Semiclassical Approach Research Articles

Charge transport in two-dimensional disordered systems with an external electric field

In this paper, we consider a square lattice with correlated random hopping terms under the effect of an external electric field. We analyzed the dynamics of an initially localized electronic wave packet using a Taylor formalism to solve the Schrödinger dynamic equation. Our calculations suggest that the correlated disorder promotes a fast electronic propagation for intermediate times. When we switch on a static electric field, we observe an oscillatory behavior similar to the well-known “Bloch oscillations” phenomenology. We calculate the frequency of these oscillations, and our results are in good agreement with those predicted by the semi-classical approach used in crystalline lattices. Based on the local disorder and in the absence of extended states in our model, we discussed the stability of these apparent “Bloch oscillations”.

Competition between Two-Photon Driving, Dissipation, and Interactions in Bosonic Lattice Models: An Exact Solution.

We present an exact solution in arbitrary dimensions for the steady states of a class of quantum driven-dissipative bosonic models, where a set of modes is subject to arbitrary two-photon driving, single-photon loss, and a global Hubbard (or Kerr)-like interaction. Our solutions reveal a wealth of striking phenomena, including the emergence of dissipative phase transitions, nontrivial mode competition physics and symmetry breaking, and the stabilization of many-body SU(1,1) pair-coherent states. Our exact solutions enable the description of spatial correlations, and are fully valid in regimes where traditional mean-field and semiclassical approaches break down.

Single- and Double-electron Capture Cross Sections for O6+ Ion in Collisions with H2 Molecules

Single- and double-electron capture (SEC and DEC) processes occurring in O6+ and H2 collisions are investigated in a wide-energy domain ranging from 0.1 to 100 keV u−1. Total and partial cross sections are calculated using a three-center, two-active-electron, semiclassical nonperturbative approach. To date, our close-coupling description of the collision is the most elaborate one in terms of accounting for electron correlation, molecular structures, and active channels. Our results are, in general, in good agreement with the available experimental ones for both total and partial cross sections. The comparison between the present calculations and available experimental data suggests that about 70% of the autoionization double capture may contribute to the measured SEC cross sections through postcollisional autoionization, while the stabilization of 30% of doubly excited states via the autotransfer to Rydberg states mechanism contributes to the measured DEC ones. Furthermore, we extend the understanding of the electron-capture processes on this system to impact energies above 20 keV u−1 for which no data exists. Our work provides new data for these electronic processes, which will be helpful for modeling astrophysical X-ray emissions induced by charge exchange.

First principles calculations to investigate structural, electronic, mechanical, thermoelectric and optical properties of Bi- and Se-doped SnTe

Lead-based thermoelectric materials have a maximum figure of merit but are hazardous to humans and the environment. For this reason, we can replace tin-based lead-free materials and achieve the same figure of merit as lead-based thermoelectric materials. In this paper, we calculate the structural, electronic, mechanical, thermoelectric and optical properties of SnTe by co-doping it with Bi and Se using first principles calculation within the Generalized Gradient Approximation (GGA) through the Perdew-Burke-Ernzerhof(PBE) correlation scheme. Cohesive energies were calculated for each co-doping material and found to be maximum for Sn0.875Bi0.125Te0.875Se0.125. Computed elastic constants of all the cubic materials were obtained using the Thomas Charpin method integrated with the World of Interacting Electron and Nuclei due-2 Walter Kohn (WIEN2k) package. We found several mechanical properties of each material based on these constant values. We have observed an improvement in ductility and good stability for the Sn0.125Bi0.875Te0.125Se0.875 material as confirmed by various mechanical properties. Boltzmann semi-classical approach as implemented in the BoltzTraP package with and without the calculation of spin-orbit coupling. Here the figure of merit is calculated without the contribution of phonons and SOC calculations were included with the ambient conditions. From the results, we achieve maximum power factor and ZT values using SOC and non-SOC calculations. We identified that the Sn0.875Bi0.125Te0.875Se0.125 material shows a maximum ZT of 0.55, which is very much higher than the undoped SnTe and Sn0.125Bi0.875Te0.125Se0.875 material shows a ZT of 0.49 using SOC calculations. The optical properties of each material were studied at ambient conditions and Sn0.875Bi0.125Te0.875Se0.125 is consistent in the visible, IR and UV regions and it is adorable for IR detectors, solar cells and optoelectronic applications.

