Semiclassical Studies Research Articles

Adsorption mechanism of Ni decorated α-CN monolayer towards CO, NO, and NH₃ gases: Insights from DFT and semi-classical studies

Toxic gases such as carbon monoxide (CO), nitric oxide (NO) and ammonia (NH3) pose serious health and environmental risks. While existing toxic gas monitors are costly, two-dimensional (2D) materials have shown promise for gas sensing applications due to their high surface-to-volume ratios and sensitivity. Among these, α-CN has been identified as a potential candidate for gas adsorption mechanisms. This study investigates the adsorption performance α-CN surface with the decoration of nickel (Ni)-atom for CO, NO, and NH₃ toxic gases using state of art density functional theory (DFT) based first principles calculations. The results indicate that the Ni-decoration significantly enhances the adsorption performance of α-CN, as evidenced by highly negative adsorption energies. Therefore, the calculated recovery times are extremely long, suggesting that Ni-decorated α-CN is more suitable for the removal of these toxic gases rather than as a sensor. The structural and electronic properties, including projected density of states (PDOS), band structure, charge density diagrams and transfer mechanisms, have been thoroughly analyzed. Additionally, sensing properties such as work function and electrical conductivity, computed using semi-classical methods, have been evaluated to validate the effectiveness of the material.

Photodissociation of water molecule at short photon wavelengths: Dynamical studies

In our last study [J. Phys. B At. Mol. Opt. Phys. 54, 125,102 (2021).], we reported the ab initio calculation of the full-dimensional potential energy surfaces of water molecule including 9 A’ and 9 A” states in Cs symmetry. In this study, we performed additional non-adiabatic semi-classical studies based on the potential energy surfaces. Our simulation successfully repeated the near picosecond lifetime of the F∼1A′ state measured by time resolved photo-electron spectra experiment [Chinese J. Chem. Phys. 32, 53 (2019)]. We also determined the dissociation branching ratio including H + OH(X, A), H + H + O and H2+O channels. In addition, the reaction path corresponding to H2+O (1S) channel is clearly marked out, which is found in recent free-electron laser experiment [Nat. Commun. 12, 6,303 (2021)].

Quantum and semiclassical studies of nonadiabatic electronic transitions between N(4S) and N(2D) by collisions with N2.

The dynamics and kinetics of spin-forbidden transitions between N(2D) and N(4S) via collisions with N2 molecules are investigated using a quantum wave packet (WP) method and the semi-classical coherent switches with decay of mixing (CSDM) method. These electronic transition processes are competing with exchange reaction channels on both the doublet and quartet potential energy surfaces. The WP and CSDM quenching rate coefficients are found in reasonable agreement with each other, and both reproduce the previous theoretical results. For the excitation process, the agreement between the two approaches is dependent on the treatment of the zero-point energy (ZPE) in the product, because the high endoergicity of this process leads to severe violation of the vibrational ZPE. The Gaussian-binning (GB) method is found to improve the agreement with the quantum result. The excitation rate coefficients are found to be two orders of magnitude smaller than that of the adiabatic exchange reaction, underscoring the inefficient intersystem crossing due to the weak spin-orbit coupling between the two spin manifolds of the N3 system.

Semiclassical Trajectory Studies of Reactive and Nonreactive Scattering of OH(A 2 Σ+ ) by H2 Based on an Improved Full-Dimensional Ab Initio Diabatic Potential Energy Matrix.

We present a new full-dimensional diabatic potential energy matrix (DPEM) for electronically nonadiabatic collisions of OH(A 2 Σ+ ) with H2 , and we calculate the probabilities of electronically adiabatic inelastic collisions, nonreactive quenching, and reactive quenching to form H2 O+H. The DPEM was fitted using a many-body expansion with permutationally invariant polynomials in bond-order functions to represent the many-body part. The dynamics calculations were carried out with the fewest-switches with time uncertainty and stochastic decoherence (FSTU/SD) semiclassical trajectory method. We present results both for head-on collisions (impact parameter b equal to zero) and for a full range of impact parameters. The results are compared to experiment and to earlier FSTU/SD and quantum dynamics calculations with a previously published DPEM. The various theoretical results all agree that nonreactive quenching dominates reactive quenching, but there are quantitative differences between the two DPEMs and between the b=0 results and the all-b results, especially for the probability of reactive quenching.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Critical Behavior of the Quantum Contact Process in One Dimension.

