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1. Using tensor network states for multi-particle Brownian ratchets

   https://doi.org/10.1063/5.0097332  

   Strand, Nils E.; Vroylandt, Hadrien; Gingrich, Todd R. (June 2022, The Journal of Chemical Physics)

   The study of Brownian ratchets has taught how time-periodic driving supports a time-periodic steady state that generates nonequilibrium transport. When a single particle is transported in one dimension, it is possible to rationalize the current in terms of the potential, but experimental efforts have ventured beyond that single-body case to systems with many interacting carriers. Working with a lattice model of volume-excluding particles in one dimension, we analyze the impact of interactions on a flashing ratchet’s current. To surmount the many-body problem, we employ the time-dependent variational principle applied to binary tree tensor networks. Rather than propagating individual trajectories, the tensor network approach propagates a distribution over many-body configurations via a controllable variational approximation. The calculations, which reproduce Gillespie trajectory sampling, identify and explain a shift in the frequency of maximum current to higher driving frequency as the lattice occupancy increases. 

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2. Chemical master equation parameter exploration using DMRG

   https://doi.org/10.1063/5.0276591  

   Zima, John P; Nicholson, Schuyler B; Gingrich, Todd R (August 2025, The Journal of Chemical Physics)

   Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories, there is interest in systematically approximating the joint distribution over the exponentially large number of possible microstates using tensor networks or tensor trains. We exploit the tensor network strategy to determine when the steady state of a seven-species gene toggle switch CRN model supports bistability as a function of two decomposition rates, both parameters of the kinetic model. We highlight how the tensor network solution captures the effects of stochastic fluctuations, going beyond mean field and indeed deviating meaningfully from a mean-field analysis. The work furthermore develops and demonstrates several technical advances that will allow steady-states of broad classes of CRNs to be computed in a manner conducive to parameter exploration. We show that the steady-state distributions can be computed via the ordinary density matrix renormalization group (DMRG) algorithm, despite having a non-Hermitian rate operator with a small spectral gap, we illustrate how that steady-state distribution can be efficiently projected to an order parameter that identifies bimodality, and we employ excited-state DMRG to calculate a relaxation timescale for the bistability. 

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3. Steady-State Convergence of Discrete Time State-Space Modeling with State-Dependent Switching

   https://doi.org/10.1109/COMPEL49091.2020.9265734  

   Baxter, Jared A.; Costinett, Daniel J. (November 2020, 2020 IEEE 21st Workshop on Control and Modeling for Power Electronics (COMPEL))

   null (Ed.)

   Steady-state modeling plays an important role in the design of advanced power converters. Typically, steady-state modeling is completed by time-stepping simulators, which may be slow to converge to steady-state, or by dedicated analysis, which is time-consuming to develop across multiple topologies. Discrete time state-space modeling is a uniform approach to rapidly simulate arbitrary power converter designs. However, the approach requires modification to capture state-dependent switching, such as diode switching or current programmed modulation. This work provides a framework to identify and correct state-dependent switching within discrete time state-space modeling and shows the utility of the proposed method within the power converter design process. 

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4. Driven responses of periodically patterned superconducting films

   Al Luhaibi, A.; Glatz, A; Ketterson, J. B. (December 2024, Physical Review B: Solid state)

   We simulate the motion of a commensurate vortex lattice in a periodic lattice of artificial circular pinning sites having different diameters, pinning strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density Jc, the vortices depin, and the resulting steady-state motion then induces an oscillatory electric field E (t) with a defect "hopping" frequency f0, which depends on the applied current density and the pinning landscape characteristics. The frequency generated can be locked to an applied AC current density over some range of frequencies, which depends on the amplitude of the DC as well as the AC current densities. Both synchronous and asynchronous collective hopping behaviors are studied as a function of the supercell size of the simulated system and the (asymptotic) synchronization threshold current densities determined. 

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5. Creation of a novel inverted charge density wave state

   https://doi.org/10.1063/4.0000132  

   Zhang, Yingchao; Shi, Xun; Guan, Mengxue; You, Wenjing; Zhong, Yigui; Kafle, Tika_R; Huang, Yaobo; Ding, Hong; Bauer, Michael; Rossnagel, Kai; et al (January 2022, Structural Dynamics)

   Charge density wave (CDW) order is an emergent quantum phase that is characterized by periodic lattice distortion and charge density modulation, often present near superconducting transitions. Here, we uncover a novel inverted CDW state by using a femtosecond laser to coherently reverse the star-of-David lattice distortion in 1T-TaSe2. We track the signature of this novel CDW state using time- and angle-resolved photoemission spectroscopy and the time-dependent density functional theory to validate that it is associated with a unique lattice and charge arrangement never before realized. The dynamic electronic structure further reveals its novel properties that are characterized by an increased density of states near the Fermi level, high metallicity, and altered electron–phonon couplings. Our results demonstrate how ultrafast lasers can be used to create unique states in materials by manipulating charge-lattice orders and couplings. 

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