Manifold Of States Research Articles

Photoproduct formation in coenzyme B12-dependent CarH photoreceptor via a triplet pathway.

CarH is a cobalamin-based photoreceptor which has attracted significant interest due to its complex mechanism involving its organometallic coenzyme-B12 chromophore. While several experimental and computational studies have sought to understand CarH's mechanism of action, there are still many aspects of the mechanism which remain unclear. While light is needed to activate the Co-C5' bond, it is not entirely clear whether reaction pathway involves singlet or triplet diradical states. A recent experimental study implicated triplet pathway and importance of intersystem crossing (ISC) as a viable mechanistic route for photoproduct formation in CarH. Herein, a combined quantum mechanics/molecular mechanics approach (QM/MM) was used to explore the involvement of triplet states in CarH. Two possibilities were explored. The first possibility involved photo-induced homolytic cleavage of the Co-C5' where the radical pair (RP) would deactivate to a triplet state (T0) on the ground state potential energy surface (PES). However, a pathway for the formation of the photoproduct, 4',5'-anhydroadenosine (anhAdo), on the triplet ground state PES was not energetically feasible. The second possibility involved exploring a manifold of low-lying triplet excited states computed using TD-DFT within the QM/MM framework. Viable crossings of triplet excited states with singlet excited states were identified using semiclassical Landau-Zener theory and the effectiveness of spin-orbit coupling by El-Sayed rules. Several candidates along both the Co-NIm potential energy curve (PEC) and Co-C5'/Co-NIm PES were identified, which appear to corroborate experimental findings and implicate the possible role of triplet states in CarH.

Surface Electronic Structure Engineering of Manganese Bismuth Tellurides Guided by Micro-Focused Angle-Resolved Photoemission.

Modification of the electronic structure of quantum matter by ad atom deposition allows for directed fundamental design of electronic and magnetic properties. This concept is utilized in the present study in order to tune the surface electronic structure of magnetic topological insulators based on MnBi2 Te4 . The topological bands of these systems are typically strongly electron-doped and hybridized with a manifold of surface states that place the salient topological states out of reach of electron transport and practical applications. In this study, micro-focused angle-resolved photoemission spectroscopy (microARPES) provides direct access to the termination-dependent dispersion of MnBi2 Te4 and MnBi4 Te7 during in situ deposition of rubidium atoms. The resulting band structure changes are found to be highly complex, encompassing coverage-dependent ambipolar doping effects, removal of surface state hybridization, and the collapse of a surface state band gap. In addition, doping-dependent band bending is found to give rise to tunable quantum well states. This wide range of observed electronic structure modifications can provide new ways to exploit the topological states and the rich surface electronic structures of manganese bismuthtellurides.

On a Kinetic Equation Describing the Behavior of a Gas Interacting Mainly with Radiation

In this article we study a kinetic model which describes the interaction between a gas and radiation. Specifically, we consider a scaling limit in which the interaction between the gas and the photons takes place much faster than the collisions between the gas molecules themselves. We prove in the homogeneous case that the solutions of the limit problem solve a kinetic equation for which a well-posedness theory is considered. The proof of the convergence to a new kinetic equation is obtained analyzing the dynamics of the gas–photon system near the slow manifold of steady states.

Quantum control via chirped coherent anti-Stokes Raman spectroscopy

A chirped-pulse quantum control scheme applicable to coherent anti-Stokes Raman scattering spectroscopy, named as C-CARS, is presented aimed at maximizing the vibrational coherence in molecules. It implies chirping of three incoming pulses in the four-wave mixing process of CARS, the pump, the Stokes and the probe, to fulfill the conditions of adiabatic passage. The scheme is derived in the framework of rotating wave approximation and adiabatic elimination of excited state manifold simplifying the four-level model system into a ‘super-effective’ two level system. We demonstrate that the selectivity of excitation of vibrational degrees of freedom can be controlled by carefully choosing the spectral chirp rate of the pulses. The robustness, spectral selectivity and adiabatic nature of this method are advantageous for improving the existing methods of CARS spectroscopy for sensing, imaging and detection.

Nonadiabatic Photodissociation and Dehydrogenation Dynamics of n-Butyl Bromide Following p-Rydberg Excitation.

