Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computational complexity while retaining high accuracy. We formally study LDR matrices in deep learning. First, we prove the universal approximation property of LDR neural networks with a mild condition on the displacement operators. We then show that the error bounds of LDR neural networks are as efficient as general neural networks with both single-layer and multiple-layer structure. Finally, we propose back-propagation based training algorithm for general LDR neural networks.

We report the coexistence of Aharonov-Bohm and Little-Parks oscillations in mesoscopic Fe(Te,Se) rings. The magnetoresistance shows two distinct periodicities: an $h/e$ component from ballistic edge interference and an $h/2e$ component from fluxoid quantization of Cooper pairs. Aharonov-Bohm oscillations persist deep into the superconducting phase, exhibit current-field symmetry, and follow a temperature dependence captured by a helical Luttinger liquid model, consistent with edge states in a topological superconductor.

Strong spatial confinement and highly reduced dielectric screening provide monolayer transition metal dichalcogenides (TMDCs) with strong many-body effects, thereby possessing optically forbidden excitonic states (i.e., dark excitons) at room temperature. Herein, we explore the interaction of surface plasmons with dark excitons in hybrid systems consisting of stacked gold nanotriangles (AuNTs) and monolayer WS2. We observe a narrow Fano resonance when the hybrid system is surrounded by water, and we attribute the narrowing of the spectral Fano linewidth to the plasmon-enhanced decay of dark K-K excitons. Our results reveal that dark excitons in monolayer WS2 can strongly modify Fano resonances in hybrid plasmon-exciton systems and can be harnessed for novel optical sensors and active nanophotonic devices.

In this article, it is pointed out that Faraday induction can be treated from an untraditional, particle-based point of view. The electromagnetic fields of Faraday induction can be calculated explicitly from approximate point-charge fields derived from the Li\'enard-Wiechert expressions or from the Darwin Lagrangian. Thus the electric fields of electrostatics, the magnetic fields of magnetostatics, and the electric fields of Faraday induction can all be regarded as arising from charged particles. Some aspects of electromagnetic induction are explored for a hypothetical circuit consisting of point charges which move frictionlessly in a circular orbit. For a small number of particles in the circuit (or for non-interacting particles), the induced electromagnetic fields depend upon the mass and charge of the current carriers while energy is transferred to the kinetic energy of the particles. However, for an interacting multiparticle circuit, the mutual electromagnetic interactions between the particles dominate the behavior so that the induced electric field cancels the inducing force per unit charge, the mass and charge of the individual current carriers become irrelevant, and energy goes into magnetic energy.

We study the Yu-Shiba-Rusinov states in materials with bulk band inversion such as iron-based topological superconductors or doped topological insulators. We show that the structure of the YSR state spectrum depends on the doping level relative to the chemical potential at which the band-inversion occurs. Moreover, we demonstrate that the transition from ferromagnetic to antiferromagnetic coupling and vice versa, which is caused by the coupling of magnetic impurities through the overlap of YSR states, is highly dependent on the doping level. Additionally, topological edge states may have a substantial impact on the YSR states, leading to a decrease in YSR state energies and the creation of new states when the magnetic impurity approaches the boundary.

It is pointed out that an electric charge oscillating in a one-dimensional purely-harmonic potential is in detailed balance at its harmonics with a radiation bath whose energy $U_{rad}$ per normal mode is linear in frequency $\omega$, $U_{rad}=const\times\omega,$ and hence is Lorentz invariant, as seems appropriate for relativistic electromagnetism. The oscillating charge is NOT in equilibrium with the Rayleigh-Jeans spectrum which arises from energy-sharing equipartition ideas which are valid only in nonrelativistic mechanics. Here we explore the contrasting behavior of harmonic oscillators connected to baths in classical mechanics and electromagnetism. It is emphasized that modern physics text are in error in suggesting that the Rayleigh-Jeans spectrum corresponds to the equilibrium spectrum of random classical radiation, and in ignoring Lorentz-invariant classical zero-point radiation which is indeed a classical equilibrium spectrum.

We present molecular dynamics computer simulations of filaments of model non-Newtonian liquid stretched in a uniaxial deformation to the point of breaking. The liquid consists of Lennard-Jones monomers bound into chains of 100 monomers by nonlinear springs, and several different constant velocity and constant strain rate deformations are considered. Generally we observe nonuniform extensions originating in an interplay between the stretching forces and elastic and capillary restoring mechanisms, leading to highly uneven shapes and alternating stretched and unstretched regions of liquid. Except at the fastest pulling speeds, the filaments continue to thin indefinitely and break only when depleted of molecules, rather than common viscoelastic rupture mechanisms.