The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a nonequilibrium phase transition into an absorbing state that has been widely investigated and shown to belong to the directed percolation universality class. When the same process is considered in a quantum setting, much less is known. So far, mainly semiclassical studies have been conducted and the nature of the transition in low dimensions is still a matter of debate. Also, from a numerical point of view, from which the system may look fairly simple-especially in one dimension-results are lacking. In particular, the presence of the absorbing state poses a substantial challenge, which appears to affect the reliability of algorithms targeting directly the steady state. Here we perform real-time numerical simulations of the open dynamics of the quantum contact process and shed light on the existence and on the nature of an absorbing state phase transition in one dimension. We find evidence for the transition being continuous and provide first estimates for the critical exponents. Beyond the conceptual interest, the simplicity of the quantum contact process makes it an ideal benchmark problem for scrutinizing numerical methods for open quantum nonequilibrium systems.

Two coupled nonlinear cavities in a driven-dissipative environment

We investigate two coupled nonlinear cavities that are coherently driven in a dissipative environment. We perform semiclassical, numerical and analytical quantum studies of this dimer model when both cavities are symmetrically driven. In the semiclassical analysis, we find steady-state solutions with different photon occupations in two cavities. Such states can be considered analogs of the closed system double well symmetry breaking states. We analyze the occurrence and properties of these localized states in the system parameter space and examine how the symmetry breaking states, in form of a bistable pair, are associated to the single cavity bistable behavior. In a full quantum calculation of the master equation dynamics that includes quantum fluctuations, the symmetry breaking states and bistability disappear due to the quantum fluctuations. In quantum trajectory picture, we observe enhanced quantum jumps and switching which indicate the presence of the underlying semiclassical symmetry breaking states. Finally, we present a set of analytical solutions for the steady state correlation functions using the complex P-representation and discuss its regime of validity.

Quantum and semiclassical studies on photodetachment cross sections of H− in a harmonic potential**Project supported by the National Natural Science Foundation of China (Grant Nos. 11421063 and 11474079), the Natural Science Foundation of Shanxi Province, China (Grant No. 2009011004), and the Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi Province, China.

The photodetachment cross section of H− in a linear harmonic oscillator potential is investigated. This system provides a rare example that can be studied analytically by both quantum and semiclassical methods with some approximations. The formulas of the cross section for different laser polarization directions are explicitly derived by both the traditional quantum approach and closed-orbit theory. In the traditional quantum approach, we calculate the cross sections in coordinate representation and momentum representation, and get the same formulas. We compare the quantum formulas with closed-orbit theory formulas, and find that when the detachment electron energy is larger than , where ω is the frequency of the oscillator potential, the quantum results are shown to be in good agreement with the semiclassical results.

Perturbative Semiclassical Trace Formulae for Harmonic Oscillators

In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting $\mathrm{U}(D)$ to $\mathrm{O}(D)$ symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative ($\hbar \rightarrow 0$) trace formula. We then show how to apply the results to even order polynomial potentials, possibly including mean-field terms. We have drawn the conclusion that the gross structure of the quantum spectrum is determined from only classical circular- and diameter-orbits for this class of systems.