Nonadiabatic Dynamics in a Continuous Circularly Polarized Laser Field with Floquet Phase-Space Surface Hopping

Nonadiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly) polarized light allows one to effectively introduce a complex-valued time-dependent Hamiltonian, which offers a new path for control or exploration through the introduction of Berry forces. Here, we investigate several inexpensive semiclassical approaches for modeling such nonadiabatic dynamics in the presence of a time-dependent complex-valued Hamiltonian, beginning with a straightforward instantaneous adiabatic fewest-switches surface hopping (IA-FSSH) approach (where the electronic states depend on position and time), continuing to a standard Floquet fewest switches surface hopping (F-FSSH) approach (where the electronic states depend on position and frequency), and ending with an exotic Floquet phase-space surface hopping (F-PSSH) approach (where the electronic states depend on position, frequency, and momentum). Using a set of model systems with time-dependent complex-valued Hamiltonians, we show that the Floquet phase-space adiabats are the optimal choice of basis as far as accounting for Berry phase effects and delivering accuracy. Thus, the F-PSSH algorithm sets the stage for future modeling of nonadiabatic dynamics under strong externally pumped circular polarization.

External pressure effects on superfluid density of isotropic s-wave superconductors

Through using BCS theory and the semi-classical approach, the effect of external pressure on the superfluid density of s-wave isotropic superconductors were explored. The pressure parameters as the energy dispersion relation and the height of the density of state were applied. The analytical formula of superfluid density under pressure were derived and the numerical calculation results were compared to the experimental results of H3S and LaH10 superconductors. We discovered that the superfluid density under pressure of H3S and LaH10 superconductors fit our results closely. As the height of the density of state increased, so did the superfluid density.

Geometrodynamic approach to conjugate points and the Maslov index.

Maslov indices are an essential ingredient in the semiclassical approaches to quantum mechanics, as they are also related to the conjugate points of the corresponding trajectory, which reflects the dynamics in its neighborhood. In this paper, we show how these important topological parameters can be computed using the geometrodynamic approach to dynamics. Illustrations in two- and three-dimensional systems are presented and discussed.

Optical forces on neutral atoms in the presence of fluctuating laser fields: numerical analysis

Doppler cooling of 88Sr atoms is studied in the presence of off-resonant red-detuned fluctuating laser fields. Using a semi-classical approach, we show that the relevant physical quantities in the cooling process, such as optical forces, the damping coefficient, Doppler temperature, and atom number in the trap, are strongly affected by the laser amplitude and phase fluctuations. We find that the Doppler cooling limit is higher than the predicted Doppler theory for non-fluctuating lasers. This implies an additional heating mechanism exists due to the laser fluctuations. Furthermore, our numerical analysis shows that the effect of laser power stability on reducing the number of trapped atoms in a magneto-optical trap is more substantial than the effect of laser linewidth.

πσ*-Mediated Nonadiabatic Tunneling Dynamics of Thiophenols in S1: The Semiclassical Approaches.

The S-H bond tunneling predissociation dynamics of thiophenol and its ortho-substituted derivatives (2-fluorothiophenol, 2-methoxythiophenol, and 2-chlorothiphenol) in S1 (ππ*) where the H atom tunneling is mediated by the nearby S2 (πσ*) state (which is repulsive along the S-H bond extension coordinate) have been investigated in a state-specific way using the picosecond time-resolved pump-probe spectroscopy for the jet-cooled molecules. The effects of the specific vibrational mode excitations and the SH/SD substitutions on the S-H(D) bond rupture tunneling dynamics have been interrogated, giving deep insights into the multidimensional aspects of the S1/S2 conical intersection, which also shapes the underlying adiabatic tunneling potential energy surfaces (PESs). The semiclassical tunneling rate calculations based on the Wentzel-Kramers-Brillouin (WKB) approximation or Zhu-Nakamura (ZN) theory have been carried out based on the ab initio PESs calculated in the (one, two, or three) reduced dimensions to be compared with the experiment. Though the quantitative experimental results could not be reproduced satisfactorily by the present calculations, the qualitative trends among different molecules in terms of the behavior of the tunneling rate versus the (adiabatic) barrier height or the number of PES dimensions could be rationalized. Most interestingly, the H/D kinetic isotope effect observed in the tunneling rate could be much better explained by the ZN theory compared to the WKB approximation, indicating that the nonadiabatic coupling matrix elements should be invoked for understanding the tunneling dynamics taking place in the proximity of the conical intersection.

