Forbidden Processes Research Articles

Fractional Complex Euler–Lagrange Equation: Nonconservative Systems

Classical forbidden processes paved the way for the description of mechanical systems with the help of complex Hamiltonians. Fractional integrals of complex order appear as a natural generalization of those of real order. We propose the complex fractional Euler-Lagrange equation, obtained by finding the stationary values associated with the fractional integral of complex order. The complex Hamiltonian obtained from the Lagrangian is suitable for describing nonconservative systems. We conclude by presenting the conserved quantities attached to Noether symmetries corresponding to complex systems. We illustrate the theory with the aid of the damped oscillatory system.

Charging Galvanic Cell for Rapid H2 Production in Neutral and/or Acidic Seawater

The hydrogen evolution reaction (HER) in existing electrochemical processes is often coupled with thermodynamically forbidden anodic processes (e.g., water or organic electrooxidation), requiring high theoretical cell voltage to initialize the reaction. Besides, there exists a severe kinetic-mismatch issue. For instance, neutral or acidic conditions favor the kinetics of HER but are unfavorable for the kinetics of water oxidation, causing a high overpotential. Herein, we demonstrate that the thermodynamically spontaneous galvanic cell which involves the anodic electrooxidation of a metallic iron sheet (FeOR) and HER can be charged to enable low voltage and convenient hydrogen production in acidic or neutral seawater. At a pH of zero, the iR-compensated anodic potential needed to achieve a current density of 400 mA cm–2 is as low as −0.05 V (vs RHE), while in NaCl-saturated neutral water, the anodic potential needed to achieve a current density of 350 mA cm–2 is as low as 0.15 V (vs RHE). Additionally, the side products from the anodic FeOR are functional nanomaterials that could be separated easily, and their composition and structure can be flexibly manipulated by adjusting the formula of the electrolyte. Moreover, as no separator or anodic electrocatalyst is required, the setup for such FeOR-coupled hydrogen production can be greatly simplified. This work has demonstrated the workability and advantages of charging the thermodynamically spontaneous galvanic replacement reaction for efficient hydrogen production from acidic or neutral seawater.

Spin-vibronic coupling in the quantum dynamics of a Fe(III) trigonal-bipyramidal complex.

The presence of a high density of excited electronic states in the immediate vicinity of the optically bright state of a molecule paves the way for numerous photo-relaxation channels. In transition-metal complexes, the presence of heavy atoms results in a stronger spin-orbit coupling, which enables spin forbidden spin-crossover processes to compete with the spin-allowed internal conversion processes. However, no matter how effectively the states cross around the Franck-Condon region, the degree of vibronic coupling, of both relativistic and non-relativistic nature, drives the population distribution among these states. One such case is demonstrated in this work for the intermediate-spin Fe(III) trigonal-bipyramidal complex. A quantum dynamical investigation of the photo-deactivation mechanism in the Fe(III) system is presented using the multi-configurational time-dependent Hartree approach based on the vibronic Hamiltonian whose coupling terms are derived from the state-averaged complete active space self-consistent field/complete active space with second-order perturbation theory (CASPT2) calculations and spin-orbit coupling of the scalar-relativistic CASPT2 states. The results of this study show that the presence of a strong (non-relativistic) vibronic coupling between the optically bright intermediate-spin state and other low-lying states of the same spin-multiplicity overpowers the spin-orbit coupling between the intermediate-spin and high-spin states, thereby lowering the chances of spin-crossover while exhibiting ultrafast relaxation among the intermediate-spin states. In a special case, where the population transfer pathway via the non-relativistic vibronic coupling is blocked, the probability of the spin-crossover is found to increase. This suggests that a careful modification of the complex by incorporation of heavier atoms with stronger relativistic effects can enhance the spin-crossover potential of Fe(III) intermediate-spin complexes.

Consequences of chirality on the response of materials

In chiral materials, mirror image symmetry is broken and as a result forbidden processes can become allowed. Here we review optoelectronic properties of materials affected by chirality.