Combinatorial theory of the semiclassical evaluation of transport moments. I. Equivalence with the random matrix approach

To study electronic transport through chaotic quantum dots, there are two main theoretical approaches. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other treats the transport in the semiclassical approximation and studies correlations among sets of classical trajectories. There are established evaluation procedures within the semiclassical evaluation that, for several linear and nonlinear transport moments to which they were applied, have always resulted in the agreement with random matrix predictions. We prove that this agreement is universal: any semiclassical evaluation within the accepted procedures is equivalent to the evaluation within random matrix theory. The equivalence is shown by developing a combinatorial interpretation of the trajectory sets as ribbon graphs (maps) with certain properties and exhibiting systematic cancellations among their contributions. Remaining trajectory sets can be identified with primitive (palindromic) factorisations whose number gives the coefficients in the corresponding expansion of the moments of random matrices. The equivalence is proved for systems with and without time reversal symmetry.

A semiclassical study of cis-trans isomerization in HONO using an interpolating moving least-squares potential.

The interpolating moving least-squares (IMLS) approach for constructing potential energy surfaces has been developed and employed in standard classical trajectory simulations in the past few years. We extend the approach to the tunneling regime by combining the IMLS fitting method and the semiclassical scheme that incorporates tunneling into classical trajectory calculations. Dynamics of cis-trans isomerization in nitrous acid (HONO) is studied as a test case to investigate various aspects of the approach such as the strategy for growing the surface, the basis set employed, the scaling of the IMLS fits, and the accuracy of the surface required for obtaining converged rate coefficients. The validity of the approach is demonstrated through comparison with other semiclassical and quantum mechanical studies on HONO.

Classical and semiclassical studies of nonlinear nano-optomechanical oscillators

This paper presents a study of the effects of geometrical nonlinearity on the behavior of a Fabry-Perot cavity whose entrance face is a fixed mirror while the rear is a moving mirror behaving as a cantilever nanobeam. The study is done in classical and semiclassical approaches. In the semiclassical approach, the expression of the anharmonic Hamiltonian describing such a system is given. The nonlinearity reduces both the cantilever energy and optical intracavity energy and tends to decouple the optical and mechanical parts of the system. The nonlinear semiclassical approach is shown to be in good agreement with the quantum limit. The optical bistable zones degenerate leading to applications in optical communications and quantum information.

Semiclassical Monte Carlo simulation studies of spin dephasing in InP and InSb nanowires

We use semiclassical Monte Carlo approach to investigate spin polarized transport in InP and InSb nanowires. D’yakonov-Perel (DP) relaxation and Elliott-Yafet (EY) relaxation are the two main relaxation mechanisms for spin dephasing in III-V channels. The DP relaxation occurs because of bulk inversion asymmetry (Dresselhaus spin-orbit interaction) and structural inversion asymmetry (Rashba spin-orbit interaction). The injection polarization direction studied is that along the length of the channel. The dephasing rate is found to be very strong for InSb as compared to InP which has larger spin dephasing lengths. The ensemble averaged spin components vary differently for both InP and InSb nanowires. The steady state spin distribution also shows a difference between the two III-V nanowires.

Gluino zero-modes for non-trivial holonomy calorons

We couple fermion fields in the adjoint representation (gluinos) to the SU(2) gauge field of unit charge calorons defined on R^3 x S_1. We compute corresponding zero-modes of the Dirac equation. These are relevant in semiclassical studies of N=1 Super-symmetric Yang-Mills theory. Our formulas, show that, up to a term proportional to the vector potential, the modes can be constructed by different linear combinations of two contributions adding up to the total caloron field strength.

Towards a differential equation for the nonrelativistic ground-state electron density of the He-like sequence of atomic ions

The early study of Schwartz [Ann. Phys. (N.Y.) 6, 156 (1959)] led to an explicit expression for the ground-state electron density {rho}(r) of He-like atomic ions with nuclear charge Ze in the limit of large Z. Much later, Gal, March, and Nagy [Chem. Phys. Lett. 305, 429 (1999)] derived a third-order linear homogeneous differential equation satisfied by the Schwartz limiting density. Our aim here has been to solve a still correlated model more closely related to the He atom itself. Motivated by semiclassical studies (as by Handke [Phys. Rev. A 50, R3561 (1994)]), we have solved a fully quantal model in which the Coulomb repulsion energy e{sup 2}/r{sub 12} of the two electrons at separation r{sub 12} is expanded in a one-center form about the atomic nucleus and only the s-wave term is retained. From the resulting analytical ground-state density, a differential equation has been derived, which is contrasted with that satisfied by the large-Z limiting form of Schwartz. Suggestions are finally made as to the way the density of the He atomic ion series may be characterized, the ionization potential I(Z) being proposed as crucial input data.

