The material ${\mathrm{ZrTe}}_5$ exhibits distinct topological phases, including a Weyl semimetal (WSM) phase, characterized by a chiral anomaly and in-plane Hall effect, and a three-dimensional quantum Hall (3D QH) phase. The relationship between these phases remains poorly understood. This work systematically explores their connection in ${\mathrm{ZrTe}}_5$ through rotatable, pressure-dependent measurements. At ambient pressure, both phases are observed; the WSM phase requires strong spontaneous electronic polarization, while the 3D QH phase appears when polarization is fully suppressed, with the characteristic resistivity peak temperature $T_{\text{p}}\sim 90\mathrm{K}$. Under applied pressure, ferroelectric polarization diminishes, weakening the WSM phase and its associated nontrivial Hall signals. Concurrently, $T_{\text{p}}$ rises dramatically from 2 K at ambient pressure to 70 K at 2.2 GPa, approaching the expected regime for the 3D QH phase. These findings clarify the conditions underlying the WSM and 3D QH phases and suggest that exploring the 3D QH phase at even higher pressures is a promising direction for future research.

We interpret the $B$-lattice flavor framework as a compositeness hierarchy: all three fermion generations are elementary chiral fields, but third-generation Yukawa couplings are undressed ($Q=0$), while lighter generations acquire their Yukawa couplings through chains of spin-0 subconstituents (“hops”) whose depth is counted by the ${\mathbb{Z}}_9$ discrete gauge symmetry. The ${\mathbb{Z}}_9$ charge admits a two-index decomposition $q_9\mapsto (a,b)$ that identifies two hop species ($\alpha , \beta$) and organizes all fundamental scales from $v_{\mathrm{EW}}$ to $M_{\mathrm{Pl}}$ on a “ninths ladder” $\mathrm{\Lambda }\times {\epsilon }^{n/9}$. The lattice structure yields the Cabibbo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata mixing parametrizations (with all mixing exponents expressible as charge differences $\mathrm{\Delta }Q$ dressed by a universal Fritzsch-Xing phase shift of $\pm 1/9$), a seesaw benchmark $m_3\simeq 51$ meV, the axion mass window $m_a\sim 7$–$12\mu \mathrm{eV}$, and the prediction $tan\beta \simeq 10$–16 (from the chain internal factor combined with the Dine-Fischler-Srednicki-Zhitnitsky-II two-Higgs-doublet structure), all from two parameters ($\mathrm{\Lambda }$ and $\epsilon =14/75$). Generation-dependent Peccei-Quinn charges restore the axion-photon coupling ($C_{a\gamma }\simeq 0.6$–1.0) from “back to invisible” suppression. An illustrative UV realization in terms of hypercolor-confined scalars communicated to the standard model by a gauge-invariant messenger chain is presented as an existence proof.

We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an $N$-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves separability and allows to characterize the entanglement of the original multipartite state. In particular, we establish a connection between the border rank and the Schmidt rank, and derive lower bounds on entanglement measures. Finally, we reveal the existence of entangled symmetric subspaces, where all bipartite states are entangled.

Despite the success of the spin-thermalized assumption in explaining hyperon spin polarizations in relativistic heavy-ion collisions, challenges begin to arise especially at lower collision energies. The present study compares the nucleon spin polarization during the collision process and at the freeze-out stage from a nonrelativistic spin-dependent transport model with spin-thermalized approaches in intermediate-energy heavy-ion collisions, where the relativistic effect and the temperature gradient have shown to be unimportant. It is found that both the global and local spin polarizations are largely overestimated from spin-thermalized approaches, compared to those generated by the spin-orbit mean-field potential in transport simulations.

Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly breaking symmetry, we propose a complementary framework based on symmetry reduction. We reformulate representations, attention mechanisms, and optimization dynamics in terms of invariant relational quantities, eliminating redundant degrees of freedom by construction. This perspective yields architectures that operate directly on relational structures, providing a principled geometric framework for reducing parameter redundancy and analyzing optimization.