Violations. How Nature Circumvents the Woodward–Hoffmann Rules and Promotes the Forbidden Conrotatory 4n + 2 Electron Electrocyclization of Prinzbach’s Vinylogous Sesquifulvalene

Woodward and Hoffmann, in their treatise on orbital symmetry in 1969, stated "Violations. There are none!" Prinzbach reported in 1978 that the electrocyclization of vinylogous sesquifulvalene occurs exclusively through the Woodward-Hoffmann orbital-symmetry-forbidden 14π-electron conrotatory pathway, despite the availability of a variety of orbital-symmetry-allowed processes. Prinzbach later demonstrated that an 18π-electron homologue exhibits the same forbidden behavior. And yet, the analogous vinylogous pentafulvalene and heptafulvalene both follow the orbital symmetry rules, each proceeding through its allowed conrotatory 12π and 16π process, respectively. We report the investigation of these reactions with ωB97X-D DFT. The physical origins of the flagrant Prinzbach violations of the Woodward-Hoffmann orbital symmetry selection rules have now been elucidated by these calculations in conjunction with extensive analyses and comparisons to electrocyclizations that obey the Woodward-Hoffmann rules. This remarkable reversal of the Rules (the 14π-electron-forbidden process is found to be 11 kcal/mol more energetically facile than the allowed process) occurs due to the high degree of polarization of this hydrocarbon, such that conrotatory electrocyclization of vinylogous sesquifulvalene behaves like a cyclopentadienide combining with a tropylium. These results are compared to other forbidden pericyclic processes driven by steric constraints and strain release or by diradical character of the reactants that facilitates the formation of diradical transition states for symmetry-forbidden reactions. We predict how strong donor-acceptor substitution can modify nodal properties to level the difference between allowed and forbidden electrocyclic reaction barriers, and we provide computational predictions of two such cases.

The Z lineshape challenge: ppm and keV measurements

The FCC-ee offers powerful opportunities for direct or indirect evidence for physics beyond the standard model, via a combination of high-precision measurements and searches for forbidden and rare processes and feebly coupled particles. A key element of FCC-ee physics program is the measurement of the Z lineshape from a total of 5times 10^{12} Z bosons and a beam-energy calibration with relative uncertainty of 10^{-6}. With this exceptionally large event sample, five orders of magnitude larger than that accumulated during the whole LEP1 operation at the Z pole, the defining parameters—m_mathrm{Z}, Gamma _mathrm{Z}, N_nu , sin ^2theta _mathrm{W}^mathrm{eff}, alpha _mathrm{S}(m_mathrm{Z}^2), and alpha _mathrm{QED}(m^2_mathrm{Z})—can be extracted with a leap in accuracy of up to two orders of magnitude with respect to the current state of the art. The ultimate goal that experimental and theory systematic errors match the statistical accuracy (4 keV on the Z mass and width, 3times 10^{-6} on sin ^2theta _mathrm{W}^mathrm{eff}, a relative 3times 10^{-5} on alpha _mathrm{QED}, and less than 0.0001 on alpha _mathrm{S}) leads to highly demanding requirements on collider operation, beam instrumentation, detector design, computing facilities, theoretical calculations, and Monte Carlo event generators. Such precise measurements also call for innovative analysis methods, which require a joint effort and understanding between theorists, experimenters, and accelerator teams.

Multifarious Roles of Hidden Chiral-Scale Symmetry: “Quenching” gA in Nuclei

I discuss how the axial current coupling constant gA renormalized in scale symmetric chiral EFT defined at a chiral matching scale impacts on the axial current matrix elements on beta decays in nuclei with and without neutrinos. The “quenched” gA observed in nuclear superallowed Gamow–Teller transitions, a long-standing puzzle in nuclear physics, is shown to encode the emergence of chiral-scale symmetry hidden in QCD in the vacuum. This enables one to explore how trace-anomaly-induced scale symmetry breaking enters in the renormalized gA in nuclei applicable to certain non-unique forbidden processes involved in neutrinoless double beta decays. A parallel is made between the roles of chiral-scale symmetry in quenching gA in highly dense medium and in hadron–quark continuity in the EoS of dense matter in massive compact stars. A systematic chiral-scale EFT, presently lacking in nuclear theory and potentially crucial for the future progress, is suggested as a challenge in the field.