Majorana fermions in multiband quantum wires: A semiclassical analysis

In this paper, we calculate the Andreev bound state spectrum in a half-infinite superconducting wire with an arbitrary number of bands crossing the chemical potential. Electrons in the wire are affected by the asymmetric (Rashba) spin–orbit coupling due to the presence of a substrate. The normal state of the wire is assumed to have an antiunitary symmetry (time reversal or its combination with a point group operation), which may be broken by the superconducting order parameter and/or the boundary. The bound state spectrum is calculated without relying on any particular microscopic model, using the semiclassical approach with the boundary conditions described by a phenomenological scattering matrix.

Quantum Gravity Emergence from Entanglement in a Multi-Fold Universe

We start from a hypothetical multi-fold universe U_MF, where the propagation of everything is slower or equal to ‎the speed of light and where entanglement extends the set of paths available to Path Integrals. This multifold ‎mechanism enables EPR (Einstein-Podolsky-Rosen) “spooky actions at distance” to result from local interactions ‎in the resulting folds. It produces gravity-like attractive effective potentials in the spacetime, between entangled ‎entities, that are caused by the curvature of the folds. When quantized, multi-folds correspond to gravitons and ‎they are enablers of EPR entanglement. Gravity emerges non-perturbative and covariant from EPR entanglement ‎between virtual particles surrounding an entity. In U_MF, we encounter mechanisms that predict gravity fluctuations ‎when entanglement is present, including in macroscopic entanglements. Besides providing a new perspective on ‎quantum gravity, when added to the Standard Model as (SMG), with non-negligible affects at its scales, and to the ‎Standard Cosmology, U_MF can contribute explanations of several open questions and challenges. It also clarifies ‎some relationships and challenges met by other quantum gravity models and Theories of Everything. It leads to ‎suggestions for these works. We also reconstruct the spacetime of U_MF, starting from the random walks of particles ‎in an early spacetime. U_MF now appears as a noncommutative, discrete, yet Lorentz symmetric, spacetime that ‎behaves roughly 2-Dimensional at Planck scales, when it is a graph of microscopic Planck size black holes on a ‎random walk fractal structure left by particles that can also appear as microscopic black holes. Of course, at larger ‎scales, spacetime appears 4-D, where we are able to explain curvature and recover Einstein’s General Relativity. We ‎also discover an entanglement gravity-like contributions and massive gravity at very small scales. This is ‎remarkable considering that no Hilbert Einstein action, or variations expressing area invariance, were introduced. ‎Our model also explains why semi classical approaches can work till way smaller scale than usually expected and ‎present a new view on an Ultimate Unification of all forces, at very small scales. We also explore opportunities for ‎falsifiability and validation of our model, as well as ideas for futuristic applications, that may be worth considering, ‎if U_MF was a suitable model for our universe U_real.‎

Nonclassical correlated optical multistability at low photon level for cavity electromagnetically induced transparency

We study the nonequilibrium dynamic behaviors in a driven-dissipative single-atom cavity electromagnetically induced transparency. The optical bistability and multistability beyond a Kerr nonlinearity are observed utilizing the optical Stark shift induced strong nonlinearity. We show that the nonequilibrium dynamical phase transition between bistability and multistability is highly tunable by the system parameters in a large parameter region. The first-order dissipative optical bistability (multistability) always corresponds to the photon-bunching quantum statistics, which indicates that the quantum fluctuations and correlations play important roles in nonequilibrium dynamics. Interestingly, bistability and multistability with photon-bunching quantum statistics occurring at extremely low steady-state cavity photon number are observed, even under a very strong cavity driven field. Furthermore, we demonstrate that the unique cavity steady-state solution of the full quantum calculation is excellently consistent with the lowest solution based on the semiclassical mean-field approach in bistability and multistability regimes when the cavity photon number is much less than unity, albeit these nonclassical quantum states should possess strong quantum fluctuations in this parameter regime. Our results pave the way to exploring nonclassical correlated optical multistability in quantum regime, which may bring exciting opportunities for potential applications from quantum information processing to quantum metrology.

Finite-temperature dynamics in gapped one-dimensional models in the sine-Gordon family

The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Here we investigate the dynamics of generic, nonintegrable systems belonging to the sine-Gordon family at finite temperature within the semiclassical approach. Focusing on timescales where the effect of nontrivial quasiparticle scatterings becomes relevant, we obtain universal results for the long-time behavior of dynamical correlation functions. We find that correlation functions of vertex operators behave neither ballistically nor diffusively but follow a stretched exponential decay in time. We also study the full counting statistics of the topological current and find that distribution of the transferred charge is non-Gaussian with its cumulants scaling nonuniformly in time.