Using numerically exact diagrammatic Monte Carlo simulations in the two-electron (single-bipolaron) sector, we explore the impact of long-range Coulomb repulsion on the dilute-limit Berezinskii-Kosterlitz-Thouless transition temperature $T_c$ of bipolarons on a two-dimensional square lattice. We study the bond Su-Schrieffer-Heeger model, in which bond phonons modulate the electron hopping. In the absence of long-range repulsion, this model was shown to support small, light bipolarons with a comparatively high transition temperature [C. Zhang, J. Sous, D. R. Reichman, M. Berciu, A. J. Millis, N. V. Prokof’ev, and B. V. Svistunov, Bipolaronic high-temperature superconductivity, Phys. Rev. X 13, 011010 (2023)]. Here, we find that long-range Coulomb repulsion suppresses the optimal $T_c$ but leaves it appreciable over a broad parameter window, including the adiabatic regime $\omega /t=0.5$ at a representative Coulomb strength $V=U/10$ (with $U$ the on-site repulsion). Our results provide controlled single-bipolaron inputs for dilute-limit $T_c$ estimates in the presence of long-range repulsion.

We explore the helical quantum two-body problem, i.e., two repulsively Coulomb interacting particles confined to move along a helix. The effective potential possesses a tunable number of potential wells superimposed on the repulsive Coulomb interaction that can be varied by changing the ratio of the pitch and radius of the helix. The anharmonicity of these wells depends crucially on this ratio and on the order of the well, which can also be seen by analyzing the individual wells’ energy eigenvalue spacing. Our main focus is the investigation of the quantum dynamics of differently prepared wave packets that scatter from the multiwell potential landscape. We show that there exists a rich pattern-forming transient evolution that depends also on the number of bound states of the individual wells. We demonstrate how the multiple wells leave their fingerprints in the dynamics leading, among others, to oscillatory structures on different spatial scales, the formation of beats, and pulsed emission from single well localized wave packets due to their intrawell dynamics.

The magnetoconductance of ${\mathrm{Ti}}_3{\mathrm{C}}_2{\mathrm{T}}_x$ MXene thin films under both perpendicular and parallel magnetic fields is systematically investigated to elucidate how finite thickness impacts weak localization (WL). In thicker films ($\sim 700\mathrm{nm}$), the magnetoconductance is nearly orientation independent, indicating a three-dimensional (3D) regime. In contrast, thinner films ($\lesssim 70\mathrm{nm}$) exhibit pronounced angle-dependent WL, consistent with two-dimensional (2D) behavior. Notably, in some of these thinner films, a small negative magnetoconductance is also detected at low temperatures in parallel fields—a hallmark of weak antilocalization arising from spin-orbit coupling. By fitting the 2D data in both orientations, the key transport parameters are extracted, including an effective thickness of around 12 nm (smaller than the physical thickness) and dephasing lengths. These findings deepen the understanding of quantum interference in MXenes and lay the groundwork for harnessing their tunable dimensionality and spin-orbit effects in emerging electronic and spintronic applications.

The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking into account a phase shift in coupling. In the thermodynamic limit, we derive dependencies of the order parameters on the coupling strength and the phase shift, and describe two transitions from disorder to partial synchrony and from partial synchrony to complete synchrony. In all cases, the first transition is discontinuous, although for phase shifts close to $\pi /2$, the jump is exponentially small. We also discuss which properties of the transition hold for distributions close to the uniform one.

