Semiclassical Research Articles

Detection of Gravitational Waves with Semi Classical Features and Resulting Cosmological Implications

Detection of Gravitational Waves with Semi Classical Features and Resulting Cosmological Implications

Semiclassical initial value representation: From Møller to Miller. II.

As shown by W. H. Miller in a seminal article [J. Chem. Phys. 53, 3578 (1970)], the most convenient and accurate semiclassical (SC) theory of molecular scattering in action-angle coordinates is based on the initial value representation (IVR) and the use of shifted angles, which are different from the natural angles usually used in the quantum and classical treatments. Here, we show for an inelastic molecular collision that the initial and final shifted angles define three-segment classical paths that are exactly those involved in the classical-limit of Tannor-Weeks quantum scattering theory [J. Chem. Phys. 98, 3884 (1993)], provided that the translational wave packets |g+⟩ and |g-⟩ into play in this theory are both taken at |0⟩. Assuming this to be the case, using van Vleck propagators, and applying the stationary phase approximation, Miller's SCIVR expression of S-matrix elements is found, with an additional cut-off factor canceling the energetically forbidden transition probabilities. This factor, however, is close to unity in most practical cases. Furthermore, these developments show that the Møller operators underlie Miller's formulation, thus confirming, for molecular collisions, the results recently established in the simpler case of light-induced rotational transitions [L. Bonnet, J. Chem. Phys. 153, 174102 (2020)]. Last but not least, we show, based on the previous results, that for processes involving long-range anisotropic forces, implementing the Skinner-Miller method [Chem. Phys. Lett. 300, 20 (1999)] in shifted coordinates makes its predictions both easier and more accurate than in natural coordinates.

Laser-assisted in-flight muon-catalyzed deuteron-triton fusion

We investigate the deuteron-triton (DT) fusion in a three-body collision system of $\mathrm{T}\ensuremath{\mu}$ (i.e, a muon bound to a triton) impacted by a deuteron in the presence of intense laser fields with a semiclassical (SC) method. In this model, the initial positions and momenta of triton and muon are sampled from microcanonical distribution, and the dynamical process of a deuteron with a given incident kinetic energy colliding with the $\mathrm{T}\ensuremath{\mu}$ atom is simulated by tracing the classical trajectories in the combined Coulomb potentials and laser fields. At the minimum distance between the deuteron and triton, quantum tunneling through the Coulomb barrier emerges, and the penetrability can be estimated with the Wentzel-Kramers-Brillouin formula. DT nuclear fusion occurs after this quantum tunneling, and the total fusion cross section takes the Gamow form. Within the framework of the SC model, we investigate the charge shielding effect, demonstrating that this effect emerges in the low energy regime, where the impact velocity of the deuteron is smaller than the average velocity of muons in the bound state. Furthermore, the tunneling penetrability is considerably enhanced because the deuteron closely approaches the triton due to the quiver motions of charged nuclei driven by intense laser fields. As a result, the fusion cross section in this in-flight muon catalyzed fusion system can be enhanced by up to six orders of magnitude. Moreover, we calculated the DT fusion sections for a wide range of laser parameters and obtained phase diagrams demonstrating the enhanced DT fusion. Finally, important implications in achieving a large number of fusion reactions catalyzed by muons assisted by laser fields are discussed.

A Semiclassical Framework for Mixed Quantum Classical Dynamics.

Semiclassical (SC) approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are limited in their ability to describe quantum effects. In practical studies of high-dimensional reactions, neither extreme is the best choice: frequently a high-level quantum mechanical description is only required for a handful of modes, while the majority of environment modes that do not play a key role in the reactive event of interest are well served with a lower level of theory. In this feature, we introduce modified Filinov filtration as a powerful tool to construct mixed quantum-classical SC theories where different subsystems can be quantized to different extents without introducing ad hoc intersubsystem interaction terms. We demonstrate that these Filinov-based SC methods can systematically tune between quantum and classical limit SC behavior, offering a practical way forward to accurate and computationally efficient simulations of high-dimensional quantum processes.

On-the-fly adiabatically switched semiclassical initial value representation molecular dynamics for vibrational spectroscopy of biomolecules.

Semiclassical (SC) vibrational spectroscopy is a technique capable of reproducing quantum effects (such as zero-pointenergies, quantum resonances, and anharmonic overtones) from classical dynamics runs even in the case of very large dimensional systems. In a previous study [Conte et al. J. Chem. Phys. 151, 214107 (2019)], a preliminary sampling based on adiabatic switching has been shown to be able to improve the precision and accuracy of semiclassical results for challenging model potentials and small molecular systems. In this paper, we investigate the possibility to extend the technique to larger (bio)molecular systems whose dynamics must be integrated by means of ab initio "on-the-fly" calculations. After some preliminary tests on small molecules, we obtain the vibrational frequencies of glycine improving on pre-existing SC calculations. Finally, the new approach is applied to 17-atom proline, an amino acid characterized by a strong intramolecular hydrogen bond.

