Publications

This paper provides an error estimate for the u-series method of the Coulomb interaction in molecular dynamics simulations. We show that the number of truncated Gaussians M in the u-series and the base of interpolation nodes b in the bilateral serial approximation are two key parameters for the algorithm accuracy, and that the errors converge as O(b−M) for the energy and O(b−3M) for the force. Error bounds due to numerical quadrature and cutoff in both the electrostatic energy and forces are obtained. Closed-form formulae are also provided, which are useful in the parameter setup for simulations under a given accuracy. The results are verified by analyzing the errors of two practical systems.

This article shows that it is, in principle, possible to make a dielectric rod completely invisible to an incident electromagnetic plane wave of a given frequency. Students can derive the conditions that make the rod invisible if they understand the concept of plane waves, the boundary conditions for electric and magnetic fields, and the complex representation of electromagnetic fields. With access to appropriate software, students can determine the bandwidth of the invisibility and investigate whether it is possible to make an invisible rod out of real-world materials. A more advanced project proposed is to use electromagnetic software to find perfectly conducting hollow structures that are invisible to an incident plane wave.

Time-dependent Wannier functions were initially proposed as a means for calculating the polarization current in crystals driven by external fields. In this work, we present a simple gauge where Wannier states are defined based on the maximally localized functions at the initial time, and are propagated using the time-dependent Bloch states obtained from established first-principles calculations, avoiding the costly Wannierization at ech time step. We show that this basis efficiently describes the time-dependent polarization of the laser driven system through the analysis of the motion of Wannier centers. We use this technique to analyze highly nonlinear and non-perturbative responses such as high harmonic generation in solids, using the hexagonal boron nitride as an illustrative example, and we show how it provides an intuitive picture for the physical mechanisms.

Embedding materials in optical cavities has emerged as an intriguing perspective for controlling quantum materials, but a key challenge lies in measuring properties of the embedded matter. Here, we propose a framework for probing strongly correlated cavity-embedded materials through direct measurements of cavity photons. We derive general relations between photon and matter observables inside the cavity, and show how these can be measured via the emitted photons. As an example, we demonstrate how the entanglement phase transition of an embedded H

The optical conductivity provides a comprehensive view of the electronic response of materials to electromagnetic fields, offering insights into transport phenomena, optoelectronic properties, and other fundamental aspects of condensed matter physics. We present an automatic, high-order accurate, and adaptive Brillouin zone integration algorithm for the calculation of the optical conductivity using the Kubo formula, with a nonzero but small broadening factor 𝜂, focusing on the case in which a Hamiltonian in a downfolded model can be evaluated efficiently using Wannier interpolation. The algorithm uses iterated adaptive integration to exploit the localization of the transport distribution near energy and energy-difference isosurfaces, yielding polylogarithmic computational complexity with respect to 𝜂, rather than the algebraic complexity of uniform integration rules. To demonstrate the method, we compute the AC optical conductivity of a three-band tight-binding model, and are able to resolve the Drude and interband peaks with broadening in the sub-meV regime to several digits of accuracy. Our algorithm automates convergence testing to a user-specified error tolerance, providing an important tool in black-box first-principles calculations of electrical transport phenomena and other response functions.

Tumor-initiating cells (TICs) share features and regulatory pathways with normal stem cells, yet how the stem cell niche contributes to tumorigenesis remains unclear. Here, we identify CXCR4+ macrophages as a niche population enriched in normal mammary ducts, where they promote the regenerative activity of basal cells in response to luminal cell-derived CXCL12. CXCL12 triggers AKT-mediated stabilization of β-catenin, which induces Wnt ligands and pro-migratory genes, enabling intraductal macrophage infiltration and supporting regenerative activity of basal cells. Notably, these same CXCR4+ niche macrophages regulate the tumor-initiating activity of various breast cancer subtypes by enhancing TIC survival and tumor-forming capacity, while promoting early immune evasion through regulatory T cell induction. Furthermore, a CXCR4+ niche macrophage gene signature correlates with poor prognosis in human breast cancer. These findings highlight the pivotal role of the CXCL12-CXCR4 axis in orchestrating interactions between niche macrophages, mammary epithelial cells, and immune cells, thereby establishing a supportive niche for both normal tissue regeneration and mammary tumor initiation.