Terraforming Mars can be evaluated with system-level constraints linking target pressure and composition to volatile inventory, target temperature to radiative control, climate agents to throughput and power, and persistence to collapse, escape, and geochemical sinks. We use transparent order-of-magnitude scalings to compare endogenous ${\mathrm{CO}}_2$ release, synthetic supergreenhouse gases, ${\mathrm{CO}}_2\text{−}{\mathrm{H}}_2$ collision-induced absorption, engineered aerosols and nanoparticles, orbital reflectors, and regional paraterraforming. Mars requires $3.89\times {10}^{15}\mathrm{kg}$ of atmosphere per millibar of global mean surface pressure, so open-surface human-relevant pressures require ${10}^{17}\text{–}{10}^{18}\text{−}\mathrm{kg}$-scale gas inventories. Accessible endogenous ${\mathrm{CO}}_2$ is best treated as an order-of-tens-of-millibar resource: A representative 20 mbar case gives $\lesssim$10 K warming and does not close melt-class climates or breathable composition. Mean surface temperatures of 250–273 K require, in a gray/window-weighted architecture model, effective window-weighted longwave optical depth of order unity to a few, or direct absorbed-solar forcing of order ${10}^2\mathrm{W}{\mathrm{m}}^{-2}$, implying ${10}^{13}\text{–}{10}^{14}\text{−}{\mathrm{m}}^2$-scale reflector area. A human-breathable open atmosphere is dominated by ${\mathrm{O}}_2$ and buffer gas: $p_{{\mathrm{O}}_2}=21$ kPa and $p_{{\mathrm{N}}_2}=50$ kPa imply $9.0\times {10}^{17}\mathrm{kg}$ and $1.9\times {10}^{18}\mathrm{kg}$, respectively, and water electrolysis requires reversible work $\sim 1.3\times {10}^{25}\mathrm{J}$ before inefficiencies and sink-management costs. These bounds apply directly to abiotic industrial oxygenation and to the terminal atmospheric inventories that any human-breathable open Mars must contain; biological bootstrapping can change the path to useful habitability, but not the final ${\mathrm{O}}_2$ and buffer-gas inventory required for an open breathable atmosphere. Under known inventories, regional and covered-area habitability is the physically favored staged path; no surveyed abiotic global open-atmosphere pathway simultaneously closes pressure, composition, warming, power, throughput, retention, sink, and operations constraints.

In modern interconnected societies, opinions and beliefs can quickly spread across large populations, giving rise to collective behaviors such as the adoption of social norms or polarization. The interest in these phenomena led to the formulation of many models aiming at reproducing relevant emergent properties from simple mechanisms of interactions between individuals. In particular, opinion dynamics models mimic how the opinions of individuals on a given topic may evolve when they interact, and study the conditions for global consensus or polarization. Most models assume that these interactions occur between pairs of agents, typically on a fixed network structure. However, discussions leading to opinion changes can occur in groups, and these groups can also undergo adaptive changes and modifications if their members disagree. Here, we propose a bounded confidence model of opinion dynamics taking into account these two mechanisms: A group discussion can lead to a global agreement among all group members, if their opinions are close enough, while a strong divergence of opinions within a group leads to its splitting, followed by merging of the resulting subgroups with other groups. We systematically study the outcome of this model as a function of the tolerance of agents for reaching an agreement. Strikingly, adaptivity seems to suppress important effects induced by group interactions, and to restore a phenomenology close to the one obtained with pairwise interactions. We show that adaptivity, which allows the formation of large groups, prevents the transition to a fragmented state at small tolerance. Moreover, it restores a phase transition from a polarized state to consensus, which would otherwise disappear due to group effects in a nonadaptive bounded confidence model with group interactions. Overall, our work shows that both adaptivity and group interactions shape the structure of social ties and the global opinion dynamics in a population.

Cavity magnonics, owing to its strong magnon-photon coupling and excellent tunability, has attracted significant interest in quantum information science. However, achieving strong and robust macroscopic entanglement remains a long-standing challenge due to the inherently linear nature of the beam-splitter interaction. Here, we propose an experimentally feasible scheme to generate and enhance macroscopic entanglement between two remote magnon modes by injecting squeezed vacuum fields (SVFs) into coupled microwave cavities. We demonstrate that even a single SVF applied to one cavity can induce steady magnon-magnon entanglement, while applying two SVFs (the double-squeezed configuration) enables selective activation of two independent entanglement channels associated with the cavity supermodes. Remarkably, quantum interference between the two SVFs allows for phase-controlled enhancement of entanglement, resulting in significantly improved robustness against cavity dissipation and thermal noise. Under realistic parameters, the survival temperature of quantum entanglement increases from approximately 260 to 450 mK. Our results establish a versatile and controllable approach to generating and enhancing quantum entanglement through quantum interference between squeezed vacuum fields.

