arXiv subjects

Zeyu Zhou

Publications and source records attributed to Zeyu Zhou.

32 records · Page 2Linked to original sources

arXiv2023

An operator-splitting optimization approach for phase-field simulation of equilibrium shapes of crystals

Computing equilibrium shapes of crystals (ESC) is a challenging problem in materials science that involves minimizing an orientation-dependent (i.e., anisotropic) surface energy functional subject to a prescribed mass constraint. The highly nonlinear and singular anisotropic terms in the problem make it very challenging from both the analytical and numerical aspects. Especially, when the strength of anisotropy is very strong (i.e., strongly anisotropic cases), the ESC will form some singular, sharp corners even if the surface energy function is smooth. Traditional numerical approaches, such as the $H^{-1}$ gradient flow, are unable to produce true sharp corners due to the necessary addition of a high-order regularization term that penalizes sharp corners and rounds them off. In this paper, we propose a new numerical method based on the Davis-Yin splitting (DYS) optimization algorithm to predict the ESC instead of using gradient flow approaches. We discretize the infinite-dimensional phase-field energy functional in the absence of regularization terms and transform it into a finite-dimensional constraint minimization problem. The resulting optimization problem is solved using the DYS method which automatically guarantees the mass-conservation and bound-preserving properties. We also prove the global convergence of the proposed algorithm. These desired properties are numerically observed. In particular, the proposed method can produce real sharp corners with satisfactory accuracy. Finally, we present numerous numerical results to demonstrate that the ESC can be well simulated under different types of anisotropic surface energies, which also confirms the effectiveness and efficiency of the proposed method.

math.NA↗

arXiv2023

On the nature of polariton transport in a Fabry-Perot Cavity

Fabry-Perot microcavities can strongly enhance interactions between light and molecules, leading to the formation of hybrid light-matter states known as polaritons. Polaritons possess much smaller effective masses and much larger group velocities when the molecules are resonant with cavity modes that have finite (non-zero) in-plane wavevectors, giving rise to the possibilities of long-range and ultrafast ballistic transport. In this paper, we present results of numerical simulations of the ultrafast ballistic transport phenomenon in real space and time during and after initialization with a short, spatially localized pulse. We find that the transport of the molecular excitons as induced by the external light field is synchronized with the evolution of the enhanced and localized electromagnetic field inside the cavity. Moreover, the synchronized transport rate is in good agreement with the group velocities predicted from a calculated dispersion relation across a wide range of frequencies. These simulations provide an intuitive tool for understanding the collective motion of light and excitons and helps to better understand how experimental observations of polaritons should be interpreted.

physics.chem-ph↗

arXiv2023

On the nature of two-photon transitions for a Collection of Molecules in a Fabry-Perot Cavity

We investigate the effect of a cavity on nonlinear two-photon transitions of a molecular system and how such an effect depends on the cavity quality factor, the field enhancement and the possibility of dephasing. We find that the molecular response to strong light fields in a cavity with variable quality factor can be understood as arising from a balance between (i) the ability of the cavity to enhance the field of an external probe and promote multiphoton transitions more easily and (ii) the fact that the strict selection rules on multiphoton transitions in a cavity support only one resonant frequency within the excitation range. Although our simulations use a classical-level description of the radiation field (i.e. we solve Maxwell-Bloch or Maxwell-Liouville equations within the Ehrenfest approximation for the field-molecule interaction), based on experience with this level of approximation in past studies of plasmonic and polaritonic systems, we believe that our results are valid over a wide range of external probing.

quant-ph↗

arXiv2022

The Interplay between Disorder, Local Relaxation and Collective Behaviors for an ensemble of emitters outside vs inside cavity

The interplay between collective optical response and molecular static and dynamic disorder is studied using simple effective Hamiltonians for an ensemble of two-level emitters inside and outside a single-mode cavity. We model environmental disorder by randomly modulating the molecular transition frequencies and the coupling between the emitters and the electromagnetic field. We also consider effects of intermolecular interactions and orientational disorder. We investigate how these effects lead to new features in the steady state absorption (outside the cavity), transmission spectra (inside the cavity) and the yield of local molecular processes such as a unimolecular reaction. Outside the cavity, the collective behavior is manifested in the linewidth of the steady state absorption, the emission spectrum, and the local chemical yield. Inside the cavity, however, the collective behavior primarily determines the Rabi splitting. Effects of intermolecular interactions under orientational disorder are also studied. For the most part, for all types of disorder, if we increase disorder, we find a reduction in the collective nature of the molecular response (smaller effective N), and therefore, the Rabi splitting contraction occurs with orientational disorder. Moreover, we find that static disorder is more destructive to collective behavior than dynamic disorder.

physics.chem-ph↗

arXiv2022

Non-adiabatic Dynamics in a Continuous Circularly Polarized Laser Field with Floquet Phase-space Surface Hopping

