We present a geometric approach to characterize quantum coherence through entropic diagrams that map the eigenvalue spectra of density matrices into a two-dimensional space defined by von Neumann and Tsallis-2 entropies. We derive the relative entropy of coherence using the Schur-Horn majorization theorem and introduce a new coherence monotone—the relative cross-entropy of coherence—which is valid only for mixed states and whose behavior under various classes of quantum operations is examined in detail. Interestingly, our approach reveals distinct entropy-coherence distillation curves and introduces the notion of degenerate coherence distillation, where coherence is concentrated into higher-dimensional, partially uniform spectral configurations. Although the degenerate coherence distillation does not always surpass standard qubit coherence distillation in asymptotic rate, it may offer an operationally meaningful alternative for protocols that require high-dimensional or symmetrically structured coherence resources. In addition, we derive a refined entropic uncertainty relation that incorporates the maximum eigenvalue of post-measurement states, which leads to state-dependent bounds that improve upon the conventional Maassen-Uffink bound. These findings suggest that entropic diagrams may serve not only as a useful visual and analytical tool but also as a guide for developing resource-efficient strategies in quantum information processing.

The well-known and celebrated first-primer classical analysis of a one-dimensional inversion-asymmetric assembly of electric point charges interconnected by mechanical springs shows that the system is piezoelectric and characterized by a parameter-dependent but constant piezoelectric coefficient $d$ defined as the ratio between the change in system length and the change in electric field. The former system is the simplest system displaying the phenomenon of piezoelectricity. We demonstrate that a quantum-mechanical analysis of the Hamiltonian for the same system of electric point charges and mechanical springs leads to a piezoelectric constant that depends not only on the system parameters but also on the eigenstate. Hence, the piezoelectric constant, determined as the ratio between the change in the expectation value of the system length and the change in the applied electric field, is quantized. It is demonstrated analytically and numerically, which is a necessary condition, that the quantized piezoelectric constant vanishes if the system Hamiltonian is inversion symmetric.

Van der Waals (vdW) layered magnetic materials have attracted much attention from the physics and materials science communities. Here we successfully obtained a monoclinic vdW ferromagnet $\mathrm{NbFeT}{\mathrm{e}}_2$ by high-temperature growth, and systematically characterized its magnetic, electrical, and magnetotransport properties. When temperature $T<53$ K (Curie temperature), $\mathrm{NbFeT}{\mathrm{e}}_2$ exhibits metamagnetism: the ferromagnetism under high magnetic fields ($H>0.7$ T) and spin-glass-like behavior at low magnetic fields ($H<0.7$ T), respectively. Analysis of temperature-dependent resistivity reveals the influence of Mott variable range hopping and magnon scattering below the Curie temperature. Based on the first-principles electronic band structure, the Mott variable range hopping is related to the pseudogaplike density of states and ferrimagnetism in $\mathrm{NbFeT}{\mathrm{e}}_2$. Notably, there are also both anomalous Hall effect and topological Hall effect observed in $\mathrm{NbFeT}{\mathrm{e}}_2$ below the Curie temperature, which correlates to the ferromagnetism and chiral-spin-glass behavior, respectively. In particular, the topological Hall effect is attributed to the finite scalar spin chirality of slightly canted Fe spin clusters in $\mathrm{NbFeT}{\mathrm{e}}_2$ with Nb deficiency. This work demonstrates that the magnetic and magnetotransport properties of $\mathrm{NbFeT}{\mathrm{e}}_2$ crystals are strongly dependent on the stoichiometry, delicate competition between exchange interactions, and spin-orbit coupling in quasi-two-dimensional crystal structure.

We theoretically discover possible dc-current induction and high-harmonic generation from photodriven chiral fermions in B20-type semimetals irradiated with circularly polarized light as nonlinear optical responses with several unconventional properties. First, we find multiple sign changes of the induced bulk dc photocurrent as a function of light parameters, which is ascribed to the nature of asymmetric photon-dressed bands in chiral systems. Moreover, we observe a parity-dependent directivity of high-harmonic generation where the odd- and even-order harmonics have intensities only in directions perpendicular and parallel to the polarization plane, respectively, which can be understood from dynamical symmetry of the present photodriven chiral systems.

A neural network-based machine learning potential energy surface (PES) expressed in a matrix product operator (NN-MPO) is proposed. The MPO form enables efficient evaluation of high-dimensional integrals that arise in solving the time-dependent and time-independent Schrödinger equation, and effectively overcomes the so-called curse of dimensionality. This starkly contrasts with other neural network-based machine learning PES methods, such as multilayer perceptrons (MLPs), where evaluating high-dimensional integrals is not straightforward due to the fully connected topology in their backbone architecture. Nevertheless, the NN-MPO retains the high representational capacity of neural networks. NN-MPO can achieve spectroscopic accuracy with a test mean absolute error (MAE) of 3.03 ${\mathrm{cm}}^{-1}$ for a fully coupled six-dimensional ab initio PES, using only 625 training points distributed across a 0 to 17 000 ${\mathrm{cm}}^{-1}$ energy range.