CP-violating transport theory for electroweak baryogenesis with thermal corrections

We derive CP-violating transport equations for fermions for electroweak baryogenesis from the CTP-formalism including thermal corrections at the one-loop level. We consider both the VEV-insertion approximation (VIA) and the semiclassical (SC) formalism. We show that the VIA-method is based on an assumption that leads to an ill-defined source term containing a pinch singularity, whose regularisation by thermal effects leads to ambiguities including spurious ultraviolet and infrared divergences.We then carefully review the derivation of the semiclassical formalism and extend it to include thermal corrections. We present the semiclassical Boltzmann equations for thermal WKB-quasiparticles with source terms up to the second order in gradients that contain both dispersive and finite width corrections. We also show that the SC-method reproduces the current divergence equations and that a correct implementation of the Fick's law captures the semiclassical source term even with conserved total current ∂μ j μ = 0. Our results show that the VIA-source term is not just ambiguous, but that it does not exist. Finally, we show that the collisional source terms reported earlier in the semiclassical literature are also spurious, and vanish in a consistent calculation.

Deuterium-tritium fusion process in strong laser fields: Semiclassical simulation

In this paper, we investigate the deuterium-tritium (DT) fusion process in the presence of strong laser fields with a semiclassical (SC) method. In this model, two nuclei with a given incident kinetic energy that closely approach each other are simulated by tracing the classical Newtonian trajectories in the combined Coulomb repulsive potentials and laser fields. At the nearest position or classical turning point, quantum tunneling through the Coulomb barrier emerges, and its penetrability is estimated with the Wentzel-Kramers-Brillouin formula. Nuclear fusion occurs after the tunneling, and the total fusion cross section takes the Gamow form. We find that the tunneling penetrability can be enhanced dramatically because the nuclei can closely approach each other due to the quiver motion of the charged nuclei driven by the intense laser fields. We then calculate the DT fusion section for a wide range of laser parameters according to various incident nuclei kinetic energies and obtain the phase diagrams for the enhanced DT fusion. We compare our SC results with the quantum results of the Kramers-Henneberger approximation and the Volkov state approximation.

Semiclassical initial value representation: From Møller to Miller.

The initial value representation (IVR) was proposed five decades ago by Miller [J. Chem. Phys. 53, 3578 (1970)] in order to improve the feasibility and accuracy of semiclassical (SC) scattering calculations. Møller operators, which play a fundamental role in quantum scattering theory, do not appear in his formulation based on action-angle coordinates. These operators were introduced much later by Garashchuk and Light [J. Chem. Phys. 114, 1060 (2001)] in SC-IVR calculations performed in Cartesian coordinates within the Tannor and Weeks [J. Chem. Phys. 98, 3884 (1993)] formulation of quantum scattering theory. Remarkably, Møller operators were found to boost the numerical efficiency of SC-IVR calculations. The purpose of this work is to show within a simple model of light-induced rotational transitions that, in fact, Møller operators were already underlying Miller's pioneering formulation. In line with the results of Garashchuk and Light [J. Chem. Phys. 114, 1060 (2001)], removing the action of these operators in Miller's theory strongly decreases its numerical efficiency.

A hybrid model for estimation of pore size from ortho-positronium lifetimes in porous materials

The present paper proposes a novel model for estimating the free-volume size of porous materials based on the analysis of various experimental ortho-positronium (o-Ps) lifetime data. The model is derived by combining the semi-classical (SE) physics model, which works in the region of large pores (pore size R> 1 nm), with the conventional Tao-Eldrup (TE) model, which is applicable only for the small-pore region (R< 1 nm). Thus, the proposed model, called the hybrid (HYB) model, is able to smoothly connect the o-Ps lifetimes in the two regions of the pore. Moreover, by introducing the o-Ps diffusion probability parameter (D), the HYB model has reproduced quite well the experimental o-Ps lifetimes in the whole region of pore sizes. It is even in a better agreement with the experimental data than the most up-to-date rectangular TE (RTE) and Tokyo models. In particular, by adjusting the value of D, the HYB model can also describe very well the two defined sets of experimental o-Ps lifetimes in the pores with spherical and channel geometries. The merit of the present model, in comparison with the previously proposed ones, is that it is applicable for the pore size in the universal range of 0.2−400 nm for most of porous materials with different geometries.

An effective semiclassical approach to IR spectroscopy.

