We investigate the prospect of using ultracold alkali diatomic molecules to implement many-body quantum systems with $\mathrm{SU}\left(N\right)$ symmetry. Experimentally accessible molecules offer large $N$ for both bosonic and fermionic systems, with both attractive and repulsive interactions. We carry out coupled-channel scattering calculations on pairs of NaK, NaRb, and NaCs molecules that are shielded from destructive collisions with static electric fields. We develop new methods to handle the very large basis sets required to include nuclear spins. We show that all the molecules studied have the properties required for $\mathrm{SU}\left(N\right)$ symmetry: the collisions are principally elastic, and the scattering lengths depend only weakly on the spin states of the molecules. The rates of spin-changing inelastic collisions are very low. We develop and test a semiclassical model of the spin dependence and find that it performs well.

Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics, when chaotic, or two-dimensional (2d) Poisson statistics, when integrable. We investigate the spectral properties of a many-body quantum spin chain, i.e., the Hermitian XXZ Heisenberg model with imaginary disorder. Its rich complex eigenvalue statistics is found to separately break both Hermiticity and integrability at different scales of the disorder strength. With no disorder, the system is integrable and Hermitian, with spectral statistics corresponding to the 1d Poisson point process. At very small disorder, we find a transition from 1d Poisson statistics to an effective $D$-dimensional Poisson point process, showing Hermiticity breaking. At intermediate disorder, we find integrability breaking, as inferred from the statistics matching that of non-Hermitian complex symmetric random matrices in class ${\mathrm{AI}}^{†}$. For large disorder, as the spins align, we recover the expected integrability (now in the non-Hermitian setup), indicated by 2d Poisson statistics. These conclusions are based on fitting the spin-chain data of numerically generated nearest- and next-to-nearest-neighbor spacing distributions to an effective 2d Coulomb gas description at inverse temperature $\beta$. We confirm that such an effective description of random matrices also applies in classes ${\mathrm{AI}}^{†}$ and ${\mathrm{AII}}^{†}$ up to next-to-nearest-neighbor spacings.

Barrier crossing is a widespread phenomenon across natural and engineering systems. While abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process have yet to be linked quantitatively to easily measurable observables. We bridge this gap by developing a microscopic representation of Brownian motion in the presence of permeable barriers that allows us to treat barriers with constant asymmetric permeabilities. Our approach relies upon reflected Brownian motion and on the crossing events being Poisson processes subordinated by the local time of the underlying motion at the barrier. Within this paradigm, we derive the exact expression for the distribution of the number of crossings and find an experimentally measurable statistical definition of permeability. We employ Feynman-Kac theory to derive and solve a set of governing birth-death diffusion equations and extend them to the case when barrier permeability is constant and asymmetric. As an application, we study a system of infinite, identical, and periodically placed asymmetric barriers for which we derive analytically effective transport parameters. This periodic arrangement induces an effective drift at long times whose magnitude depends on the difference in the permeability on either side of the barrier as well as on their absolute values. As the asymmetric permeabilities act akin to localized ratchet potentials that break spatial symmetry and detailed balance, the proposed arrangement of asymmetric barriers provides an example of a noise-induced drift without the need to time modulate any external force or create temporal correlations on the motion of a diffusing particle. By placing only one asymmetric barrier in a periodic domain, we also show the emergence of a nonequilibrium steady state.

Using holography, we study the universal scaling laws governing the coarsening dynamics of strongly coupled domain walls. Specifically, we studied the universal dependence of the length of the domain wall interfaces on the quench rate. The relation satisfies the Kibble-Zurek scaling shortly after the critical point. However, as time goes by, the coarsening dynamics suppresses the Kibble-Zurek scaling in favor of a universal dynamical scaling of the characteristic length and the adiabatic growth of the system. Theoretical predictions of the universal scaling laws are consistent with numerical findings in both regimes for both weak and strongly coupled systems.

The vitrification of aqueous solutions through rapid cooling is a remarkable achievement that launched the field of cryo-electron microscopy (cryo-EM) and has enabled the cryopreservation of biological specimens. For judging the feasibility of a vitrification experiment, the critical cooling rate of pure water is a frequently cited reference quantity. However, an accurate determination has remained elusive, with estimates varying by several orders of magnitude. Here, we employ time-resolved electron microscopy to obtain a precise measurement of this quantity. We use shaped microsecond laser pulses to briefly melt an amorphous ice sample before flash freezing it with a variable, well-defined cooling rate. This allows us to directly measure the critical cooling rate of water, which we determine to be $6.4\times {10}^6\mathrm{K}/\mathrm{s}$. This result provides important insights into the question of how closely the conformational ensembles in plunge-frozen cryo samples reflect the structure of a protein at room temperature. Moreover, our experimental approach expands the toolkit of microsecond time-resolved cryo-EM, an emerging technique, in which a cryo sample is flash melted and revitrified with a laser pulse in order to enable time-resolved observations of protein dynamics.