Femtosecond time-resolved mass spectrometry, correlation mapping, and density functional theory calculations are employed to reveal the mechanism of C═C and C≡C formation (and related H2 production) following excitation to the p-Rydberg states of n-butyl bromide. Ultrafast pump-probe mass spectrometry shows that nonadiabatic relaxation operates as a multistep process reaching an intermediate state within ∼500 fs followed by relaxation to a final state within 10 ps of photoexcitation. Absorption of three ultraviolet photons accesses the dense p-Rydberg state manifold, which is further excited by the probe beam for C─C bond dissociation and dehydrogenation reactions. Rapid internal conversion deactivates the dehydrogenation pathways, while activating carbon backbone dissociation pathways. Thus, unsaturated carbon fragments decay with the lifetime of p-Rydberg (∼500 fs), matching the growth recorded in saturated hydrocarbon fragments. The saturated hydrocarbon signals subsequently decay on the picosecond time scale as the molecule relaxes below the Rydberg states and into halogen release channels.

On static manifolds satisfying an overdetermined Robin type condition on the boundary

In this work, we consider static manifolds M M with nonempty boundary ∂ M \partial M . In this case, we suppose that the potential V V also satisfies an overdetermined Robin type condition on ∂ M \partial M . We prove a rigidity theorem for the Euclidean closed unit ball B 3 B^3 in R 3 \mathbb {R}^3 . More precisely, we give a sharp upper bound for the area of the zero set Σ = V − 1 ( 0 ) \Sigma =V^{-1}(0) of the potential V V , when Σ \Sigma is connected and intersects ∂ M \partial M . We also consider the case where Σ = V − 1 ( 0 ) \Sigma =V^{-1}(0) does not intersect ∂ M \partial M .

Transverse Magnetization in Spin-Orbit Coupled Antiferromagnets.

Some antiferromagnets under a magnetic field develop magnetization perpendicular to the field as well as more conventional ones parallel to the field. So far, the transverse magnetization (TM) has been attributed to either the spin canting effect or the presence of cluster magnetic multipolar ordering. However, a general theory of TM based on microscopic understanding is still missing. Here, we construct a general microscopic theory of TM in antiferromagnets with cluster magnetic multipolar ordering by considering classical spin Hamiltonians with spin anisotropy that arises from the spin-orbit coupling. First, from general symmetry analysis, we show that TM can appear only when all crystalline symmetries are broken other than the antiunitary mirror, antiunitary twofold rotation, and inversion symmetries. Moreover, by analyzing spin Hamiltonians, we show that TM always appears when the degenerate ground state manifold of the spin Hamiltonian is discrete, as long as it is not prohibited by symmetry. On the other hand, when the degenerate ground state manifold is continuous, TM generally does not appear except when the magnetic field direction and the spin configuration satisfy specific geometric conditions under single-ion anisotropy. Finally, we show that TM can induce the anomalous planar Hall effect, a unique transport phenomenon that can be used to probe multipolar antiferromagnetic structures. We believe that our theory provides a useful guideline for understanding the anomalous magnetic responses of the antiferromagnets with complex magnetic structures.

Nonadiabatic dynamics near metal surface with periodic drivings: A Floquet surface hopping algorithm.

We develop a Floquet surface hopping approach to deal with nonadiabatic dynamics of molecules near metal surfaces subjected to time-periodic drivings from strong light-matter interactions. The method is based on a Floquet classical master equation (FCME) derived from a Floquet quantum master equation (FQME), followed by a Wigner transformation to treat nuclear motion classically. We then propose different trajectory surface hopping algorithms to solve the FCME. We find that a Floquet averaged surface hopping with electron density (FaSH-density) algorithm works the best as benchmarked with the FQME, capturing both the fast oscillations due to the driving and the correct steady-state observables. This method will be very useful to study strong light-matter interactions with a manifold of electronic states.

Excitation gratings in cross-beam filament wake channels in a dense argon gas: Formation, control, and Rabi sideband manifestation.

When two intense laser beams cross at a small angle, the interference in the crossing area results in a finite intensity grating. We consider femtosecond laser filamentation in such a grating, in a situation when the process is largely confined to the grating maxima and leads to formation of a structured filament wake channel. In a dense gas, electron impact processes during the laser pulse cause a copious excitation of neutral atoms, resulting in formation of a finite grating of the density of excited atoms. Numerically solving the equations of laser-driven kinetics, we obtain the properties of this grating, as depending on the characteristics of the interfering beams and especially on the interbeam phase delay. The excitation gratings thus formed give rise to a hallmark effect of Rabi sideband emission when probed by a picosecond 800 nm laser pulse, which couples with transitions in the excited states manifold. Spectral and spatial interference of the emitted radiation forms four-dimensional spatial-spectral fringe patterns accessible for observation on a remote screen. The patterns are indicative of the excitation grating structure; their sensitivity to the phase delay between the crossing pump pulses warrants experimental verification.