Non-adiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly) polarized light allows one to effectively introduce a complex-valued time-dependent Hamiltonian, which offers a new path for control or exploration through the introduction of Berry forces. Here, we investigate several inexpensive semiclassical approaches for modeling such nonadiabatic dynamics in the presence of a time-dependent complex-valued Hamiltonian, beginning with a straightforward instantaneous adiabatic fewest-switches surface hopping (IA-FSSH) approach (where the electronic states depend on position and time), continuing to a standard Floquet fewest switches surface hopping (F-FSSH) approach (where the electronic states depend on position and frequency), and ending with an exotic Floquet phase-space surface hopping (F-PSSH) approach (where the electronic states depend on position, frequency, and momentum). Using a set of model systems with time-dependent complex-valued Hamiltonians, we show that the Floquet phase-space adiabats are the optimal choice of basis as far as accounting for Berry phase effects and delivering accuracy. Thus, the F-PSSH algorithm sets the stage for modeling nonadiabatic dynamics under strong externally pumped circular polarization in the future.

physics.chem-ph↗

arXiv2022

A regularized model for wetting/dewetting problems: asymptotic analysis and $Γ$-convergence

By introducing height dependency in the surface energy density, we propose a novel regularized variational model to simulate wetting/dewetting problems. The regularized model leads to the appearance of a precursor layer which covers the bare substrate, with the precursor height depending on the regularization parameter $\varepsilon$. The new model enjoys lots of advantages in analysis and imulations. With the help of the precursor layer, the regularized model is naturally extended to a larger domain than that of the classical sharp-interface model, and thus can be solved in a fixed domain. There is no need to explicitly track the contact line motion, and difficulties arising from free boundary problems can be avoided. In addition, topological change events can be automatically captured. Under some mild and physically meaningful conditions, we show the positivity-preserving property of the minimizers of the new model. By using asymptotic analysis and $Γ$-convergence, we investigate the convergence relations between the new regularized model and the classical sharp-interface model. Finally, numerical results are provided to validate our theoretical analysis, as well as the accuracy and efficiency of the new regularized model.

math.AP↗

arXiv2022

Interplay Between Disorder and Collective Coherent Response: Superradiance and Spectral Motional Narrowing in the Time Domain

The interplay between static and dynamic disorder and collective optical response in molecular ensembles is an important characteristic of nanoplasmonic and nanophotonic molecular systems. Here we investigate the cooperative superradiant response of a molecular ensemble of quantum emitters under the influence of environmental disorder, including inhomogeneous broadening (as induced by static random distribution of the molecular transition frequencies) and motional narrowing (as induced by stochastic modulation of these excitation energies). The effect of inhomogeneous broadening is to destroy the coherence of the collective molecular excitation and suppress superradiant emission. However, fast stochastic modulation of the molecular excitation energy can effectively restore the coherence of the quantum emitters and lead to a recovery of superradiant emission, which is an unexpected manifestation of motional narrowing. For a light scattering process as induced by an off-resonant incident pulse, stochastic modulation leads to inelastic fluorescence emission at the average excitation energy at long times and suggests that dynamic disorder effects can actually lead to collective excitation of the molecular ensemble.

physics.optics↗

arXiv2022

Iterative Alignment Flows

The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate multiple flows independently, which is equivalent to learning multiple full generative models. Other approaches require adversarial learning, which can be computationally expensive and challenging to optimize. Thus, we aim to jointly align multiple distributions while avoiding adversarial learning. Inspired by efficient alignment algorithms from optimal transport (OT) theory for univariate distributions, we develop a simple iterative method to build deep and expressive flows. Our method decouples each iteration into two subproblems: 1) form a variational approximation of a distribution divergence and 2) minimize this variational approximation via closed-form invertible alignment maps based on known OT results. Our empirical results give evidence that this iterative algorithm achieves competitive distribution alignment at low computational cost while being able to naturally handle more than two distributions.

cs.LG↗

arXiv2020

On the Proper Derivation of the Floquet-based Quantum Classical Liouville Equation and Surface Hopping Describing a Molecule or Material Subject to an External Field

We investigate two approaches to derive the proper Floquet-based quantum-classical Liouville equation (F-QCLE) for laser-driven electron-nuclear dynamics. The first approach projects the operator form of the standard QCLE onto the diabatic Floquet basis, then transforms to the adiabatic representation. The second approach directly projects the QCLE onto the Floquet adiabatic basis. Both approaches yield a form which is similar to the usual QCLE with two modifications: 1. The electronic degrees of freedom are expanded to infinite dimension. 2. The nuclear motion follows Floquet quasi-energy surfaces. However, the second approach includes an additional cross derivative force due to the dual dependence on time and nuclear motion of the Floquet adiabatic states. Our analysis and numerical tests indicate that this cross derivative force is a factitious artifact, suggesting that one cannot safely exchange the order of Floquet state projection with adiabatic transformation. Our results are in accord with similar findings by Izmaylov et al., who found that transforming to the adiabatic representation must always be the last operation applied, though now we have extended this result to a time-dependent Hamiltonian. This paper and the proper derivation of the F-QCLE should lay the basis for further improvements of Floquet surface hopping.

