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DOE OSTI2026

Powers of magnetic graph matrix: Fourier spectrum, walk compression, and applications

Magnetic graphs, originally developed to model quantum systems under magnetic fields, have recently emerged as a powerful framework for analyzing complex directed networks. Existing research has primarily used the spectral properties of the magnetic graph matrix to study global and stationary network features. However, their capacity to model local, nonequilibrium behaviors, often described by matrix powers, remains largely unexplored. We present a combinatorial interpretation of the magnetic graph matrix powers through directed walk profiles—counts of graph walks indexed by the number of edge reversals. Crucially, we establish that walk profiles correspond to a Fourier transform of magnetic matrix powers. The connection allows exact reconstruction of walk profiles from magnetic matrix powers at multiple discrete potentials, and more importantly, an even smaller number of potentials often suffices for accurate approximate reconstruction in real networks. This shows the empirical compressibility of the information captured by the magnetic matrix. This fresh perspective suggests further applications; for example, we illustrate how powers of the magnetic matrix can identify frustrated directed cycles (e.g., feedforward loops) and can be effectively employed for link prediction by encoding local structural details in directed graphs.

complex networks↗

DOE OSTI2021

Laser-induced electron diffraction of the ultrafast umbrella motion in ammonia

Visualizing molecular transformations in real-time requires a structural retrieval method with Ångström spatial and femtosecond temporal atomic resolution. Imaging of hydrogen-containing molecules additionally requires an imaging method sensitive to the atomic positions of hydrogen nuclei, with most methods possessing relatively low sensitivity to hydrogen scattering. Laser-induced electron diffraction (LIED) is a table-top technique that can image ultrafast structural changes of gas-phase polyatomic molecules with sub-Ångström and femtosecond spatiotemporal resolution together with relatively high sensitivity to hydrogen scattering. Here, we image the umbrella motion of an isolated ammonia molecule (NH3) following its strong-field ionization. Upon ionization of a neutral ammonia molecule, the ammonia cation (NH3+) undergoes an ultrafast geometrical transformation from a pyramidal (ΦHNH=107°) to planar (ΦHNH=120°) structure in approximately 8 femtoseconds. Using LIED, we retrieve a near-planar (ΦHNH=117 ± 5°) field-dressed NH3+ molecular structure 7.8−9.8 femtoseconds after ionization. Our measured field-dressed NH3+ structure is in excellent agreement with our calculated equilibrium field-dressed structure using quantum chemical ab initio calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Fermi’s Golden Rule Rate Expression for Transitions Due to Nonadiabatic Derivative Couplings in the Adiabatic Basis

Starting from a general molecular Hamiltonian expressed in the basis of adiabatic electronic and nuclear position states, where a compact and complete expression for the nonadiabatic derivative coupling (NDC) Hamiltonian term is obtained, we provide a general analysis of the Fermi’s golden rule (FGR) rate expression for nonadiabatic transitions between adiabatic states. We then consider a quasi-adiabatic approximation that uses crude adiabatic states and NDC couplings, both evaluated at the minimum potential energy configuration of the initial adiabatic state, for the definition of the zeroth and first-order terms of the Hamiltonian. Although the application of this approximation is rather limited, it allows deriving a general FGR rate expression without further approximation while accounting for non-Condon contribution to the FGR rate arising from momentum operators of NDC terms and its coupling with vibronic displacements. For a generic and widely used model where all nuclear degrees of freedom and environmental effects are represented as linearly coupled harmonic oscillators, we derive a closed-form FGR rate expression that requires only Fourier transform. The resulting rate expression includes quadratic contributions of NDC terms and their couplings to Franck–Condon modes, which require evaluation of two additional bath spectral densities in addition to the conventional one that appears in a typical FGR rate theory based on the Condon approximation. Model calculations for the case where nuclear vibrations consist of both a sharp high-frequency mode and an Ohmic bath spectral density illustrate new features and implications of the rate expression. We then apply our theoretical expression to the nonradiative decay from the first excited singlet state of azulene, which illustrates the utility and implications of our theoretical results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Upgrades to the ion cyclotron emission diagnostic on the DIII-D tokamak

The ion cyclotron emission diagnostic on the DIII-D tokamak comprises seven single-turn loops that measure high-frequency (1–100 MHz) magnetic field fluctuations that are often excited by energetic particles in the plasma. The raw voltage signals induced in the loops in response to these fluctuations travel through a series of cables, isolation transformer DC blocks, low-pass filters, and finally a digitizer before being analyzed in frequency space. The diagnostic has been recently upgraded, most notably to include four additional graphite tile loops and a new eight-channel digitizer. The previous three loops are all on the low-field side of the tokamak. The measurement capabilities of the system have been expanded by the addition of a new horizontally oriented loop on the low-field side, an additional toroidal loop on the low-field side, and two toroidal loops on the high-field side. These loops will be used to provide approximate mode polarization, improved toroidal mode number calculations, and information on modes in inward-shifted plasmas, respectively.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Multi-mode lasing in terahertz metasurface quantum-cascade VECSELs

To date, terahertz quantum-cascade vertical-external-cavity surface-emitting lasers (QC-VECSELs) have tended to oscillate in only one or two lasing modes at a time. This is due to the fact that the interaction between all of the longitudinal external cavity modes and the QC gain material is mediated through a single metasurface resonance, whose spatial overlap changes little with frequency; this suppresses spatial-hole-burning induced multi-mode operation. In this Letter, a VECSEL external cavity is demonstrated using an output coupler based upon a high-resistivity silicon etalon, which presents a periodic reflectance spectrum that is nearly matched with the external cavity mode spectrum. As the cavity length is varied, a systematic transition between a single/double-mode lasing regime and a multi-mode lasing regime is realized due to the Vernier effect. Up to nine modes lasing simultaneously with a free-spectral-range of approximately 21 GHz is demonstrated. Furthermore, this result provides a path toward the multi-mode operation necessary for eventual frequency comb operation.

47 OTHER INSTRUMENTATION↗