We present a novel approach to calculate molecular infrared (IR) spectra based on semiclassical (SC) molecular dynamics. The main advance from a previous SC method [M. Micciarelli et al. J. Chem. Phys. 149, 064115 (2018)] consists of the possibility to avoid state-to-state calculations making applications to systems characterized by sizable densities of vibrational states feasible. Furthermore, this new method accounts not only for positions and intensities of the several absorption bands which make up the IR spectrum but also for their shapes. We show that accurate SC IR spectra including quantum effects and anharmonicities for both frequencies and intensities can be obtained starting from SC power spectra. The approach is first tested against the water molecule and then applied to the 10-atom glycine amino acid.

Reactivity, relaxation and dissociation of vibrationally excited molecules in low-temperature plasma modeling

Accurate modeling of low-temperature plasmas requires molecular collision input data, including the detail over the whole ladder of vibrational states. Obtaining this kind of detailed data is a big challenge, both theoretically and experimentally. These data can be calculated with the aid of simple models (for inelastic processes essentially based on forced harmonic oscillator mechanism), or with molecular dynamics at various levels, namely quasiclassical (QCT), semiclassical (SC), approximate and exact quantum mechanical methods, with computational cost rapidly increasing with accuracy. However, while accurate methods can become unfeasible when applied to the wide total energy ranges typically required in plasma modeling, more approximate semiclassical methods rapidly become efficient and accurate for increasing total energy, as shown in the literature. The best strategy is to study the limits of application of less accurate methods, to use them as a seamless continuation of accurate calculations on the total energy axis. In this sense, it is the current development about inelastic processes treated by QCT and SC methods. The aspect of special interest is the indication of a criterion for easily extracting the reliable QCT contribution to the inelastic process, treating the missing contributions by other SC methods in a restricted range. This procedure allows to optimize the use of different methods to maintain both a high level of accuracy and a high computational efficiency. As a consequence of the study about inelastic processes, a better comprehension and possible treatment of the dissociation mechanisms are obtained, with an indication of reliability of QCT results about this kind of process.

A hierarchical-equation-of-motion based semiclassical approach to quantum dissipation

We present a semiclassical (SC) approach for quantum dissipative dynamics, constructed on basis of the hierarchical-equation-of-motion (HEOM) formalism. The dynamical components considered in the developed SC-HEOM are wavepackets’ phase-space moments of not only the primary reduced system density operator but also the auxiliary density operators (ADOs) of HEOM. It is a highly numerically efficient method, meanwhile taking into account the high-order effects of system-bath couplings. The SC-HEOM methodology is exemplified in this work on the hierarchical quantum master equation [J. Chem. Phys. 131, 214111 (2009)] and numerically demonstrated on linear spectra of anharmonic oscillators.

Geometry of magnetic rotational (MR) band-crossing phenomenon in MR bands

A semiclassical (SC) approach is proposed to calculate the B(M1) transition rates in the band-crossing region of two magnetic rotational (MR) bands. In the present work, a geometry is suggested for the shear blades to govern its behaviour during the band-crossing. In the crossing region, gradual alignment of two nucleons is responsible for the crossing behaviour and it must give a quantised resultant angular momentum. As an example, it is successfully implemented for the MR bands in the mass $$A=110$$ and $$A=200$$ regions. A good agreement of the present semiclassical calculations with the experimental values is presented and furthermore, it is seen that the present proposal is also helpful to see the core contribution in the MR phenomenon.

Electronic wave function and binding effects in M-shell ionization of gold by protons

Abstract The measured M-X-ray production cross sections for protons, which are used in the particle induced X-ray emission (PIXE) technique, are systematically underestimated for low impact energies by the ECPSSR and ECUSAR theories. These theories, which are based on the plane wave Born approximation (PWBA) and use the screened hydrogenic wave functions, include corrections for the projectile Coulomb deflection and electron relativistic and binding effects. In the present paper, in order to interpret the observed disagreement at low impact energies, the systematic calculations of the M-shell ionization cross sections for gold were performed using the semiclassical (SCA) and the binary encounter (BEA) approximations in order to identify a role of the electronic wave function and electron binding effects. In these calculations the different wave functions, from nonrelativistic hydrogenic to selfconsistent Dirac-Hartree-Fock, were considered and the binding effect was treated within extreme separated- (SA) and united-atoms (UA) limits. The results are discussed in details and the observed discrepancies are attributed to inadequate description of the electron binding effect at the lowest impact energies for which the molecular approach is required.

Validating and implementing modified Filinov phase filtration in semiclassical dynamics.

The Mixed Quantum-Classical Initial Value Representation (MQC-IVR) is a recently introduced approximate semiclassical (SC) method for the calculation of real-time quantum correlation functions. MQC-IVR employs a modified Filinov filtration (MFF) scheme to control the overall phase of the SC integrand, extending the applicability of SC methods to complex systems while retaining their ability to accurately describe quantum coherence effects. Here, we address questions regarding the effectiveness of the MFF scheme in combination with SC dynamics. Previous work showed that this filtering scheme is of limited utility in the context of semiclassical wavepacket propagation, but we find that the MFF is extraordinarily powerful in the context of correlation functions. By examining trajectory phase and amplitude contributions to the real-time SC correlation function in a model system, we clearly demonstrate that the MFF serves to reduce noise by damping amplitude only in regions of highly oscillatory phase leading to a reduction in computational effort while retaining accuracy. Further, we introduce a novel and efficient MQC-IVR formulation that allows for linear scaling in computational cost with the total simulation length, a significant improvement over the more-than quadratic scaling exhibited by the original method.