In this work we investigate the effects that multimode photonic environments, e.g., optical cavities, have on the properties of quantum matter. We highlight the importance of the nonperturbative mass renormalization procedure for ab initio quantum electrodynamics simulations and how it connects to common approximations used in polaritonic chemistry and cavity materials engineering. We focus on one-dimensional systems which can be solved exactly for large number of photon modes. First, we apply mass renormalization to free particles. The value of the renormalized mass depends on the details of the photonic environment and on the number of particles. We then show how the multimode photon field influences various ground- and excited-state properties of atomic and molecular systems. For instance, we observe the enhancement of particle confinement in the binding potential for the atomic system, and the modification of the potential energy surfaces of the molecular dimer due to photon-mediated long-range interactions. We also highlight how these changes compare to the common free-space mass-renormalization approximation employed in electronic structure theory and quantum chemistry. Since such phenomena are enhanced under strong light-matter coupling in a cavity environment they will become relevant for the emerging fields of polaritonic chemistry and cavity materials engineering.

We introduce two disorder-free variants of the Sachdev-Ye-Kitaev (SYK) model, demonstrate their integrability, and study their static and dynamical properties. Unlike diagrammatic techniques, the integrability of these models allows us to obtain dynamical correlation functions even when the number of Majorana fermions is finite. From the solutions, we find that out-of-time-order correlators (OTOCs) in these models exhibit exponential growth at early times, resembling that of many-body quantum chaotic systems, such as those with disorder or external kick terms, despite their large $N$ behavior differing from that of typical chaotic systems. Conversely, our analysis shows no evidence of random-matrix behavior in level spacing statistics or the spectral form factor. Our findings illustrate that the clean versions of the SYK models represent simple but nontrivial examples of disorder-free quantum many-body systems displaying chaoslike behavior of OTOCs.

Asymmetric radiation in upward and downward directions supported by leaky modes can be generally exhibited in the reciprocal but geometrical up-down mirror-symmetry-breaking structures, i.e., photonic crystal slabs. Here, we theoretically propose and numerically demonstrate a scheme to break the reciprocity, and to generate and manipulate the unidirectional guided resonances (UGRs) in a one-dimensional magneto-optical (MO) grating, which radiate solely toward one side with no emission in the opposite direction. Under an external magnetic field, it is found that genuine UGRs (or quasi-UGRs) in topological nature, depicted by a phase winding number of far-field radiation, can be created by hybridizing the different orthogonal bands in such a nonreciprocal grating. We further investigate the evolution, annihilation, and band transition for residential position of UGRs in three-dimensional parameter space, and we also notice that the emission direction may be switched from one side to the other due to the tuning of the asymmetric coupling. Finally, the excitation of UGRs is examined in a lossless system related to directional coupling of external waves, and it can also be utilized to realize perfect absorption in a lossy MO grating structure under single-sided illumination. The general principles presented here may lead to an efficient and active approach for the dynamic manipulation of topological radiation asymmetry, and they may serve as new inspiration to control flexibly the resonant and topological properties of light-matter interactions.

We show the existence of Borromean bound states in a one-dimensional quantum three-body system composed of two identical bosons and a distinguishable particle. It is assumed that there is no interaction between the two bosons, while the mass-imbalanced two-body subsystems can be tuned to be either bound or unbound. Within the framework of the Faddeev equations, the three-body spectrum and the corresponding wave functions are computed numerically. In addition, we identify the parameter-space region for the two-body interaction, where the Borromean states occur, evaluate their geometric properties, and investigate their dependence on the mass ratio.

The interplay between topology and dissipation can give rise to a wealth of new phenomena and pave the way for novel topological lasers, sensors, and other quantum devices. Along these lines, we propose here an optomechanical setup in which the concomitant presence of a spatially modulated external drive and dissipation gives rise to a topologically nontrivial state for mechanical and optical excitations. We are able to show that the one-dimensional system considered here exhibits topologically protected end states for which mechanical and optical degrees of freedom are entangled. We show such entanglement to be robust with respect to the presence of nonzero-temperature baths and we propose a protocol for experimental observation of the entanglement.

Geometric effects in curvilinear nanomagnets can enable chiral, anisotropic, and even magnetoelectric responses. Here, we study the effects of magnetic frustration in curvilinear (quasi-)one-dimensional magnets represented by spin chains arranged along closed space curves of constant torsion. Considering the cases of easy- and hard-axis anisotropy in ferro- and antiferromagnetic samples, we determine their ground states and analyze the related magnetoelectric multipoles. A constant torsion along the chain results in alternating regions of high and low curvature, facilitating the spin spiral state perturbed by the (anti)periodic boundary conditions on the magnetic order parameter. While easy-axis ferromagnetic chains develop a purely toroidal configuration with the magnetic toroidal moment oriented along the geometry symmetry axis, hard-axis antiferromagnetic chains support multiple magnetic toroidal domains. Our findings suggest that tailoring curvature and torsion of a spin chain enables a different physical mechanism for magnetic frustration, which can be observed in the inhomogeneity of the magnetic order parameter and in the local ferrotoroidal responses.