A three-step model of high harmonic generation using complex classical trajectories

We present a new trajectory formulation of high harmonic generation that treats classically allowed and classically forbidden processes within a single dynamical framework. Complex trajectories orbit the nucleus, producing the stationary Coulomb ground state. When the field is turned on, these complex trajectories continue their motion in the field-dressed Coulomb potential and therefore tunnel ionization, unbound evolution and recollision are described within a single, seamless framework. The new formulation can bring mechanistic understanding to a broad range of strong field physics effects.

Temperature-dependent photoluminescence in Ge: Experiment and theory

We report a photoluminescence study of high-quality Ge samples at temperatures 12 K $\leq$ T $\leq$ 295 K, over a spectral range that covers phonon-assisted emission from the indirect gap (between the lowest conduction band at the L point of the Brillouin zone and the top of the valence band at the $\Gamma$ point), as well as direct gap emission (from the local minimum of the conduction band at the $\Gamma$ point). The spectra display a rich structure with a rapidly changing lineshape as a function of T. A theory is developed to account for the experimental results using analytical expressions for the contributions from LA, TO, LO, and TA phonons. Coupling of states exactly at the $\Gamma$ and L points is forbidden by symmetry for the latter two phonon modes, but becomes allowed for nearby states and can be accounted for using wave-vector dependent deformation potentials. Excellent agreement is obtained between predicted and observed photoluminescence lineshapes. A decomposition of the predicted signal in terms of the different phonon contributions implies that near room temperature indirect optical absorption and emission are dominated by forbidden processes, and the deformation potentials for allowed processes are smaller than previously assumed.

Afterburst thermal relaxation in neutron star crusts

We study thermal relaxation in a neutron star after internal heating events (outbursts) in the crust. We consider thin and thick spherically symmetric heaters, superfluid and non-superfluid crusts, stars with open and forbidden direct Urca processes in their cores. In particular, we analyze long-term thermal relaxation after deep crustal heating produced by nuclear transformations in fully or partly accreted crusts of transiently accreting neutron stars. This long-term relaxation has a typical relaxation time and an overall finite duration time for the crust to thermally equilibrate with the core. Neutron superfluidity in the inner crust greatly affects the relaxation if the heater is located in the inner crust. It shortens and unifies the time of emergence of thermal wave from the heater to the surface. This is important for the interpretation of observed outbursts of magnetars and transiently accreting neutron stars in quasi-persistent low-mass X-ray binaries.

Search for geo-neutrinos and rare nuclear processes with Borexino

Borexino was designed to measure solar neutrinos in the MeV or sub-MeV energy range. The unprecedented radiopurity of the detector has allowed the detection of geo-neutrinos and the determination of competitive limits on the rate of rare or forbidden processes. In this paper, we review the basic principle of neutrinos and antineutrinos detection in Borexino and we describe the results of the geo-neutrinos measurements and their implications. Then we summarize the search for Borexino events correlated with gamma ray bursts and for axion induced signals, and the limits achieved on Pauli forbidden transitions and on the electron charge conservation.

Quantum mechanical analysis of nonlinear optical response of interacting graphene nanoflakes

We propose a distant-neighbor quantum-mechanical (DNQM) approach to study the linear and nonlinear optical properties of graphene nanoflakes (GNFs). In contrast to the widely used tight-binding description of the electronic states that considers only the nearest-neighbor coupling between the atoms, our approach is more accurate and general, as it captures the electron-core interactions between all atoms in the structure. Therefore, as we demonstrate, the DNQM approach enables the investigation of the optical coupling between two closely separated but chemically unbound GNFs. We also find that the optical response of GNFs depends crucially on their shape, size, and symmetry properties. Specifically, increasing the size of nanoflakes is found to shift their accommodated quantum plasmon oscillations to lower frequency. Importantly, we show that by embedding a cavity into GNFs, one can change their symmetry properties, tune their optical properties, or enable otherwise forbidden second-harmonic generation processes.

Wavepacket revivals via complex trajectory propagation

Complex-valued semiclassical methods hold out the promise of treating classically allowed and classically forbidden processes on the same footing. In addition, they provide a natural way to describe optical excitation with complex fields within the trajectory framework. Despite their promise, these methods have until now been limited to short time propagation, due to the numerical difficulties introduced by the complexification. Using a new Final Value Representation of the Coherent State Propagator (FINCO), combined with an analysis of the complex classical phase space, we achieve accurate wavepacket propagation all the way to the revival time of a strongly anharmonic system.