The NV$^{-}$ color center in diamond has been demonstrated as a nanoscale sensor for quantum metrology. However, the properties that make it ideal for measuring, e.g., minute electric and magnetic fields also make it sensitive to imperfections in the diamond host. In this work, we quantify the impact of nearby native defects on the many-body states of NV$^{-}$. We combine previous quantum embedding results of strain and electric-field susceptibilities of NV$^{-}$ with density-functional theory calculations on native defects. The latter are used to parametrize continuum models in order to extrapolate the effects of native defects up to the micrometer scale. We show that under ideal measuring conditions, the optical properties of NV$^{-}$ are measurably affected by the strain caused by single carbon interstitials and vacancies up to 200 nm away; in contrast, the NV$^{-}$ is measurably affected by the electric field of such charged (neutral) native defects within a micron (100 nm). Finally, we show how measuring multiple individual NV$^{-}$ centers in the vicinity of a native defect can be used to determine the nature of the defect and its charge state.

Bell's Theorem proved that one cannot in general reproduce the results of quantum theory with a classical, deterministic local model. However, Einstein originally considered the case where one could define an 'element of reality', namely for the much simpler case where one could predict with certainty a definite outcome for an experiment. For this simple case, Bell's Theorem says nothing. But by using a slightly more complicated model than Bell, one can show that even in this simple case where one can make definite predictions, one still cannot generally introduce deterministic, local models to explain the results.

Based upon thermodynamic ideas, two new derivations of the Planck blackbody spectrum are given within classical physics which includes classical zero-point radiation. The first and second laws of thermodynamics, applied to a harmonic oscillator or a radiation normal mode, require that the canonical potential $\phi(\omega/T)$ is a function of a single variable corresponding to the ratio of the oscillation frequency to the temperature. The second law of thermodynamics involves extremum ideas which may be applied to thermal radiation. Our first derivation of the Planck spectrum is based upon the idea that the canonical potential $\phi(\omega/T)$ is a monotonic function and all its derivatives are monotonic when interpolating between zero-point energy at low temperature and energy equipartition at high temperature; the monotonic behavior precludes the canonical potential from giving a preferred value for the ratio $\omega/T.$ Our second derivation of the Planck spectrum is based upon the requirement that the change in the Helmholtz free energy of the radiation in a partitioned box held at constant temperature should be a minimum at thermal equilibrium. Finally, the change in Casimir energy with change in partition position for the radiation in a partitioned box is shown to correspond at high temperature to the absence of zero-point energy when the spectral energy per normal mode is chosen as the traditional Planck spectrum which omits zero-point energy at low temperature; thus the idea of zero-point energy is embedded in the traditional Planck spectrum. It is emphasized that thermal radiation is intimately connected with zero-point radiation and the structure of spacetime in classical physics.

We use Stokesian Dynamics simulations to study the microscopic motion of particles suspended in fluids passing through porous media. We construct model porous media with fixed spherical particles, and allow mobile ones to move through this fixed bed under the action of an ambient velocity field. We first consider the pore scale motion of individual suspended particles at pore junctions. The relative particle flux into different possible directions exiting from a single pore, for two and three dimensional model porous media is found to approximately equal the corresponding fractional channel width or area. Next we consider the waiting time distribution for particles which are delayed in a junction, due to a stagnation point caused by a flow bifurcation. The waiting times are found to be controlled by two-particle interactions, and the distributions take the same form in model porous media as in two-particle systems. A simple theoretical estimate of the waiting time is consistent with the simulations. We also find that perturbing such a slow-moving particle by another nearby one leads to rather complicated behavior. We study the stability of geometrically trapped particles. For simple model traps, we find that particles passing nearby can ``relaunch'' the trapped particle through its hydrodynamic interaction, although the conditions for relaunching depend sensitively on the details of the trap and its surroundings.

Mechanical motion can break the symmetry in which sound travels in a medium, but significant non-reciprocity is typically achieved only for very large motion speeds. Here we combine moving media with zero-index acoustic propagation, yielding extreme non-reciprocity and induced bianisotropy for modest applied speeds. The metamaterial is formed by an array of waveguides loaded by Helmholtz resonators, and it exhibits opposite signs of the refractive index sustained by asymmetric Willis coupling for propagation in opposite directions. We use this response to design a non-reciprocal acoustic lens focusing only when excitation from one side, with applications for imaging and ultrasound technology.

