective dynamics. In the transport regime, continuum hydrodynamics breaks down, giving rise to superlubric flow, anisotropic diffusion, and quantized single-file motion. Across these systems, confinement transforms water from a fluctuating three-dimensional liquid into a tunable, ordered medium bridging molecular and solid-state physics. By unifying results across structural, spectroscopic, and transport studies, this review provides a coherent physical framework for understanding confined water in low-dimensional materials and highlights its implications for nanofluidics, energy storage, and bio-inspired systems.

Understanding how vibrational energy is generated, redistributed, and dissipated at the nanoscale is central to contemporary molecular and chemical physics. Plasmonic nanostructures offer highly efficient channels for both driving and probing molecular vibrations, enabling access to regimes where steady-state populations markedly depart from thermal equilibrium. This perspective examines how anti-Stokes surface-enhanced Raman scattering (SERS) has become a quantitative tool for resolving such thermal and non-thermal vibrational populations within nanoscale hotspots. We first outline the general framework linking Stokes and anti-Stokes Raman/SERS intensities to vibrational occupation, followed by experimental approaches that realize and probe thermal excitation (nanoscale thermometry) and non-thermal excitation pathways. We conclude by highlighting key methodological challenges-especially plasmonic bias correction and quantitative population analysis-and discuss future opportunities for employing anti-Stokes SERS as a molecular-level probe of energy flow in next-generation nanophotonic and catalytic systems.

We propose a comprehensive rotation-minimizing (RM) Darboux framework for the study of curve theory and relativistic ruled surfaces in Minkowski three-space E13. The construction merges the adaptability of the classical Darboux frame to surface geometry with the reduced rotational behavior characteristic of RM frames, yielding a natural geometric description of curves in a Lorentzian environment. For unit speed non-null curves, the governing equations of the RM Darboux frame are derived, and precise connections between the RM curvature functions and the classical Frenet and Darboux invariants are obtained, thereby elucidating the geometric significance of RM curvatures in Lorentzian geometry. Within this setting, multiple classes of ruled surfaces are generated using RM Darboux frame vector fields. Necessary and sufficient conditions for developability, minimality, and flatness are formulated exclusively in terms of RM curvature quantities. The role of the causal character of the generating curve is analyzed in detail, revealing distinct geometric behaviors for space-like and time-like cases. These findings indicate that the RM Darboux framework constitutes a flexible and effective approach for modeling curve-induced surface geometries in Minkowski space, with potential relevance to relativistic kinematics, world sheet constructions, and geometric problems arising in mathematical physics.

Yield-stress fluid flow through porous media is governed by a strong coupling between rheology and pore-scale geometry, leading to nonlinear, non-Darcy transport and pronounced channelisation near yielding. We develop a pore-network model for Herschel-Bulkley flow in two-dimensional disordered porous media, including optional wall slip. The network is closed by a physics-based pressure-flow relation for a converging-diverging throat, so that yielding and post-yield transport emerge directly from the pore-scale fluid mechanics without fitted resistance parameters. Benchmarking against direct numerical simulations shows that the model captures both the bulk pressure drop and the evolution of the flow topology from spatially distributed transport to strongly channelised flow. The framework also captures the leading effect of wall slip, which lowers the pressure gradient required for transport and reactivates pathways that remain blocked in the no-slip case. Using the model across different porous geometries, we show that near-yield pressure losses are governed by constriction statistics rather than by an obstacle-scale length. In particular, rescaling with the domain-averaged minimum throat width collapses the plastic-dominated response across porosities, identifying the dissipation-relevant geometric scale for viscoplastic transport in this regime.

Recent molecular-level simulations suggest that slip at solid–liquid interfaces can depend on shear. This work integrates molecular dynamics (MD) and direct numerical simulations (DNS) to quantify how shear-dependent slip modifies near-wall turbulence in wall-bounded flows. The MD is used to characterise how the slip length depends on wall shear stress across a range of solid–liquid affinities, revealing a threshold-like, bimodal response: the slip length is approximately constant at low and high stresses, with a sharp transition near a slip-activation threshold. This MD-derived relation is then implemented as a wall boundary condition in DNS of turbulent channel flow at friction Reynolds numbers 180, 400 and 1000, using five threshold values to represent different interfacial affinities. The DNS show that the logarithmic region is largely preserved, aside from an approximately constant upward shift, while the near-wall turbulence is modified through changes in the streamwise Reynolds stress. In particular, the streamwise turbulence intensity in the viscous sublayer is strongest when the mean wall stress is close to the slip-activation threshold, and it weakens as the mean stress moves away from that threshold. Analysis further indicates that shear-dependent slip reduces near-wall dissipation and promotes elongated near-wall coherent structures. Finally, a mean flow model that incorporates shear-dependent slip shows good agreement with the DNS mean velocity profiles. Overall, this work provides a multiscale framework that links molecular interfacial physics to continuum-scale turbulence.

In this work, we investigate the dynamics of an inhomogeneous coupled nonlinear Schrodinger system with quadratic-type interactions. Such systems arise naturally in nonlinear dynamics and mathematical physics, particularly in nonlinear optics, plasma physics, and wave propagation in inhomogeneous dispersive media. We establish a sharp criterion characterizing the dichotomy between global existence and finite-time blow-up of solutions to the associated initial value problem. This criterion is formulated in terms of conserved quantities, namely mass and energy, measured relative to the ground state solutions of the corresponding elliptic system. The analysis combines variational methods, conservation laws, and sharp Gagliardo-Nirenberg-type inequalities to obtain local and global well-posedness results in both subcritical and intercritical regimes. Our results extend and unify previous studies on single and multi-component nonlinear Schrodinger equations, providing a general analytical framework applicable to a broad class of coupled systems with spatially inhomogeneous nonlinearities and quadratic growth.

Interstellar polycyclic aromatic hydrocarbon (PAHs) are an important component of the interstellar medium of galaxies, containing some 10 percent of the elemental carbon. Their vibrational emission dominates the mid-infrared spectra of galactic and extragalactic objects. PAHs control the heating of interstellar neutral gas and the charge balance of molecular clouds. PAHs are formed in the outflows from late type stars through chemical processes akin to those in sooting flames and then further processed in the interstellar medium by UV photolysis and strong shock waves. PAHs are also formed through ion molecule reactions and neutral radical reactions in dense cloud cores. The James Webb Space Telescope has provided a wealth of high-quality spectra that have provided new insights in the characteristics of the interstellar PAH family. Their analysis is supported by dedicated laboratory and quantum chemistry studies, feeding into detailed molecular physics models relevant to astronomical environments. Laboratory studies have also provided deeper insight in the chemical evolution of PAHs in the interstellar medium. This paper will review progress in the field and chart its future.

A PLASEN (Precision LAser Spectroscopy for Exotic Nuclei) system, consisting of a compact radio-frequency quadrupole cooler-buncher (RFQ-cb) and a collinear resonance ionization spectroscopy setup, has now been fully commissioned with radioactive ion beams at the Beijing Radioactive Ion-beam Facility (BRIF). Using both stable and radioactive Rb ion beams from BRIF, we demonstrated that the large beam energy spread observed at BRIF has been successfully handled by employing the RFQ-cb, enabling the delivery of high-quality bunched radioactive ion beams for collinear resonance ionization spectroscopy experiments. Under these conditions, we performed laser spectroscopy of exotic nuclei, achieving high resolution (about 100 MHz spectral linewidth) and high sensitivity (up to 1:200 efficiency). This fully operational PLASEN system will serve as a state-of-the-art experimental platform at BRIF for research in multiple fields such as nuclear, atomic and molecular physics.