Electron hydrodynamics refers to the transport regime where electrons collectively behave like a fluid. Its realization requires pure materials, some of which, such as bilayer graphene or ${\mathrm{PdCoO}}_2$, are anisotropic so that different in-plane transport directions can be defined. Collective electron flow also benefits from geometrically engineered devices because it is highly dependent on the nonuniformity of the electron flow. Here we analyze carrier transport in anisotropic materials where remarkable effects emerge after the proper directional design of the device. Simulations based on the Boltzmann transport equation demonstrate that electrical properties are clearly different when the device is set in the easy or the hard transport directions, namely, when the transport channel is aligned or not aligned to the group velocity at the Fermi level, respectively. Most importantly, the standard signatures of viscous electron flow, such as Poiseuille flow, superballistic conduction, and the formation of whirlpools, are enhanced when the anisotropic device operates in the hard transport directions. As a result, we demonstrate that electron hydrodynamics leads to a different route for efficient charge transport in the hard in-plane transport directions.

We propose a framework to design concurrently a frustration-free quantum many-body Hamiltonian and its numerically exact ground states on a sufficiently large finite-size cluster in one and two dimensions using an elementary matrix product state (MPS) representation. Our approach strategically chooses a local cluster Hamiltonian, which is arranged to overlap with neighboring clusters on a designed lattice. The frustration-free Hamiltonian is given as the sum of the cluster Hamiltonians by ensuring that there exists a state that has its local submanifolds as the lowest-energy eigenstate of every cluster. The key to find such a solution is a systematic protocol, which projects out excited states on every cluster using MPS and effectively entangles the cluster states. This algorithm not only offers an exact solution to general frustration-free Hamiltonian, but even provide the excited eigenstates by setting a proper target. It has several advantages, including the ability to achieve the calculation of states at nearly equal cost in one and two dimensions including those belonging to gapless or long-range entangled classes, flexibility in designing Hamiltonians unbiasedly across various forms of models, and numerically feasible validation of exactness through energy calculations. It enables the exploration of exact phase boundaries and the analysis of even a spatially nonuniform random system, providing platforms for quantum simulations and benchmarks.

Reliable numerical computation of quantum dynamics is a fundamental challenge when the long-ranged quantum entanglement plays essential roles as in the cases governed by quantum criticality in strongly correlated systems. Here we apply a method that utilizes reliable short-time data of physical quantities to accurately forecast long-time behavior of the strongly entangled systems. We straightforwardly employ the simple dynamic mode decomposition (DMD), which is commonly used in fluid dynamics. Despite the simplicity of the method, the effectiveness and applicability of the DMD in quantum many-body systems such as the Ising model in the transverse field at the critical point are demonstrated, even when the time evolution at long time exhibits complicated features such as a volume-law entanglement entropy and consequential power-law decays of correlations characteristic of systems with long-ranged quantum entanglements unlike fluid dynamics. The present method, though simple, enables accurate forecasts amazingly at time as long as nearly an order of magnitude longer than that of the short-time training data. Effects of noise on the accuracy of the forecast are also investigated, because they are important especially when dealing with the experimental data. We find that a few percentages of noise do not affect the prediction accuracy destructively.

Nonlinear multimode optical systems have attracted substantial attention due to their rich physical properties. Complex interplay between the nonlinear effects and mode couplings makes it difficult to understand the collective dynamics of photons. Authors of recent studies have shown that such collective phenomena can be effectively described by Rayleigh-Jeans thermodynamics theory, which is a powerful tool for the study of nonlinear multimode photonic systems. These systems, in turn, offer a compelling platform for investigating fundamental issues in statistical physics, attributed to their tunability and the ability to access negative temperature regimes. However, to date, a theory for nonequilibrium transport and fluctuations is yet to be established. Here, we employ full counting statistics theory to study the nonequilibrium transport of particles and energy in nonlinear multimode photonic systems in both positive and negative temperature regimes. Furthermore, we discover that, in situations involving two reservoirs of opposite temperatures and chemical potentials, an intriguing phenomenon known as the loop current effect can arise, wherein the current in the positive energy sector runs counter to that in the negative energy sector. In addition, we numerically confirm that the fluctuation theorem remains applicable in optical thermodynamics systems across all regimes, from positive temperatures to negative ones. Our findings closely align with numerical simulations based on first-principles nonlinear wave equations. In this paper, we seek to deepen the understanding of irreversible nonequilibrium processes and statistical fluctuations in nonlinear many-body photonic systems which will enhance our grasp of collective phenomena of photons and foster a fruitful intersection between optics and statistical physics.