We study a fourfold symmetric dispersion relation of a quantum material, which exhibits a single high-order Van Hove singularity of $X_9$ type at the Fermi energy. First, we analyze in detail its form, type, and density of states when the energy dispersion is in its canonical form. Subsequently, we study the possibility of a superconducting state when Hubbard repulsive interactions are taken into account. By solving the gap equation, it is shown that triplet state superconductivity with power-law dependence of the critical temperature $T_c$ on the interaction strength can be formed when a single singularity is present in the Brillouin zone. We discuss the effects of fluctuations and provide an upper bound of a possible superconducting critical temperature for the ruthenate ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, which has been shown to exhibit this type of singularity.

This paper presents the technical details and commissioning results of a newly upgraded platform for ion-irradiation experiments under multi-GPa static pressure conditions at the GSI Helmholtz Center for Heavy Ion Research (Darmstadt, Germany), now accessible to external users. The GSI SIS18 accelerator provides heavy ions with tens of GeV kinetic energies, capable of penetrating through diamond anvil cells and depositing extremely high energy densities within the pressurized samples. This energy deposition triggers ultrafast, localized structural and phase transformations at the nanoscale. The platform integrates online optical microscopy and Raman spectroscopy, providing real-time monitoring of material modifications during stepwise fluence accumulation. By enabling controlled studies of structural responses and phase transitions under coupled extreme conditions, this setup opens unprecedented opportunities for research across condensed-matter physics, materials science, geoscience, high-pressure chemistry, and planetary science.

Circularly polarized phonons conventionally carry an angular momentum and a magnetic moment arising from circular motions of the atoms. Here, we present three anomalous cases that lead to phonon magnetic moments, which cannot be described in the conventional framework: rotationless axial phonons, which exhibit magnetic responses despite only carrying pseudoangular momentum, divergent gyromagnetic ratios of phonons, in which a magnetic moment is produced despite vanishing angular momentum, and anisotropic gyromagnetic ratios of phonons, which make the phonon angular momentum and magnetic moment noncollinear. Our results shed light on the origin and nature of phonon magnetism and suggest the existence of phononomagnetic hidden order.

We investigate Turing pattern formation in a stochastic reaction-diffusion model defined on $N$ lattice sites, where each lattice site is associated with a reaction vessel of volume $\mathrm{\Omega }$. We focus on a regime where spatial discreteness plays a crucial role, namely, when the characteristic length of patterns is comparable to the lattice spacing. This setting is motivated by mesoscopic and microscopic reaction-diffusion systems, in which continuum descriptions can break down. In this regime, we compare two different limiting procedures and show that they lead to qualitatively different outcomes. If we first take the deterministic limit $\mathrm{\Omega }\to \infty$ and then the long-time limit $t\to \infty$, the stationary solutions of the corresponding spatially discrete deterministic equations become spatially chaotic in the limit $N\to \infty$. In contrast, if we first take the limit $t\to \infty$ and then take an appropriate limit of $\mathrm{\Omega }\to \infty$ and $N\to \infty$, the resulting patterns are spatially periodic.

The quantum Zeno effect typically refers to freezing the dynamics of a quantum system through frequent observations. In general, quantum Zeno dynamics is obtained with an error of order $\mathcal{O}(1/N)$, where $N$ is the number of projective measurements performed within a fixed evolution time. In this work, we develop higher-order Zeno sequences that achieve faster convergence to Zeno dynamics, yielding an improved error scaling of $\mathcal{O}(1/N^{2k})$, where $k$ describes the order of the Zeno sequence. This is achieved by relating higher-order Zeno sequences to higher-order Trotter formulas that achieve similar convergence behavior. We leverage this relation to develop higher-order Zeno sequences for different manifestations of the quantum Zeno effect, including frequent projective measurements and unitary kicks. We go on to discuss achieving quantum Zeno dynamics through periodic control fields of high frequency. We explicitly develop control fields that yield a second-order type improvement in the Zeno error scaling and present shorter Zeno sequences. Finally, we discuss the connection to randomized and Uhrig dynamical decoupling to develop more efficient implementations in the weak-coupling regime.

Limit-cycle oscillators are the basic building blocks for synchronization; yet, the notion of a quantum limit cycle has remained unclear. Here, we study quantum limit cycles and synchronization in the presence of continuous heterodyne measurement. The resulting quantum trajectories, i.e., time evolutions of the quantum state conditioned on the measurement outcome, make the quantum limit cycles apparent. We focus on the paradigmatic model of the quantum van der Pol oscillator and on two-level systems. Our work provides insights into limit cycles in quantum systems, emphasizing their similarity to classical limit cycles subject to noise. Additionally, we connect theoretical measures of quantum synchronization to quantities experimentally accessible via heterodyne detection.