Hybrid light-matter systems provide a powerful route to distributing quantum correlations across scalable architectures. Here, we investigate tripartite entanglement in a driven-dissipative system composed of two evanescently coupled optical resonators, one of which interacts with a two-level atom by Jaynes-Cummings-type interaction. In the weak-excitation regime, we derive an analytical steady-state description that captures how a single excitation becomes coherently shared among the three subsystems. By evaluating bipartite concurrences and the concurrence-fill measure, we identify parametric regimes where genuine tripartite entanglement between photon-atom-photon emerges despite photon loss and atomic decay. We further demonstrate how this entanglement can be controlled through experimentally accessible parameters, including detuning, light-matter coupling, photon tunneling, and coherent drive strength. The analytical predictions are fully supported by master-equation simulations, establishing a practical framework for engineering continuous-wave multipartite entanglement and enabling entanglement-assisted routing in hybrid photonic-atom quantum networks.

We investigate the interplay between altermagnetic band structures and electronic correlations by focusing on the $d_{x^2-y^2}$ altermagnetic generalization of the Hatsugai-Kohmoto model. We find that with increasing interaction, a many-body Lifshitz transition takes place when doubly occupied regions disappear from the Fermi surface and almost all momentum states become fully spin polarized. This is termed interaction-enhanced altermagnet. We find that the dynamical susceptibility, which possesses only transverse nonzero components for small wave vectors, develops a gap proportional to the interaction strength and displays a sharp peak at a frequency increasing with the interaction. Above the Lifshitz transition, this peak moves to the lower gap edge and becomes log divergent. The signal intensity increases with the interaction up until the Lifshitz transition and saturates afterward. The static susceptibility remains unaffected by the correlations and altermagnetism reduces the static transverse response.

Quantum systems achieve objectivity by redundantly encoding information about themselves into the surrounding environment, through a mechanism known as quantum Darwinism. When this happens, observers measure the environment and infer the system to be in one of its pointer states. We study the emergence of objectivity whenever the Hamiltonian of the system and the interaction Hamiltonian between system and environment do not commute, a condition where it becomes difficult to identify pointer states, and the use of methods such as the predictability sieve becomes necessary. We show in an explicit qubit model to what degree the noncommuting evolution allows for the emergence of objective states, and show that a definition of pointer states based on spectrum broadcast structure is more natural in this context, and coincides with the one based on the predictability sieve for commuting evolutions.

Quantitative evaluation of magnetic moment distributions in microstructures with high spatial resolution is essential to advance the development of next-generation spintronic devices. In this study, we successfully imaged the magnetic domain structure of micropatterned subnanometer thin films by combining high-resolution and high-sensitivity imaging using soft x-ray ptychography and x-ray magnetic circular dichroism. Furthermore, by measuring hyperspectral images of magnetic thin-film patterns and applying the sum rule to absorption spectra at each pixel of the image, quantitative two-dimensional measurements of spin and orbital magnetic moments within magnetic domains were achieved. Such measurements provide a powerful evaluation method for the design of devices based on physical phenomena such as spin and orbital currents.

