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Dynamic structure factor (DSF) is important for understanding excitations in many-body physics; it reveals information about the spectral and spatial correlations of fluctuations in quantum systems. Collective phenomena like quantum phase transitions of ultracold atoms are addressed by harnessing density fluctuations. Here, we calculate the DSF of a nonequilibrium spinless Bose–Hubbard model from the perspective of dissipative phase transition (DPT) in a steady state. Our methodology uses a homogeneous mean-field approximation to make the single-site hierarchy simpler and applies the Lindbladian perturbation method (LPM) to go beyond the single site, limited by the ratio of the inter-site hopping term to the Liouvillian gap as a small parameter. Our results show that the DSF near a DPT point is characteristically different from that away from the transition point, providing a clear density spectral signature of the DPT. In addition to comparing the two numerical frameworks, the mean-field results serve as a benchmark for proof-of-principle robustness of LPM. Despite the numerical difficulty, our methodology provides a computationally accessible route for studying density fluctuations in an open lattice quantum system without requiring large-scale computation.

Particle transport in complex environments such as the interior of living cells is often (transiently) non-Fickian or anomalous, that is, it deviates from the laws of Brownian motion. Such anomalies may be the result of small-scale spatio-temporal heterogeneities in, or viscoelastic properties of, the medium, molecular crowding, etc. Often the observed dynamics displays multi-state characteristics, i.e. distinct modes of transport dynamically interconverting between each other in a stochastic manner. Reliably distinguishing between single- and multi-state dynamics is challenging and requires a combination of distinct approaches. To complement the existing methods relying on the analysis of the particle’s mean squared displacement, position- or displacement-autocorrelation function, and propagators, we here focus on ‘scattering fingerprints’ of multi-state dynamics. We develop a theoretical framework for two-state scattering signatures—the intermediate scattering function and dynamic structure factor—and apply it to the analysis of simple model systems as well as particle-tracking experiments in living cells. We consider inert tracer-particle motion as well as systems with an internal structure and dynamics. Our results may generally be relevant for the interpretation of state-of-the-art differential dynamic microscopy experiments on complex particulate systems, as well as inelastic or quasielastic neutron (incl. spin-echo) and x-ray scattering probing structural and dynamical properties of macromolecules, when the underlying dynamics displays two-state transport.

A spin-1/2 lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the Q = M point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.

The dynamical structure factor is one of the experimental quantities crucial in scrutinizing the validity of the microscopic description of strongly correlated systems. However, despite its long-standing importance, it is exceedingly difficult in generic cases to numerically calculate it, ensuring that the necessary approximations involved yield a correct result. Acknowledging this practical difficulty, we discuss in what way results on the hardness of classically tracking time evolution under local Hamiltonians are precisely inherited by dynamical structure factors and, hence, offer in the same way the potential computational capabilities that dynamical quantum simulators do: We argue that practically accessible variants of the dynamical structure factors are bounded-error quantum polynomial time (BQP)-hard for general local Hamiltonians. Complementing these conceptual insights, we improve upon a novel, readily available measurement setup allowing for the determination of the dynamical structure factor in different architectures, including arrays of ultra-cold atoms, trapped ions, Rydberg atoms, and superconducting qubits. Our results suggest that quantum simulations employing near-term noisy intermediate-scale quantum devices should allow for the observation of features of dynamical structure factors of correlated quantum matter in the presence of experimental imperfections, for larger system sizes than what is achievable by classical simulation.

Employing the spin-wave formalism within and beyond the harmonic-oscillator approx-imation, we study the dynamic structure factors of spin-12 nearest-neighbor quantum Heisenberg antiferromagnets on two-dimensional quasiperiodic lattices with particular emphasis on a mag-netic analog to the well-known confined states of a hopping Hamiltonian for independent electrons on a two-dimensional Penrose lattice. We present comprehensive calculations on the C5v Penrose tiling in comparison with the C8v Ammann–Beenker tiling, revealing their decagonal and octagonal antiferromagnetic microstructures. Their dynamic spin structure factors both exhibit linear soft modes emergent at magnetic Bragg wavevectors and have nearly or fairly flat scattering bands, signifying magnetic excitations localized in some way, at several different energies in a self-similar manner. In particular, the lowest-lying highly flat mode is distinctive of the Penrose lattice, which is mediated by its unique antiferromagnons confined within tricoordinated sites only, unlike their itinerant electron counterparts involving pentacoordinated, as well as tricoordinated, sites. Bringing harmonic antiferromagnons into higher-order quantum interaction splits, the lowest-lying nearly flat scattering band in two, each mediated by further confined antiferromagnons, which is fully demonstrated and throughly visualized in the perpendicular as well as real spaces. We disclose superconfined antiferromagnons on the two-dimensional Penrose lattice.