Muonium (Mu), a bound state of a positively charged muon and an electron, can diffuse through crystal lattices and interact with defect centers in insulators and semiconductors. We demonstrate that this Mu’s diffusive property can be used to probe defects in a diamond crystal lattice, specifically, substitutional nitrogen atoms (${\mathrm{N}}_{\text{s}}^0$) and nitrogen-vacancy (NV) centers in type-Ib diamond. Upon interaction with these defects, Mu can exchange its electron’s spin or change its charge state, which results in muon spin relaxation. However, muons in diamond (and semiconductors in general) can be in a few distinctive muonium states, with each state contributing to the muon signal. In addition, these states can undergo site and charge exchange interaction, forming a dynamic network. Hence, to study the Mu interaction with point defects, the muon data have to be deconvoluted to isolate signals from the diffusing species. To achieve this goal, we have modeled the Mu state exchange dynamics and numerically simulated the time evolution of muon spin polarization by the density matrix method. With a global curve fit to a set of longitudinal field scan data, one can extract the Mu transition rates that involve interaction with the defect centers. The diffusing tetrahedral interstitial Mu was found to interact with the paramagnetic ${\mathrm{N}}_{\text{s}}^0$ center via electron spin exchange. In contrast, they are converted to form a diamagnetic center upon interaction with the negatively charged NV center.

Two-color attosecond x-ray pulses are the key to advancing the study of ultrafast dynamics in quantum systems. In this work, we propose a single-pass free-electron laser scheme generating synchronized attosecond two-color x-ray pulses with femtosecond separation and tens-of-gigawatts peak power. By modulating a chirped electron beam with an infrared laser, we create a periodic train of ultrashort current spikes. This scheme utilizes the limited gain bandwidth of the free-electron laser as a filter, allowing only two adjacent current spikes with different resonance wavelengths to lase. This scheme holds promise for delivering sub-300-as two-color x-ray pulses with an intrinsic timing jitter below 100 as. This work provides insights and technical support for generating two-color attosecond x-ray free-electron laser pulses with robust time jitter.

The influence of the quantum state of light on strong-field ionization has emerged as a frontier in attosecond physics. Here, we develop a quantum-optical extension of the quantum-trajectory Monte Carlo framework to study the ionization of hydrogen atoms driven by an orthogonally polarized two-color quantum field, composed of an 800 nm coherent field and a 1600 nm squeezed coherent field. We show that the quantum properties of light significantly influence the subcycle dynamics of photoelectron wave packets. We systematically analyze how the quantum statistics of light influence the photoelectron phase, momentum, yield, and number distribution. Our results reveal a direct correspondence between the quantum fluctuations of the driving field and the electron final state, unveiling an avenue for controlling electron wave packet interference via the quantum properties of light.

Theories of self-organized active fluid surfaces have emerged as an important class of minimal models for the shape dynamics of biological membranes, cells, and tissues. However, due to their inherent geometric nonlinearities and the absence of general minimization principles in active systems, it remains a major challenge to systematically study the emergent shape spaces that such theories give rise to. Here, we introduce a variational approach that allows for a direct computation of stationary surface geometries and flows, which enables the classification of nonequilibrium phase transitions in shape spaces described by active surface theories. To achieve this, we construct a dissipation functional systematically from the entropy production in active surfaces and show how generic symmetries imposed by Onsager relations can be exploited to also account for reactive nondissipative terms in constitutive laws. This functional is supplemented by Lagrange multipliers that relax nonlinear geometric constraints, which leads to a tractable variational problem suitable for implicit dynamic simulations and explicit calculations of nontrivial steady state geometries and flows. We apply this framework to study the dynamics of open fluid membranes and closed active fluid surfaces, and characterize the space of stationary solutions that corresponding surfaces and flows occupy. These analyses rationalize the interplay of first-order shape transitions of internally and externally forced fluid membranes, reveal degenerate regions in stationary shape spaces of mechanochemically active surfaces, and identify a mechanism by which hydrodynamic screening controls the geometry of active surfaces undergoing cell divisionlike shape transformations.

Hydrodynamic interactions can generate rich emergent structures in active matter systems. Using large-scale hydrodynamic simulations, we demonstrate that inertial hydrodynamic coupling alone can drive spontaneous self-organization across a hierarchy of spatial and temporal scales in confined suspensions of torque-driven particles at moderate Reynolds numbers. Spinners first self-assemble into dimers, which crystallize into a hexatic lattice and subsequently undergo a collective tilting instability. The resulting tilted dimers rotate and synchronize through hydrodynamic repulsion, which can be tuned by the Reynolds number. Upon synchronization, the polar director develops splay and bend deformations and nucleates topological defects with charges of $\pm 1$. These defects induce long-wavelength concentration gradients and drive crystal vortex dynamics spanning hundreds of particle diameters. Our results reveal a purely hydrodynamic route to synchronization and defect-mediated dynamics in chiral active matter, without explicit alignment rules or long-range interparticle forces.