Quantum and semiclassical study of magnetic quantum dots

We study the energy level structure of two-dimensional charged particles in inhomogeneous magnetic fields. In particular, for magnetic anti-dots the magnetic field is zero inside the dot and constant outside. Such a device can be fabricated with present-day technology. We present detailed semiclassical studies of such magnetic anti-dot systems and provide a comparison with exact quantum calculations. In the semiclassical approach we apply the Berry-Tabor formula for the density of states and the Borh-Sommerfeld quantization rules. In both cases we found good agreement with the exact spectrum in the weak magnetic field limit. The energy spectrum for a given missing flux quantum is classified in six possible classes of orbits and summarized in a so-called phase diagram. We also investigate the current flow patterns of different quantum states and show the clear correspondence with classical trajectories.

Adiabatic Bohr-Sommerfeld calculations for the hydrogenic Stark effect

A general prescription is presented for the semiclassical calculation of quantized energy levels of a class of parametric quantum systems. Starting with the Bohr-Sommerfeld quantization conditions of an exactly solvable system in parabolic coordinates, the calculation evolves the classical equations of motion while adiabatically introducing a nonzero parameter. We present accurate results for the quadratic Stark effect in addition to the linear Stark effect, an improvement over previous semiclassical studies.

Loop Operators and the Kondo Problem

We analyse the renormalisation group flow for D-branes in WZW models from the point of view of the boundary states. To this end we consider loop operators that perturb the boundary states away from their ultraviolet fixed points, and show how to regularise and renormalise them consistently with the global symmetries of the problem. We pay particular attention to the chiral operators that only depend on left-moving currents, and which are attractors of the renormalisation group flow. We check (to lowest non-trivial order in the coupling constant) that at their stable infrared fixed points these operators measure quantum monodromies, in agreement with previous semiclassical studies. Our results help clarify the general relationship between boundary transfer matrices and defect lines, which parallels the relation between (non-commutative) fields on (a stack of) D-branes and their push-forwards to the target-space bulk.

Canonical transformations and non-unitary evolution

We test the idea that transformations which, at the classical level, can be interpreted as evolutions are represented within quantum mechanics by unitary operators. To this end, we consider non-trivial canonical transformations which leave invariant the form of the Hamilton function of a system. We demonstrate that infinite families of such transformations exist for a variety of familiar conservative systems of one degree of freedom. We show how the precise form of integral equations for the stationary state wavefunctions implied by the existence of these canonical transformations can be pinned down by exploiting the algebra of the transformations and a symmetry of their generating functions. We recover several integral equations found in the literature on standard special functions of mathematical physics. We find that when one of the classical canonical transformations we consider is non-linear, its quantum implementation is non-unitary. We end with some comments on the implications of our findings for semiclassical studies and a brief discussion relevant to string theory of the generalization to scalar field theories in 1 + 1 dimensions.

Reversible adaptive regularization: perturbed Kepler motion and classical atomic trajectories

Reversible and adaptive integration methods based on Kustaanheimo–Stiefel regularization and modified Sundman transformations are applied to simulate general perturbed Kepler motion and to compute classical trajectories of atomic systems (e.g. Rydberg atoms). The new family of reversible adaptive regularization methods also conserve angular momentum and exhibit superior energy conservation and numerical stability in long–time integrations. The schemes are appropriate for scattering, for astronomical calculations of escape time and long–term stability, and for classical and semiclassical studies of atomic dynamics. The components of an algorithm for trajectory calculations are described. Numerical experiments illustrate the effectiveness of the reversible approach.