The NV$^{-}$ color center in diamond has been demonstrated as a powerful nanosensor for quantum metrology due to the sensitivity of its optical and spin properties to external electric, magnetic, and strain fields. In view of these applications, we use quantum embedding to derive a many-body description of strain and charge induced Stark effects on the NV$^{-}$ center. We quantify how strain longitudinal to the axis of NV$^{-}$ shifts the excited states in energy, while strain with a component transverse to the NV$^{-}$ axis splits the degeneracies of the $^{3}E$ and $^{1}E$ states. The largest effects are for the optically relevant $^{3}E$ manifold, which splits into $E_{x}$ and $E_{y}$ with transverse strain. From these responses we extract strain susceptibilities for the $E_{x/y}$ states within the quasi-linear regime. Additionally, we study the many-body dipole matrix elements of the NV$^{-}$ and find a permanent dipole 1.64 D at zero strain, which is somewhat smaller than that obtained from recent density functional theory calculations. We also determine the transition dipole between the $E_{x}$ and $E_{y}$ and how it evolves with strain.

We analyze the interaction between a self-diffusiophoretic spherical Janus motor and an inert spherical cargo particle in an axisymmetric configuration in the Stokes regime. To study the different configurations of the two spheres and their motions, we develop an analog to the twin multipole approach to numerically determine the axisymmetric stream function for the flow field. We verify the validity and accuracy of this approach using existing literature and COMSOL Multiphysics. We study the effects of the size of the Janus cap, the relative ratio of sizes of the two spheres, and their separation distance on their interactions. For the case of a stationary cargo, we identify the existence of a distinct regime where the Janus motor hovers at a finite separation distance from the cargo and summarize the results using a phase diagram. In the presence of a freely moving cargo, we analyze the steady terminal velocities of the Janus motor and the cargo to identify distinct conditions at which the two spheres can translate with equal velocities while maintaining a finite separation distance.

We study the effects of strain on exciton dynamics in transition metal dichalcogenides (TMDs). Using the Bethe-Salpeter formalism, we derive the exciton dispersion relation in strained TMDs and demonstrate that strain-induced pseudo-gauge fields significantly influence exciton transport and interactions. Our results show that low-energy excitons occur at finite center-of-mass momentum, leading to modified diffusion properties. Furthermore, the exciton dipole moment depends on center-of-mass momentum, which enhances exciton-exciton interactions. These findings highlight the potential of strain engineering as a powerful tool for controlling exciton transport and interactions in TMD-based optoelectronic and quantum devices.

Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall (FQH) phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the non-perturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that captures the geometric properties and graviton dynamics of FQH states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimally-compiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimal-control-based variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.

We introduce a novel method for the renormalization of the Hamiltonian operator in Quantum Field Theory in the spirit of the Wilson renormalization group. By a series of unitary transformations that successively decouples the high-frequency degrees of freedom and partially diagonalizes the high-energy part, we obtain the effective Hamiltonian for the low energy degrees of freedom. We successfully apply this technique to compute the 2-loop renormalized Hamiltonian in scalar $\lambda \phi^4$ theory.

Using a novel approach to renormalization in the Hamiltonian formalism, we study the connection between asymptotic freedom and the renormalization group flow of the configuration space metric. It is argued that in asymptotically free theories the effective distance between configuration decreases as high momentum modes are integrated out.

Sub-wavelength nanostructured systems with tunable electromagnetic properties, such as hyperbolic metamaterials (HMMs), provide a useful platform to tailor spontaneous emission processes. Here, we investigate a system comprising $Eu^{ 3+}(NO_{3})_{3}6H_{2}O$ nanocrystals on an HMM structure featuring a hexagonal array of Ag-nanowires in a porous $Al_{2}O_{3}$ matrix. The HMM-coupled $Eu^{ 3+}$ ions exhibit up to a 2.4-fold increase of their decay rate, accompanied by an enhancement of the emission rate of the $^{ 5}D_{0}\rightarrow$ $^{ 7}F_{2}$ transition. Using finite-difference time-domain modeling, we corroborate these observations with the increase in the photonic density of states seen by the $Eu^{ 3+}$ ions in the proximity of the HMM. Our results indicate HMMs can serve as a valuable tool to control the emission from weak transitions, and hence hint at a route towards more practical applications of rare-earth ions in nanoscale optoelectronics and quantum devices.

I consider quantum field theories that admit charged non-topological solitons of the Q-ball type, and use the fact that in a first-order cosmological phase transition, below the critical temperature, there is a value of the soliton charge above which the soliton becomes unstable and expands, converting space to the true vacuum, much like a critical bubble in the case of ordinary tunneling. Using a simple model for the production rate of Q-balls through charge accretion during a random walk out of equilibrium, I calculate the probability for the formation of critical charge solitons and estimate the amount of supercooling needed for the phase transition to be completed.