Twisted light carries orbital angular momentum (OAM) and can drive excitations of confined, interacting electrons that are dark to uniform dipolar probes. Here, we show how this “beyond-Kohn's-theorem” optical channel can become a concrete control primitive for quantum computing. Correlation sectors in few-electron quantum dots—characterized by the relative angular momentum quantum number—form a tunable ladder of many-body states that are robust in the limited sense of symmetry-protected selection rules and persistent chiral spectroscopic fingerprints; full topological gap protection requires three or more electrons. A twisted-light pulse with prescribed OAM index and polarization provides fast optical write, read, and scalable addressing of these sectors via the selection rule $\mathrm{\Delta }\left|m\right|=\pm (l+\sigma )$. In the analytically solvable Calogero ($1/r^2$) interaction limit, both the energy spectrum and the twisted-light matrix elements are closed-form functions of the interaction strength, allowing gate parameters (Rabi frequency, qubit frequency, anharmonicity, and leakage rates) to be written down explicitly. We map these results onto a universal single-qubit gate set, propose a concrete two-qubit entangling mechanism via state-dependent Coulomb coupling between adjacent dots, and identify the dominant decoherence channel (quadrupolar charge noise). A semianalytic $N=3$ extension using the $1/N$ expansion provides a design-level scaffold for the topological roadmap, including quasihole sector addressing. The central operational message is that twisted light enables WRITE (pulse-create a correlation sector), READ (spectroscopically diagnose correlations), and SCALE (optical addressing via spatial light modulator) in a unified photonic control layer. Throughout, screened and Coulomb interactions preserve the same qualitative chiral fingerprints established in the solvable limit.

We investigate the dynamics of a run-and-tumble particle in a double-well potential and demonstrate that, in stark contrast to Brownian particles, active dynamics can lead to strong ergodicity breaking. When the barrier height exceeds a critical threshold, the long-time position distribution depends crucially on the initial condition: If the particle starts within the basin of attraction of one well, it remains trapped there, while if it begins between the two basins, it can reach either well with a finite probability, which we compute exactly via hitting probabilities. Below the critical barrier height, ergodicity is restored and the system converges to a unique stationary distribution, which we derive analytically. Using this result, we also estimate the characteristic barrier-crossing time and show that it violates Kramers-Arrhenius law and displays a divergence near the critical height following a Vogel-Fulcher-Tammann-like form with an anomalous exponent $1/2$.

In this paper, we consider fluctuations in a three-stroke cycle based on quantum measurement. In the first stroke, the engine is fueled by a nonselective quantum measurement; in the second stroke, an appropriate unitary operation is applied to extract work; and finally, the working medium is thermalized to complete the cycle. This protocol is analogous to charging, then discharging, and finally thermalizing a quantum battery. Using the Kirkwood-Dirac quasiprobability, we derive equations that provide insights into the fluctuations of heat and work, and thus into the charging and discharging processes. We then propose a quantum circuit to measure the cumulants of work and heat using a qubit ancilla. Afterward, we derive important upper and lower bounds on fluctuations in heat; this is thanks to the way we decompose heat fluctuations and the Kadison-Schwarz inequality. We also show, for the first time, that the imaginary part of the second cumulant of work equals the linear response of an average work (to be defined in the main text) or the quantum cross entropy. We further introduce an operator whose average defines the battery capacity and whose variance quantifies the corresponding fluctuations of the battery capacity. Our analytical results are illustrated and discussed through representative examples. We believe that our study will, on the one hand, be useful for understanding fluctuations in energy extracted from and injected into quantum batteries based on quantum measurements and, on the other hand, contribute to the foundations of quantum thermodynamics. More generally, our results can be applied beyond the three-stroke cycle considered here, especially to quantum batteries subject to environmental noise and decoherence.

Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. However, this threshold strongly depends on the classical method used to decode the measurements of the syndrome. These classical algorithms traditionally only interpret binary data, ignoring valuable information contained in complete analog measurement data. We present the first large-scale experimental verification of soft decoding by implementing repetition codes up to distance 51 on superconducting hardware. Unlike previous demonstrations limited to small code distances, this extensive range allows us to confirm a fundamental improvement in the exponential scaling of error suppression rather than a mere constant-factor reduction in error rates. We observe a 25% increase in the threshold, which yields logical error rates up to 30 times lower than standard hard decoding. Analyzing the trade-off between information volume and decoding performance, we show that a single byte of information per measurement suffices to reach optimal decoding. This underscores the effectiveness and practicality of soft decoding on hardware, including in time-sensitive contexts such as real-time decoding.