We study the non-Fermi-liquid state formed by an isotropic, degenerate Fermi gas in two spatial dimensions interacting with a U(1) gauge field. Our calculation uses the functional renormalization group (fRG) with a soft frequency cutoff for the fermions. The fRG scheme we employ takes account of the gauge symmetry, which imposes relations (modified Ward-Takahashi identities) between the couplings which constrain the RG flow. The critical exponents and couplings we find for the resulting non-Fermi liquid are mostly insensitive to whether we enforce the gauge symmetry constraints, which signifies either that the constraints are superfluous or that the frequency-cutoff scheme is particularly robust. The exception is the gauge-boson mass term, which is RG-relevant about the fixed point without the constraints but is irrelevant when they are enforced. The latter is physically accurate, as a gauge symmetry cannot be spontaneously broken. In addition, we find $z=2$ and $\mathrm{\Sigma }(\omega ,k_F)\sim {\omega }^{1/2}$ for the boson dynamical exponent and scaling of the fermion self-energy, respectively. These results differ considerably from those of past works on the model, though we argue for their plausibility.

Interactions of molecules with their environment influence the course and outcome of almost all chemical reactions. However, classical computers struggle to accurately simulate complicated molecule-environment interactions because of the steep growth of computational resources with both molecule size and environment complexity. Therefore, many quantum-chemical simulations are restricted to isolated molecules, whose dynamics can dramatically differ from what happens in an environment. Here, we show that analog quantum simulators can simulate open molecular systems by using the native dissipation of the simulator and injecting additional controllable dissipation. By exploiting the native dissipation to simulate the molecular dissipation—rather than seeing it as a limitation—our approach enables longer simulations of open systems than are possible for closed systems. In particular, we show that trapped-ion simulators using a mixed qudit-boson (MQB) encoding could simulate molecules in a wide range of condensed phases by implementing widely used dissipative processes within the Lindblad formalism, including pure dephasing and both electronic and vibrational relaxation. The MQB open-system simulations require significantly fewer additional quantum resources compared to both classical and digital quantum approaches.

In this study, we investigate the dynamics of dispersive photonic time crystals (PTCs) and their potential applications for controlling light-matter interaction. Using the Lorentz-Drude as dispersive material model, we analyze the effects of periodic modulation of dispersion parameters through both theoretical and numerical analysis, revealing the emergence of hybrid bandgaps from the interaction of polaritonic branches with distinctive characteristics. Our study demonstrates that dispersive PTCs offer novel excitation channels and amplification possibilities, that require lower modulation frequencies compared to nondispersive systems thus alleviating experimental challenges for the realization of PTCs in the optical regime. These findings pave the way for advancements in polaritonic lasing and resonant Raman scattering.

We demonstrate asymmetric enzyme kinetics of a biomolecular motor ${\mathrm{F}}_1\text{−}\mathrm{ATPase}$ between synthesis and hydrolysis of adenosine triphosphate (ATP). Our experiments show that ATP hydrolysis follows Michaelis-Menten kinetics, but ATP synthesis, which is an ${\mathrm{F}}_1$-ATPase's primary biological role, deviates from it. Specifically, the synthesis rate is sustained even at low substrate concentrations. Analysis of a theoretical model consistent with the experimental results reveals that ATP synthesis implements a rotation-assisted mechanism, in which a limited binding rate at low substrate concentration is partially compensated for by rotation to an angle where the binding rate is high. The results may imply that ${\mathrm{F}}_1\text{−}\mathrm{ATPase}$ implements a regulatory mechanism of enhancing substrate binding for ATP synthesis.

An information entropy for turbulence systems with multiple field quantities is formulated, as a new paradigm to explore the nonlinear dynamics and pattern formations. Combining quantum state descriptions in quantum mechanics into the turbulence field analysis, the von Neumann entropy (vNE) and the entanglement entropy (EE) are derived from a density matrix for the turbulence state in terms of the multifield singular value decomposition (MFSVD). Applying the information-theoretic entropy analyses to spatio-temporal dynamics in turbulent plasmas with phase-transition–like behavior, we discover a new nontrivial transition threshold regarding the vNE, which significantly deviates from the transition threshold of the field energy considered in the conventional approaches. These findings provide us with physically more diverse classifications of the turbulence state from the new perspective of “information”, in addition to the energetics of turbulent vortices. It is also revealed that the EE for nonlinear interactions in turbulence extracts the information regarding the strength of nonlinear mode couplings and the direction of net energy transfer. A plausible application of the EE to the turbulence measurements is demonstrated, as well as the associated reconstruction technique for fluctuation fields.