physics.chem-ph↗

arXiv2020

A Protocol for Spectroscopists to Isolate The Effect of Berry Geometric Magnetic Forces on Molecular Dynamics

We propose a novel means to isolate and quantify the effects of Berry force on molecular dynamics using two reasonably strong continuous wave (CW) laser fields with frequencies $ω$ and $2ω$. For molecules or materials with three frequency-matching bright transitions ($|{0}\rangle\rightarrow|{1}\rangle$, $|{1}\rangle\rightarrow|{2}\rangle$, $|{0}\rangle\rightarrow|{2}\rangle$) at frequencies ($ω$, $ω$, $2ω$) respectively, the effects of Berry curvature can be isolated by varying the phase between the two laser fields ($Δϕ$) and monitoring the dynamics. Moreover, we find that the resulting chemical dynamics can depend critically on the sign of $Δϕ$; in other words, the effects of Berry curvature can be enormous. Thus, this manuscript represents an unusual step forward towards using light-matter interactions to affect chemical dynamics, suggesting that topological concepts usually invoked in adiabatic quantum optics and condensed matter can be directly applied to non-adiabatic chemical excited state dynamics.

physics.chem-ph↗

arXiv2019

Non-adiabatic Dynamics in a Laser Field with Floquet Fewest Switches Surface Hopping: The Need for An Accurate Treatment of Coherence and Decoherence Remains

We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard adiabatic states, which just happen to evolve in time. The second formalism replaces the role of the usual adiabatic states by the time-independent adiabatic Floquet states. For a set of modified Tully model problems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for both transmission and reflection probabilities than the instantaneous adiabatic FSSH (IA-FSSH) formalism. More importantly, only F-FSSH predicts the correct final scattering momentum. Finally, in order to use Floquet theory accurately, we find that it is crucial to account for the interference between Floquet states. Our results should be of interest to all those interested in laser induced molecular dynamics.

physics.chem-ph↗

arXiv2019

A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the cases of Trivial & Near Trivial Crossings

We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon consideration of the overlap matrix ($\mathbf{U}$) between basis functions at successive points in time and selecting the phases so as to minimize the matrix norm of $\log(\mathbf{U})$. In so doing, one can extend the concept of parallel transport to cases with sharp curve crossings. We demonstrate that this algorithm performs well under extreme situations where dozens of states cross each other either through trivial crossings (where there is zero effective diabatic coupling), or through nontrivial crossings (when there is a nonzero diabatic coupling), or through a combination of both. In all cases, we compute the time-derivative coupling matrix elements (or equivalently non-adiabatic derivative coupling matrix elements) that are as smooth as possible. Our results should be of interest to all who are interested in either non-adiabatic dynamics, or more generally, parallel transport in large systems.

physics.chem-ph↗

arXiv2019

Active Suppression of Microphonics Detuning in high $Q_L$ Cavities

Operation of Superconducting Radio Frequency (SRF) cavities with high loaded quality factors is becoming increasingly preferred for applications which involve low beam loading including Energy Recovery Linacs (ERL). Vibration induced microphonics detuning poses a major operational bottleneck in these low bandwidth systems, adversely affecting field stability. Besides passive measures of mitigating the vibration sources, modern SRF cavities are also attached to fast tuners incorporating piezo-electric actuators. We demonstrate the narrow band active noise control algorithm for realizing active resonance control and propose a modification based on the Least Mean Square approach to adaptively tune the control parameters and study it's stability and performance. We discuss our experience of using passive mitigation techniques while commissioning the Main Linac Cryomodule of the Cornell-BNL ERL Test Accelerator (CBETA) and report a net reduction in peak detuning by more than a factor of 2 in its unstiffened cavities. Finally, we demonstrate stable performance of our resonance control system with consistent reduction of peak microphonics detuning by almost a factor of 2 on multiple cavities.

physics.acc-ph↗

arXiv2018

Per-Flow Cardinality Estimation Based On Virtual LogLog Sketching

Flow cardinality estimation is the problem of estimating the number of distinct elements in a data flow, often with a stringent memory constraint. It has wide applications in network traffic measurement and in database systems. The virtual LogLog algorithm proposed recently by Xiao, Chen, Chen and Ling estimates the cardinalities of a large number of flows with a compact memory. The purpose of this thesis is to explore two new perspectives on the estimation process of this algorithm. Firstly, we propose and investigate a family of estimators that generalizes the original vHLL estimator and evaluate the performance of the vHLL estimator compared to other estimators in this family. Secondly, we propose an alternative solution to the estimation problem by deriving a maximum-likelihood estimator. Empirical evidence from both perspectives suggests the near-optimality of the vHLL estimator for per-flow estimation, analogous to the near-optimality of the HLL estimator for single-flow estimation.

cs.IT↗