The confinement of electromagnetic radiation within extremely small volumes offers an effective means to significantly enhance light-matter interactions, to the extent that zero-point quantum vacuum fluctuations can influence and control the properties of materials. Here, we develop a theoretical framework for the quantum electrodynamics of graphene Landau levels embedded in a deep-subwavelength hyperbolic cavity, where light is confined into ultrasmall mode volumes. By studying the spectrum, we discuss the emergence of polaritons, and disentangle the contributions of resonant quantum vacuum effects from those of purely electrostatic interactions. Finally, we study the hybridization between magnetoplasmons and the cavity modes.

The dynamics of time-reversible systems are statistically indistinguishable when observed forward or backward in time. A rich literature of statistical methods to distinguish irreversible dynamics from the reversible dynamics of linear Gaussian processes can provide insights into underlying mechanisms and aid modeling and statistical quantification of time-series data. However, existing time-reversibility metrics have been developed individually, forming a fragmented body of research that makes it challenging to identify the most effective approaches developed to date, and the most promising directions for development. Here, we address these issues by systematically evaluating over 6000 time-series summary statistics, derived from across the time-series analysis literature, on their ability to distinguish the time irreversibility of data simulated from a diverse range of 35 systems. Our large-scale data-driven comparison highlights the effectiveness of several key families of statistics, including time-asymmetric forms of generalized autocorrelation functions, time-series symbolic sequences, and forecasting-related methods. All irreversible systems studied here could be accurately distinguished by a well-chosen time-series statistic, but no single statistic could accurately index the statistical form of irreversibility for all irreversible systems. This challenges the assumption that a given time-reversibility statistic will accurately capture time reversibility in general, and underscores the importance of tailoring statistical approaches to the time-reversal characteristics of a given system. Our results provide a unified understanding of the key algorithmic structures through which irreversibility can be effectively quantified from data, providing a foundation for connecting patterns in time series to the underlying mechanisms of the systems that generate them.

The fermion sign problem constitutes a fundamental computational bottleneck across a plethora of research fields in physics, quantum chemistry, and related disciplines. Recently, it has been suggested to alleviate the sign problem in ab initio path integral molecular dynamics and path integral Monte Carlo (PIMC) calculations based on the simulation of fictitious identical particles that are represented by a continuous quantum statistics variable $\xi$ [Xiong and Xiong, J. Chem. Phys. 157, 094112 (2022)]. This idea facilitated a host of applications including the interpretation of an x-ray scattering experiment with strongly compressed beryllium at the National Ignition Facility [Dornheim et al., Nat. Commun. 16, 5103 (2025)]. In the present work, we express the original isothermal $\xi$ extrapolation method as a special case of a truncated Taylor series expansion around the $\xi =0$ limit of distinguishable particles. We derive PIMC estimators that allow us to evaluate the Taylor coefficients up to arbitrary order and we carry out extensive PIMC simulations of the warm dense electron gas to systematically analyze the sign problem from this perspective. This gives us important insights into the applicability of the $\xi$ extrapolation method for different levels of quantum degeneracy in terms of the Taylor series radius of convergence. Moreover, the direct PIMC evaluation of the $\xi$ derivatives, in principle, removes the necessity for simulations at different values of $\xi$ and can facilitate more efficient simulations that are designed to maximize compute time in those regions of the full permutation space that contribute most to the final Taylor estimate of the fermionic expectation value of interest.

We investigate fermionic atoms subjected to an optical lattice and coupled to a high finesse optical cavity with photon losses. A transverse pump beam introduces a coupling between the atoms and the cavity field. We explore the steady-state phase diagram taking fluctuations around the mean field of the atoms-cavity coupling into account. Our approach allows us to investigate both one- and higher-dimensional atomic systems. The fluctuations beyond mean field lead to an effective temperature that changes the nature of the self-organization transition. We find a strong dependence of the results on the atomic filling, in particular when contrasting the behavior at low filling and at half filling. At low filling, the transition to a self-organized phase takes place at a critical value of the pump strength. In the self-organized phase, the cavity field takes a finite expectation value and the atoms show a modulation in the density. Surprisingly, at even larger pump strengths a strongly nonmonotonous behavior of the temperature is found and hints toward effects of cavity cooling at many-body resonances. Additionally multiple self-organized stable solutions of the cavity field and the atoms occur, signaling the presence of a fluctuation-induced bistability, with the two solutions having different effective temperatures previously discussed by Tolle et al. [Phys. Rev. Lett. 134, 133602 (2025)]. In contrast, at half filling a bistable region arises at the self-organization transition already neglecting the fluctuations. The presence of the fluctuations induce an effective temperature, as at lower fillings, and change the behavior of the transition and the steady states drastically. We analyze the properties of the occurring steady states of the coupled atoms-cavity system.