Dissipation in microwave quantum circuits with hybrid nanowire Josephson elements

Recent experiments on hybrid Josephson junctions have made the argument a topical subject. However, a quantity which remains still unknown is the tunneling (or response) time, which is strictly connected to the role that dissipation plays in the dynamics of the complete system. A simple way for evaluating dissipation in microwave circuits, previously developed for describing the dynamics of conventional Josephson junctions, is now presented as suitable for application even to non-conventional junctions. The method is based on a stochastic model, as derived from the telegrapher's equation, and is particularly devoted to the case of junctions loaded by real transmission lines. When the load is constituted by lumped-constant circuits, a connection with the stochastic model is also maintained. The theoretical model demonstrated its ability to analyze both classically-allowed and forbidden processes, and has found a wide field of applicability, namely in all cases in which dissipative effects cannot be ignored.

Similarity of gas discharge in low‐pressure argon gaps between two plane‐parallel electrodes

The similarity of gas discharge in low-pressure argon gaps between two plane-parallel electrodes was investigated by experiments, numerical simulations and theoretical analysis. It was found by the experiments that the breakdown voltages depend not only on the product of gas pressure and gap length, but also on the aspect ratio of the gap, i.e. U b = f ( pd , d/r ). It was theoretically proved that U b = f ( pd , d/r ) is also a special case, the non-uniform electric field between plane-parallel electrodes, of similarity theorem of gas discharge. It was found by the experiments that there exist similar glow discharges only in two gaps with a limited scaled-down factor k . By theoretical analysis, it was explained that the forbidden processes such as the stepwise ionisation and the inelastic collision of the second kind violate the similarity of discharge as k increases, which was verified by the numerical simulations of the discharges with or without these two forbidden processes taken into account.

Effect of Solvent on the O2(a(1)Δg) → O2(b(1)Σg(+)) Absorption Coefficient.

Radiative transitions between the three lowest-lying electronic states of molecular oxygen have long provided a model to study how collision-dependent perturbations influence forbidden processes. In an isolated oxygen molecule, transitions between the O2(X(3)Σg(-)), O2(a(1)Δg), and O2(b(1)Σg(+)) states are forbidden as electric-dipole processes. For oxygen dissolved in organic solvents, the probabilities of radiative transitions between these states increase appreciably. Attempts to interpret solvent-dependent changes in the radiative rate constants have principally relied on O2(b(1)Σg(+)) and O2(a(1)Δg) emission experiments. However, the dominant nonradiative deactivation channels of O2(b(1)Σg(+)) make it difficult to quantify solvent effects on the O2(b(1)Σg(+)) → O2(a(1)Δg) radiative process. Thus, an appreciable amount of important information has heretofore not been available. In the present study, we examined the effect of 17 common organic solvents on the O2(a(1)Δg) → O2(b(1)Σg(+)) absorption transition at ∼5200 cm(-1) (i.e., ∼1925 nm). The solvent-dependent absorption coefficients at the band maximum, εmax, range from 5 to 50 M(-1) cm(-1) and correlate reasonably well with the solvent refractive index; εmax is largest in solvents with the largest refractive index. This observation is consistent with a model in which oxygen is perturbed to a greater extent by solvents with a large electronic polarizability. Through the Strickler-Berg equation, we also used these absorption data to obtain the radiative rate constant for the O2(b(1)Σg(+)) → O2(a(1)Δg) transition, and the results are consistent with a model in which the O2(a(1)Δg) → O2(X(3)Σg(-)) transition is said to steal intensity from the O2(b(1)Σg(+)) → O2(a(1)Δg) transition.

Towards thermally stable cyclophanediene-dihydropyrene photoswitches.