A Posteriori Validation of Generalized Polynomial Chaos Expansions

Generalized polynomial chaos (gPC) expansions are a powerful tool for studying differential equations with random coefficients, allowing, in particular, one to efficiently approximate random invariant sets associated with such equations. In this work, we use ideas from validated numerics in order to obtain rigorous a posteriori error estimates together with existence results about gPC expansions of random invariant sets. This approach also provides a new framework for conducting validated continuation, i.e., for rigorously computing isolated branches of solutions in parameter-dependent systems, which generalizes in a straightforward way to multiparameter continuation. We illustrate the proposed methodology by rigorously computing random invariant periodic orbits in the Lorenz system, as well as branches and 2 dimensional manifolds of steady states of the Swift–Hohenberg equation.

Homoclinic bifurcation and switching of edge state in plane Couette flow.

We identify the presence of three homoclinic bifurcations that are associated with edge states in a system that is governed by the full Navier-Stokes equation. In plane Couette flow with a streamwise period slightly longer than the minimal unit, we describe a rich bifurcation scenario that is related to new time-periodic solutions and the Nagata steady solution [M. Nagata, J. Fluid Mech. 217, 519-527 (1990)]. In this computational domain, the vigorous time-periodic solution (PO3) with comparable fluctuation amplitude to turbulence and the lower branch of the Nagata steady solution are considered as edge states at different ranges of Reynolds number. These edge states can help in understanding the mechanism of subcritical transition to turbulence in wall-bounded shear flows. At the Reynolds numbers at which the homoclinic bifurcations occur, we find the creation (or destruction) of the time-periodic solutions. At a higher Reynolds number, we observe the edge state switching from the lower-branch Nagata steady solution to PO3 at the creation of this vigorous cycle due to the homoclinic bifurcation. Consequently, the formation of the boundary separating the basins of attraction of the laminar attractor and the time-periodic/chaotic attractor also switches to the respective stable manifolds of the edge states, providing a change in the behavior of a typical amplitude of perturbation toward triggering the transition to turbulence.

Bifurcation analysis of static stability of a tractor-semitrailer under circular motions

This paper analyses a general qualitative depiction of changes in the configuration of the non-linear model of a tractor-semitrailer with excessive turnability under stationary circular motions within a broad range of control parameters, such as the longitudinal velocity of motion and angle of rotation of the wheels of the controlled unit. It allows us to foresee the jackknifing effect and to estimate the conditions necessary for safe travel. The proposed analysis combines the transparent geometric approach to analyse the configuration of a tractor-semitrailer, which was developed earlier by J.P. Pauwelussen, and the ability to investigate real bifurcations of the non-linear equation of handling and the non-linear equation of folding angle tractor-semitrailer analytically. Based on this approach, we obtain new analytical dependencies that determine the boundaries of divergent loss of stability of the entire manifold of stationary states of a tractor-semitrailer model and estimates of the maximum values of the angle of folding under different values of the vehicle's longitudinal velocity. This is achieved without the prior determination of the manifold of stationary states itself.

Recombination of N Atoms in a Manifold of Electronic States Simulated by Time-Reversed Nonadiabatic Photodissociation Dynamics of N2.

Following a single photon VUV absorption, the N2 molecule dissociates into distinct channels leading to N atoms of different reactivities. The optically accessible singlets are bound, and dissociation occurs through spin-orbit induced transfer to the triplets. There is a forest of coupled electronic states, and we here aim to trace a path along the nonadiabatic couplings toward a particular exit channel. To achieve this, we apply a time-reversed quantum dynamical approach that corresponds to a dissociation running back. It begins with an atom-atom relative motion in a particular product channel. Starting with a Gaussian wave packet at the dissociation region of N2 and propagating it backward in time, one can see the population transferring among the triplets due to a strong nonadiabatic interaction between these states. Simultaneously, the optically active singlets get populated because of spin-orbit coupling to the triplets. Thus, backward propagation traces the nonradiative association of nitrogen atoms.