People's cooperation in adopting protective measures is effective in epidemic control and creates herd immunity as a public good. Similarly, the presence of an epidemic is a driving factor for the formation and improvement of cooperation. Here, we study the coevolution of epidemic dynamics and the public goods game as a paradigm of cooperation dynamics. Using simulations and a mean-field description, we show that the interaction of the evolutionary dynamics of cooperation and epidemic spreading leads to a feedback loop between the two dynamics. The higher disease transmission rate can promote cooperation and lead to the reduction of disease spread; in turn, the higher benefit of cooperation leads to the more efficient control of epidemics. Additionally, our work shows that a higher altruistic effect of cooperation in controlling the disease can only be detrimental to the evolution of cooperation and disease control. Rather, individuals' choices in adopting costly preventive measures are predominantly driven by the self-interested effect of such measures in reducing the probability of getting infected.

The dynamics of relativistic particles in an intense electromagnetic field can be described by the Landau-Lifshitz (LL) equation, where the radiation reaction (RR) is accounted for via a self-force, and interparticle fields are often neglected as an approximation. However, the inclusion of interparticle fields is necessary to ensure energy-momentum conservation, particularly during coherent emission. Here we present (i) an analytical proof showing that the energy-momentum conservation law of the Hamilton-Rohrlich-Dirac action, which is divergence free and describes a generic system of interacting charges, respects causality and provides physically sensible results; (ii) a simple generalization of the LL equation for many particles evaluated as a function of the total field, i.e., the sum of the external and interparticle fields. By performing first-principles numerical simulations of a neutral, relativistic bunch of electrons and positrons ($e^{-}/e^{+}$) colliding with a laser pulse, this theory is shown to satisfy energy-momentum conservation when interparticle fields and RR are simultaneously taken into account; and (iii) the combined effect of interparticle fields and RR primarily affects the tail of the particle energy distribution. Additionally, our first-principles simulations show that the effect of interparticle fields on beam energy loss becomes smaller when most of the radiated energy is incoherent.

We conceptualize and numerically simulate a resonant metamaterial interface incorporating nonlocal, or beyond-nearest-neighbor, coupling that acts as a discrete angular filter. It can be designed to yield perfect transmission at customizable angles of incidence, without diffraction, allowing for tailored transmission in arbitrarily narrow wave-number windows. The theory is developed in the setting of discrete, infinitely periodic quantum graphs and we realize it numerically as an acoustic metagrating. The theory is then applied to continuous acoustic waveguides, first for the medium surrounding the interface and then for the interface itself, showing the efficacy of quantum graph theory in interface design.

Linear-optics-based multibeam interference (MBI), like the Fabry-Pérot interferometer, plays an important role in precision optical metrology applications such as laser stabilization in optical clocks, precision spectroscopy, and gravitational wave detection. Here, we propose and experimentally verify a nonlinear optics-based MBI principle with the assistance of cascading and recycling harmonics generation of two-beam interference. By cascading and recycling the harmonics processes, in combining with optical power amplification (OPA) to compensate for power losses arising from limited nonlinear conversion efficiency, a total 16th harmonic is achieved, and the observed interference fringes gradually evolve from a sinusoidal curve to a Lorentz-like curve. In principle, there is no limitation on the number of cascading and recycling nonlinear processes with the assistance of OPAs, and sharp interference fringes, analogous to those in a high-finesse cavity, can be obtained. The nonlinear-optics-based MBI mechanism revealed here will find promising applications in precision optical metrology.

Soil is a complex, dynamic material with physical properties that depend on its biological content. We propose a cellular automaton model for self-organizing soil structure, where soil aggregates serve as food for microbial species. These, in turn, produce nutrients that facilitate self-amplification, establishing a cyclical dynamic of consumption and regeneration. Our model explores the spatial interactions between these components and their role in the sustainability of a balanced ecosystem. The main results demonstrate that (1) spatial structure supports a stable living state, preventing population collapse or uncontrolled growth; (2) the spatial model allows for the coexistence of parasitic species, which exploit parts of the system without driving it to extinction; and (3) optimal growth conditions for microbes are associated with diverse length scales in the soil structure, suggesting that heterogeneity is key to ecosystem resilience. These findings highlight the importance of spatiotemporal dynamics of life in soil ecology.