The theoretical study of dendrimers is reviewed, considering both analytical approaches and molecular simulation methods. We discuss the effect of molecular symmetry on the degeneracy of the relaxation times, and then the calculation of observable quantities, in particular the intrinsic viscosity, and then the viscoelastic complex modulus and the dynamic structure factor, in comparison with the available experimental data. In particular, the maximum intrinsic viscosity with increasing molar mass is analyzed in some detail. The approximations and/or assumptions of the adopted methods are also described in connection with analogous results for polymer of a different topology, in particular linear and star polymers.

We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen-Cooper-Schrieffer superfluids to Bose-Einstein condensates, by developing an improved random phase approximation within the framework of a density functional theory (DFT)-the so-called superfluid local density approximation. Compared with the previous random-phase-approximation studies based on the standard Bogoliubov-de Gennes equations, the use of the DFT greatly improves the accuracy of the equation of state at the crossover, and leads to a better description of both collective Bogoliubov-Anderson-Goldstone phonon mode and single-particle fermionic excitations at small transferred momentum. Near unitarity, where the s-wave scattering length diverges, we show that the single-particle excitations start to significantly contribute to the spectrum of dynamic structure factor once the frequency is above a threshold of the energy gap at 2 Δ . The sharp rise in the spectrum at this threshold can be utilized to measure the pairing gap Δ. Together with the sound velocity determined from the phonon branch, the dynamic structure factor provides us some key information of the crossover Fermi superfluid. Our predictions could be examined in experiments with 6Li or 40K atoms using Bragg spectroscopy.

We investigate the effect of intra-molecular cross-links on the properties of polymer bulks. To do this, we apply a combination of thermal, rheological, diffraction, and neutron spin echo experiments covering the inter-molecular as well as the intermediate length scales to melts of single-chain nano-particles (SCNPs) obtained through ‘click’ chemistry. The comparison with the results obtained in a bulk of the corresponding linear precursor chains (prior to intra-molecular reaction) and in a bulk of SCNPs obtained through azide photodecomposition process shows that internal cross-links do not influence the average inter-molecular distances in the melt, but have a profound impact at intermediate length scales. This manifests in the structure, through the emergence of heterogeneities at nanometric scale, and also in the dynamics, leading to a more complex relaxation behavior including processes that allow relaxation of the internal domains. The influence of the nature of the internal bonds is reflected in the structural relaxation that is slowed down if bulky cross-linking agents are used. We also found that any residual amount of cross-links is critical for the rheological behavior, which can vary from an almost entanglement-free polymer bulk to a gel. The presence of such inter-molecular cross-links additionally hinders the decay of density fluctuations at intermediate length scales.

We investigate collective excitations of density fluctuations and a dynamic density structure factor in a mixture of Bose and Fermi gases in a normal phase. With decreasing temperature, we find that the frequency of the collective excitation deviates from that of the hydrodynamic sound mode. Even at a temperature much lower than the Fermi temperature, the collective mode frequency does not reach the collisionless limit analogous to zero sound in a Fermi gas, because of collisions between bosons and fermions.

In this work, we present an improved model for ionization potential depression (IPD) in dense plasmas that builds upon the approach introduced by Lin et al., which utilizes a dynamical structure factor (SF) to account for ionic microfield fluctuations. The main refinements include the following: (1) replacing the Wigner–Seitz radius with an ion-sphere radius, thereby treating individual ionization events as dynamically independent; (2) incorporating electron degeneracy through a tailored interpolation between Debye–Hückel and Thomas–Fermi screening lengths. Additionally, we solve the Saha equation iteratively, ensuring self-consistent determination of the ionization balance and IPD corrections. These modifications yield significantly improved agreement with recent high-density and high-temperature experimental data on warm dense aluminum, especially in regimes where strong coupling and partial degeneracy are crucial. The model remains robust over a broad parameter space, spanning temperatures from 1 eV up to 1 keV and pressures beyond the Mbar range, thus making it suitable for applications in high-energy-density physics, inertial confinement fusion, and astrophysical plasma research. Our findings underscore the importance of accurately capturing ion microfield fluctuations and electron quantum effects to properly describe ionization processes in extreme environments.