Rationalizing the environment-dependent photophysical behavior of a DNA luminescent probe by classical and non-adiabatic molecular dynamics simulations.

Environment-sensitive fluorescent nucleoside analogs are of utmost importance to investigate the structure of nucleic acids, their intrinsic flexibility, and sequence-specific DNA- and RNA-binding proteins. The latter play indeed a key role in transcription, translation as well as in the regulation of RNA stability, localization and turnover, and many other cellular processes. The sensitivity of the embedded fluorophore to polarity, hydration, and base stacking is clearly dependent on the specific excited-state relaxation mechanism and can be rationalized combining experimental and computational techniques. In this work, we elucidate the mechanisms leading to the population of the triplet state manifold for a versatile nucleobase surrogate, namely the 2-thienyl-3-hydroxychromone in gas phase, owing to non-adiabatic molecular dynamics simulations. Furthermore, we analyze its behavior in the B-DNA environment via classical molecular dynamics simulations, which evidence a rapid extrusion of the adenine facing the 2-thienyl-3-hydroxychromone nucleobase surrogate. Our simulations provide new insights into the dynamics of this family of chromophores, which could give rise to an integrated view and a fine tuning of their photochemistry, and namely the role of excited-state intramolecular proton transfer for the rational design of the next generation of fluorescent nucleoside analogs.

Frustration shapes multi-channel Kondo physics: a star graph perspective

We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalisation group technique. Our results display the importance of ground state degeneracy in explaining various important properties like the breakdown of screening and the presence of local non-Fermi liquids (NFLs). The impurity susceptibility of the intermediate coupling fixed point Hamiltonian in the zero-bandwidth (or star graph) limit shows a power-law divergence at low temperature. Despite the absence of inter-channel coupling in the MCK fixed point Hamiltonian, the study of mutual information between any two channels shows non-zero correlation between them. A spectral flow analysis of the star graph reveals that the degenerate ground state manifold possesses topological quantum numbers. Upon disentangling the impurity spin from its partners in the star graph, we find the presence of a local Mott liquid arising from inter-channel scattering processes. The low energy effective Hamiltonian obtained upon adding a finite non-zero conduction bath dispersion to the star graph Hamiltonian for both the two and three-channel cases displays the presence of local NFLs arising from inter-channel quantum fluctuations. Specifically, we confirm the presence of a local marginal Fermi liquid in the two channel case, whose properties show logarithmic scaling at low temperature as expected. Discontinuous behaviour is observed in several measures of ground state entanglement, signalling the underlying orthogonality catastrophe associated with the degenerate ground state manifold. We extend our results to underscreened and perfectly screened MCK models through duality arguments. A study of channel anisotropy under renormalisation flow reveals a series of quantum phase transitions due to the change in ground state degeneracy. Our work thus presents a template for the study of how a degenerate ground state manifold arising from symmetry and duality properties in a multichannel quantum impurity model can lead to novel multicritical phases at intermediate coupling.

On the Energy-specific Photodissociation Pathways of 14N2 and 14N15N Isotopomers to N Atoms of Different Reactivity: A Quantum Dynamical Perspective

Photodissociation of the nitrogen molecule in the vacuum ultraviolet (VUV) is a major source of reactive nitrogen atoms in the upper atmosphere of Earth and throughout the solar system. Recent experimental studies have revealed strong energy dependence of the VUV photodissociation branching ratios to the N(4S3/2)+N(2D J ) and N(4S3/2)+N(2P J ) product channels, the primary dissociation pathways in the 108,000–116,000 cm−1 energy region. This produces N(2D J ) and N(2P J ) excited atoms that differ significantly in their chemical reactivity. The branching ratios oscillate with increase in the VUV excitation energy. We use high-level ab initio quantum chemistry to compute the potential curves of 17 electronic excited states and their nonadiabatic and spin–orbit couplings. The dynamics follow the sequential evolution from the optically excited but bound singlets. Spin–orbit coupling enables transfer to the dissociative triplet and quintet states. We compute the photodissociation yields through the dense manifold of electronic states leading to both exit channels. The dynamical simulations accurately capture the branching oscillations and enable a detailed look into the photodissociation mechanism. The major contribution to the dissociation is through the two lowest 3Π u states. However, for both isotopomers, at about 110,000 cm−1 there is an abnormally low dissociation rate into the N(4S3/2)+N(2P J ) channel that enables comparable participation of triplet and quintet 5Π u electronic states. This leads to the first peak in the branching ratio. At higher energies, trapping of the population in the 33Π u bound triplet state occurs. This favors dissociation to the lower-energy N(4S3/2)+N(2D J ) channel and results in the observed second switch in branching ratios.