Cyclophanediene dihydropyrenes (CPD-DHP) are photochromic compounds because they change their color by irradiation with lights of different color. Potential use of CPD-DHP photoswitch in memory devices requires a very slow thermal return in the dark in the absence of any side reaction. Herein, thermal return of CPDs to DHPs, and an unwanted sigmatropic shift in DHP is studied through density functional theory calculations at (U)B3LYP/6-31+G(d). The thermal return occurs through symmetry forbidden conrotatory electrocyclic reaction. Dimethyl amino CPD-DHP photoswitch pair has the highest activation barrier for electrocyclization and sigmatropic shifts. The lowest activation barrier for symmetry forbidden electrocyclization is observed for GeBr3 functionalized CPD. An unprecedented decomposition pathway involving elimination of the internal substituents is predicted for Cl, Br and SMe functionalized DHPs. This study shows great promise in understanding the Woodward Hoffmann forbidden processes and, in reducing the synthetic efforts toward robust photochromes for memory applications.

Efficient dynamic nuclear polarization of phosphorus in silicon in strong magnetic fields and at low temperatures

Efficient manipulation of nuclear spins is important for utilizing them as qubits for quantum computing. In this work we report record high polarizations of ${}^{31}\mathrm{P}$ and $^{29}\mathrm{Si}$ nuclear spins in P-doped silicon in a strong magnetic field (4.6 T) and at temperatures below 1 K. We reached ${}^{31}\mathrm{P}$ nuclear polarization values exceeding $98%$ after 20 min of pumping the high-field electron spin resonance (ESR) line with a very small microwave power of 0.4 $\ensuremath{\mu}\mathrm{W}$. We evaluate that the ratio of the hyperfine-state populations increases by three orders of magnitude after 2 hours of pumping, and an extremely pure nuclear spin state can be created, with less than 0.01 ppb impurities. A negative dynamic nuclear polarization has been observed by pumping the low-field ESR line of ${}^{31}\mathrm{P}$ followed by the flip-flip cross relaxation, the transition which is fully forbidden for isolated donors. We estimate that while pumping the ESR transitions of ${}^{31}\mathrm{P}$ also the nuclei of $^{29}\mathrm{Si}$ get polarized, and polarization exceeding $60%$ has been obtained. We performed measurements of relaxation rates of flip-flop and flip-flip transitions which turned out to be nearly temperature independent. Temperature dependence of the ${}^{31}\mathrm{P}$ nuclear relaxation was studied down to 0.75 K, below which the relaxation time became too long to be measured. We found that the polarization evolution under pumping and during relaxation deviates substantially from a simple exponential function of time. We suggest that the nonexponential polarization dynamics of ${}^{31}\mathrm{P}$ donors is mediated by the orientation of $^{29}\mathrm{Si}$ nuclei, which affect the transition probabilities of the forbidden cross-relaxation processes.

Influence of Forbidden Processes on Similarity Law in Argon Glow Discharge at Low Pressure

The similarity law of gas discharge is not always valid due to the occurrence of some elementary processes, such as the stepwise ionization process, which are defined as the forbidden processes. To research the influence of forbidden processes on the similarity law, physical parameters (i.e., the electric field, electron density, electron temperature) in similar gaps are investigated based on the fluid model of gas discharge. The products of gas pressure p and dimensions are kept to be constant in similar gaps and the discharge model is solved with and without the forbidden processes, respectively. Discharges in similar gaps are identified as glow discharges and the typical similarity relations all are investigated. The results show that the forbidden processes cause significant deviations of similarity relations from the theoretical ones and the deviations are enlarged as the scaled-down factor k increases. If the forbidden processes are excluded from the model, the similarity law will be valid in argon glow discharge at low pressure.

Enabling Forbidden Processes: Quantum and Solvation Enhancement of Nitrate Anion UV Absorption

We present simulated electronic absorption spectra of isolated and solvated nitrate anion in the UV region, focusing primarily on the absorption into the first absorption band around 300 nm. This weak absorption band in this spectral region is responsible for the generation of NOx in the polar areas or OH(•) radicals in the hydrosphere. The 300 nm absorption band is symmetrically strongly forbidden and coupling of at least two vibrational modes is needed to allow the transition in the isolated nitrate anion. Further symmetry breaking is provided by solvation. In this study we model the absorption spectra of nitrate-water clusters using the combined reflection principle path integral molecular dynamics (RP-PIMD) method. Condensed phase UV spectra are modeled within a cluster-continuum model. The calculated spectra are compared with experimental bulk phase measurements and reasonable agreement is found. We also provide a benchmarking of the DFT functionals to be used for a description of the electronically excited states of solvated nitrate anion.