We present a new implementation of the driven similarity renormalization group (DSRG) based on a density matrix renormalization group (DMRG) reference. The explicit build of high-order reduced density matrices is avoided by forming matrix-product-state compressed intermediates. This algorithm facilitates the application of DSRG second- and third-order perturbation theories to dodecacene with an active space of 50 electrons in 50 orbitals. This active space appears the largest employed to date within the framework of internally contracted multireference formalism. The DMRG-DSRG approach is applied to several challenging systems, including the singlet-triplet gaps ($\Delta_{\rm ST}$) of oligoacenes ranging from naphthalene to dodecacene, the vertical excitation energies of zeaxanthin, and the ground-state potential energy curve (PEC) of Cr$_2$ molecule. Our best estimate for the vertical $\Delta_{\rm ST}$ of dodecacene is 0.22 eV, showing an excellent agreement with that of the linearized adiabatic connection method (0.24 eV). For zeaxanthin, all DSRG schemes suggest the order of $\rm 2\, ^1 A_g^- < 1\, ^1 B_u^+ < 1\, ^1 B_u^-$ for excited states. Both the equilibrium and the shoulder regions of the Cr$_2$ PEC are reasonably reproduced by the linearized DSRG with one- and two-body operators.

Suspensions of swimming particles exhibit complex collective behaviors driven by hydrodynamic interactions, showing persistent large-scale flows and long-range correlations. While heavily studied, it remains unclear how such structures depend on the system size and swimmer concentration. To address these issues, we simulate very large systems of suspended swimmers across a range of system sizes and volume fractions. For this we use high-performance simulation tools that build on slender body theory and implicit resolution of steric interactions. At low volume fractions and long times, the particle simulations reveal dynamic flow structures and correlation functions that scale with the system size. These results are consistent with a mean-field limit and agree well with a corresponding kinetic theory. At higher concentrations, the system departs from mean-field behavior. Flow structures become cellular, and correlation lengths scale with the particle size. Here, translational motion is suppressed, while rotational dynamics dominate. These findings highlight the limitations of dilute mean-field models and reveal new behaviors in dense active suspensions.

We examine theoretically the flow interactions and forward flight dynamics of tandem or in-line flapping wings. Two wings are driven vertically with prescribed heaving-and-plunging motions, and the horizontal propulsion speeds and positions are dynamically selected through aero- or hydro-dynamic interactions. Our simulations employ an improved vortex sheet method to solve for the locomotion of the pair within the collective flow field, and we identify 'schooling states' in which the wings travel together with nearly constant separation. Multiple terminal configurations are achieved by varying the initial conditions, and the emergent separations are approximately integer multiples of the wavelength traced out by each wing. We explain the stability of these states by perturbing the follower and mapping out an effective potential for its position in the leader's wake. Each equilibrium position is stabilized since smaller separations are associated with in-phase follower-wake motions that constructively reinforce the flow but lead to decreased thrust on the follower; larger separations are associated with antagonistic follower-wake motions, increased thrust, and a weakened collective wake. The equilibria and their stability are also corroborated by a linearized theory for the motion of the leader, the wake it produces, and its effect on the follower. We also consider a weakly-flapping follower driven with lower heaving amplitude than the leader. We identify 'keep-up' conditions for which the wings may still 'school' together despite their dissimilar kinematics, with the 'freeloading' follower passively assuming a favorable position within the wake that permits it to travel significantly faster than it would in isolation.

Time-resolved single-cell omics data offers high-throughput, genome-wide measurements of cellular states, which are instrumental to reverse-engineer the processes underpinning cell fate. Such technologies are inherently destructive, allowing only cross-sectional measurements of the underlying stochastic dynamical system. Furthermore, cells may divide or die in addition to changing their molecular state. Collectively these present a major challenge to inferring realistic biophysical models. We present a novel approach, \emph{unbalanced} probability flow inference, that addresses this challenge for biological processes modelled as stochastic dynamics with growth. By leveraging a Lagrangian formulation of the Fokker-Planck equation, our method accurately disentangles drift from intrinsic noise and growth. We showcase the applicability of our approach through evaluation on a range of simulated and real single-cell RNA-seq datasets. Comparing to several existing methods, we find our method achieves higher accuracy while enjoying a simple two-step training scheme.