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1. Wave Excitation and Dynamics in Non-Hermitian Disordered Systems

   https://doi.org/10.1103/PhysRevResearch.4.013102  

   Huang, Y.; Kang, Yuhao; Genack, Azriel Z. (February 2022, Physical review research)

   Dynamic and steady-state aspects of wave propagation are deeply connected in lossless open systems ‎in which the scattering matrix is unitary. There is then an equivalence among the energy excited within ‎the medium through all channels, the Wigner time delay, which is the sum of dwell times in all ‎channels coupled to the medium, and the density of states. But these equivalences fall away in the ‎presence of material loss or gain. In this paper, we use microwave measurements, numerical ‎simulations, and theoretical analysis to discover the changing relationships among fundamental wave ‎properties with loss and gain, and their dependence upon dimensionality and spectral overlap. We ‎begin with the demonstrations that the transmission time in random 1D media is equal to the density ‎of states even in the presence of ultrastrong absorption and that its ensemble average is independent ‎of the strengths of scattering and absorption. In contrast, the Wigner time becomes imaginary in the ‎presence of loss, with real and imaginary parts that fall with absorption. In multichannel media, the ‎transmission time remains equal to the density of states and is independent of the scattering strength ‎in unitary systems but falls with absorption to a degree that increases with the strengths of absorption ‎and scattering, and the number of channels coupled to the medium. We show that the relationships ‎between key propagation variables in non-Hermitian systems can be understood in terms of the ‎singularities of the phase of the determinant of the transmission matrix. The poles of the transmission ‎matrix are the same as those of the scattering matrix, but the transmission zeros are fundamentally ‎different. Whereas the zeros of the scattering matrix are the complex conjugates of the poles, the ‎transmission zeros are topological: in unitary systems they occur only singly on the real axis or as ‎conjugate pairs. We follow the evolution and statistics of zeros in the complex plane as random ‎samples are deformed. The sensitivity of the spacing of zeros in the complex plane with deformation ‎of the sample has a square-root singularity at a zero point at which two single zeros and a complex ‎pair interconvert. The transmission time is a sum of Lorentzian functions associated with poles and ‎zeros. The sum over poles is the density of states with an average that is independent of scattering ‎and dissipation. But the sum over zeros changes with loss, gain, scattering strength and the number of ‎channels in ways that make it possible to control ultranarrow spectral features in transmission and ‎transmission time. We show that the field, including the contribution of the still coherent incident ‎wave, is a sum over modal partial fractions with amplitudes that are independent of loss and gain. The ‎energy excited may be expressed in terms of the resonances of the medium and is equal to the dwell ‎time even in the presence of loss or gain.‎ 

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2. Velocities of transmission eigenchannels and diffusion

   https://doi.org/10.1038/s41467-024-46748-0  

   Genack, Azriel Z.; Huang, Yiming; Maor, Asher; Shi, Zhou (March 2024, Nature Communications)

   Abstract The diffusion model is used to calculate both the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered samples, such as a layer of paint or a tissue sample, the flux transmitted through the sample may be dramatically enhanced or suppressed relative to predictions of diffusion theory when the sample is excited by a waveform corresponding to a transmission eigenchannel. Even so, it is widely assumed that the velocity of waves is irretrievably randomized in scattering media. Here we demonstrate in microwave measurements and numerical simulations that the statistics of velocity of different transmission eigenchannels are distinct and remains so on all length scales and are identical on the incident and output surfaces. The interplay between eigenchannel velocities and transmission eigenvalues determines the energy density within the medium, the diffusion coefficient, and the dynamics of propagation. The diffusion coefficient and all scattering parameters, including the scattering mean free path, oscillate with the width of the sample as the number and shape of the propagating channels in the medium change. 

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3. Determination of short-range order in TiVNbHf(Al)

   https://doi.org/10.1063/5.0145289  

   Xu, Michael; Wei, Shaolou; Tasan, C_Cem; LeBeau, James_M (May 2023, Applied Physics Letters)

   The presence of short-range chemical order can be a key factor in determining the mechanical behavior of metals, but directly and unambiguously determining its distribution in complex concentrated alloy systems can be challenging. Here, we directly identify and quantify chemical order in the globally single phase BCC-TiVNbHf(Al) system using aberration corrected scanning transmission electron microscopy (STEM) paired with spatial statistics methods. To overcome the difficulties of short-range order (SRO) quantification with STEM when the components of an alloy exhibit large atomic number differences and near equiatomic ratios, “null hypothesis” tests are used to separate experiment from a random chemical distribution. Experiment is found to deviate from both the case of an ideal random solid solution and a fully ordered structure with statistical significance. We also identify local chemical order in TiVNbHf and confirm and quantify the enhancement of SRO with the addition of Al. These results provide insight into local chemical order in the promising TiVNbHf(Al) refractory alloys while highlighting the utility of spatial statistics in characterizing nanoscale SRO in compositionally complex systems. 

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4. On the number variance of zeta zeros and a conjecture of Berry

   https://doi.org/10.1112/mtk.12184  

   Lugar, Meghann Moriah; Milinovich, Micah B.; Quesada‐Herrera, Emily (January 2023, Mathematika)

   Abstract Assuming the Riemann hypothesis, we prove estimates for the variance of the real and imaginary part of the logarithm of the Riemann zeta function in short intervals. We give three different formulations of these results. Assuming a conjecture of Chan for how often gaps between zeros can be close to a fixed non‐zero value, we prove a conjecture of Berry (1988) for the number variance of zeta zeros in the non‐universal regime. In this range, Gaussian unitary ensemble statistics do not describe the distribution of the zeros. We also calculate lower order terms in the second moment of the logarithm of the modulus of the Riemann zeta function on the critical line. Assuming Montgomery's pair correlation conjecture, this establishes a special case of a conjecture of Keating and Snaith (2000). 

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5. Computing time-periodic steady-state currents via the time evolution of tensor network states

   https://doi.org/10.1063/5.0099741  

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

   We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted, but the approach extends naturally to other interacting lattice models with time-dependent driving. Although trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy can be beneficial. 

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