Interference-induced anisotropy in a two-dimensional dark-state optical lattice

We describe a two-dimensional optical lattice for ultracold atoms with spatial features below the diffraction limit created by a bichromatic optical standing wave. At every point in space these fields couple the internal atomic states in a three-level Lambda coupling configuration. Adiabatically following the local wavefunction of the resulting dark state yields a spatially uniform Born-Oppenheimer potential augmented by geometric scalar and vector potentials appearing due to spatially rapid changes of the wavefunction. Depending on system parameters, we find that the geometric scalar potential can interpolate from a 2D analogue of the Kronig-Penney lattice, to an array of tubes with a zig-zag shaped barrier. The geometric vector potential induces a spatially periodic effective magnetic field (the Berry's curvature) that can be tuned to cause destructive interference between neighboring tubes, thereby decoupling them at a critical point in parameter space. We numerically investigate the energy spectrum including decay from the excited state, and find that the adiabatic approximation is sound for strong coupling strengths, leading to negligible loss in the dark state manifold. Furthermore, the spectrum is well-described by a non-Hermitian tight binding model with on-site losses, and hopping characterized by both loss and, surprisingly, gain.

Generalized deep thermalization for free fermions

In noninteracting isolated quantum systems out of equilibrium, local subsystems typically relax to nonthermal stationary states. In the standard framework, information on the rest of the system is discarded, and such states are described by a generalized Gibbs ensemble (GGE), maximizing the entropy while respecting the constraints imposed by the local conservation laws. Here we show that the latter also completely characterize a recently introduced projected ensemble (PE), constructed by performing projective measurements on the rest of the system and recording the outcomes. By focusing on the time evolution of fermionic Gaussian states in a tight-binding chain, we put forward a random ensemble constructed out of the local conservation laws, which we call deep GGE (dGGE). For infinite-temperature initial states, we show that the dGGE coincides with a universal Haar random ensemble on the manifold of Gaussian states. For both infinite and finite temperatures, we use a Monte Carlo approach to test numerically the predictions of the dGGE against the PE. We study, in particular, the $k$ moments of the state covariance matrix and the entanglement entropy, finding excellent agreement. Our work provides a first step towards a systematic characterization of projected ensembles beyond the case of chaotic systems and infinite temperatures.

The Mass of the Static Extension of Small Spheres

Abstract We give a simple proof to the computation of ADM mass of the static extensions of small spheres in Wiygul [13, 14]. It makes use of the mass formula $m = \frac {1}{4\pi } \int _{\partial M} \frac {\partial V}{\partial \nu }$ for an asymptotically flat static manifold with boundary.

Energy natural orbital characterization of nonadiabatic electron wavepackets in the densely quasi-degenerate electronic state manifold.

Dynamics and energetic structure of largely fluctuating nonadiabatic electron wavepackets are studied in terms of Energy Natural Orbitals (ENOs) [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 154, 094103 (2021)]. Such huge fluctuating states are sampled from the highly excited states of clusters of 12 boron atoms (B12), which have densely quasi-degenerate electronic excited-state manifold, each adiabatic state of which gets promptly mixed with other states through the frequent and enduring nonadiabatic interactions within the manifold. Yet, the wavepacket states are expected to be of very long lifetimes. This excited-state electronic wavepacket dynamics is extremely interesting but very hard to analyze since they are usually represented in large time-dependent configuration interaction wavefunctions and/or in some other complicated forms. We have found that ENO gives an invariant energy orbital picture to characterize not only the static highly correlated electronic wavefunctions but also those time-dependent electronic wavefunctions. Hence, we first demonstrate how the ENO representation works for some general cases, choosing proton transfer in water dimer and electron-deficient multicenter chemical bonding in diborane in the ground state. We then penetrate with ENO deep into the analysis of the essential nature of nonadiabatic electron wavepacket dynamics in the excited states and show the mechanism of the coexistence of huge electronic fluctuation and rather strong chemical bonds under very random electron flows within the molecule. To quantify the intra-molecular energy flow associated with the huge electronic-state fluctuation, we define and numerically demonstrate what we call the electronic energy flux.