Thermodynamically-consistent semi-classical ℓ-changing rates

We compare the results of the semi-classical (SC) and quantum-mechanical (QM) formalisms for angular-momentum changing transitions in Rydberg atom collisions given in a series of papers by Vrinceanu et al, most recently Vrinceanu et al (2012 Astrophys. J. 747 56), with those of the SC formalism using a modified Monte Carlo realization. We find that this revised SC formalism agrees well with the QM results. This provides further evidence that the rates derived from the QM treatment are appropriate to be used when modeling recombination through Rydberg cascades, an important process in understanding the state of material in the early universe. The rates for derived from the QM formalism diverge when integrated to sufficiently large impact parameter, b. Further to the empirical limits to the b integration suggested by Pengelly and Seaton (1964 Mon. Not. R. Astron. Soc. 127 165), we suggest that the fundamental issue causing this divergence in the theory is that it does not fully cater for the finite time taken for such distant collisions to complete.

A direct potential fitting RKR method: Semiclassical vs. quantal comparisons

Quantal and semiclassical (SC) eigenvalues are compared for three diatomic molecular potential curves: the X state of CO, the X state of Rb2, and the A state of I2. The comparisons show higher levels of agreement than generally recognized, when the SC calculations incorporate a quantum defect correction to the vibrational quantum number, in keeping with the Kaiser modification. One particular aspect of this is better agreement between quantal and SC estimates of the zero-point vibrational energy, supporting the need for the Y00 correction in this context. The pursuit of a direct-potential-fitting (DPF) RKR method is motivated by the notion that some of the limitations of RKR potentials may be innate, from their generation by an exact inversion of approximate quantities: the vibrational energy Gυ and rotational constant Bυ from least-squares analysis of spectroscopic data. In contrast, the DPF RKR method resembles the quantal DPF methods now increasingly used to analyze diatomic spectral data, but with the eigenvalues obtained from SC phase integrals. Application of this method to the analysis of 9500 assigned lines in the I2A←X spectrum fails to alter the quantal-SC disparities found for the A-state RKR curve from a previous analysis. On the other hand, the SC method can be much faster than the quantal method in exploratory work with different potential functions, where it is convenient to use finite-difference methods to evaluate the partial derivatives required in nonlinear fitting.

Modeling comparison of graphene nanoribbon field effect transistors with single vacancy defect

In this paper, some important circuit parameters of a monolayer armchair graphene nanoribbon (GNR) field effect transistor (GNRFET) in different structures are studied. Also, these structures are Ideal with no defect, 1SVGNRFET with one single vacancy defect, and 3SVsGNRFET with three SV defects. Moreover, the circuit parameters are extracted based on Semi Classical Top of Barrier Modeling (SCTOBM) method. The I-V characteristics simulations of Ideal GNRFET, 1SVGNRFET and 3SVsGNRFET are used for comparing with SCTOBM method. These simulations are solved with Poisson-Schrodinger equation self-consistently by using Non- Equilibrium Green Function (NEGF) and in the real space approach. The energy band structure of nanoribbon is obtained by using nearest–neighbour interactions within an approximation tight-binding method. The modeling results show that 3SVsGNRFET in comparison to 1SVGNRFET has higher transconductance, cut-off frequency, electron average velocity, mobile charge, and quantum capacitance. Also, 3SVsGNRFET has smaller gate, drain and source capacitances than Ideal GNRFET. Furthermore, Drain-induced barrier lowering (DIBL) and sub-threshold swing (SS) of 3SVsGNRFET are smaller than 1SVGNRFET.

Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach

We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions for a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors.

Efficient importance sampling in semiclassical initial value representation calculations for time correlation functions

The semiclassical (SC) theory based on an initial value representation (IVR) methodology provides a practical way to describe quantum effects in complex molecular systems. The efficiency of SC–IVR calculations for time correlation functions depends heavily on how to perform the Monte Carlo sampling of initial conditions. Here, we compare a variety of possibilities of sampling initial conditions in the SC calculations by choosing the sampling function to be either time-dependent or time-independent (TI). The implementation of these importance sampling protocols to two benchmark system-bath models demonstrates its advantages over the standard sampling method. In particular, the recently developed TI importance sampling which incorporates path correlation in the bath degrees of freedom shows a great potential in describing many-body quantum dynamics efficiently and accurately.