Semiclassical approach to perturbation theory

The problem of constructing approximate solution methods and finding convenient recurrent algorithms for the study of bound states of quantum mechanical equations is one of the central problems of modern theoretical physics. In this paper an explicit semiclassical treatment of perturbation theory for non-relativistic bound states based on ℏ–­expansions and corresponding quantization conditions of one­dimensional problems is developed. The wave functions are chosen in the same way as in the logarithmic perturbation theory. Due to the introduction of new quantization conditions, this method made it possible to obtain recurrent relations, which are convenient for finding the energy eigenvalues and wave functions of bound states in the case when nodes of wave functions are taken into account. Avoiding the flaws of the standard approach, the obtained recurrent relations have the same form both for the ground and perturbed states.

Thermal spin dynamics of Kitaev magnets: Scattering continua and magnetic field induced phases within a stochastic semiclassical approach

The honeycomb magnet $\alpha-$RuCl$_3$ is a prime candidate material for realizing the Kitaev quantum spin liquid (QSL), but it shows long-range magnetic order at low temperature. Nevertheless, its broad inelastic neutron scattering (INS) response at finite frequency has been interpreted as that of a 'proximate QSL'. A moderate in-plane magnetic field indeed melts the residual zigzag order, giving rise to peculiar intermediate field phases before the high-field polarized state. In INS measurements the low-frequency spin waves disappear, leading to a broad scattering continuum in the field-induced intermediate regime, whose nature is currently under debate. Here, we study the magnetic field dependent spin dynamics of the $K-\Gamma-\Gamma'-$model within a stochastic semiclassical treatment, which incorporates the effect of finite-temperature fluctuations. At temperatures relevant for INS experiments, we show how the excitations of the zigzag phase broaden and that the different intermediate phases all show a similar continuum response. We discuss the implications of our results for experiments and highlight the importance of distinguishing finite temperature fluctuations from genuine quantum fractionalization signatures in frustrated magnets.

Particle Creation and the Schwinger Model

We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage of the fact that the full quantized model is solvable and equivalent to a (massive) gauge field with a non-local effective action. Alternatively, one can also face the problem by following the standard semiclassical route. This means quantizing the massless Dirac field and considering the electromagnetic field as a classical background. We evaluate the energy created by a generic, homogeneous, and time-dependent source. The results match exactly in both approaches. This proves in a very direct and economical way the validity of the semiclassical approach for the (massless) Schwinger model, in agreement with a previous analysis based on the linear response equation. Our discussion suggests that a similar analysis for the massive Schwinger model could be used as a non-trivial laboratory to confront a fully quantized solvable model with its semiclassical approximation, therefore mimicking the long-standing confrontation of quantum gravity with quantum field theory in curved spacetime.

Surface energy coefficient of an N2LO Skyrme energy functional: A semiclassical extended Thomas-Fermi approach

We generalize to N2LO Skyrme functionals the semi-classical approach of Grammaticos and Voros in order to calculate the Extended Thomas Fermi expressions of the new densities and currents appearing at the N2LO level. Within a one dimensional symmetric semi infinite nuclear matter model and using a simple Fermi-like density profile, we obtain an easy-to-use formula for the surface energy including the contributions of the central, density-dependent and spin-orbit terms up to $\hbar^2$. Such a formula can be easily used as a first attempt to constrain the surface properties of new N2LO Skyrme parametrizations. The N2LO parametrization tested in this paper is shown to exhibit a shift (compared to a full Hartree-Fock calculation) which is quantitatively similar to the one obtained with the traditional Skyrme parametrizations.

Unified theory of the anomalous and topological Hall effects with phase-space Berry curvatures.

Spontaneously broken time-reversal symmetry in magnetic materials leads to a Hall response, with a nonzero voltage transverse to an applied current, even in the absence of external magnetic fields. It is common to analyze the Hall resistivity of chiral magnets as the sum of two terms: an anomalous Hall effect arising from spin-orbit coupling and a topological Hall signal coming from skyrmions, which are topologically nontrivial spin textures. The theoretical justification for such a decomposition has long remained an open problem. Using a controlled semiclassical approach that includes all phase-space Berry curvatures, we show that the solution of the Boltzmann equation leads to a Hall resistivity that is just the sum of an anomalous term arising from momentum-space curvature and a topological term related to the real-space curvature. We also present numerically exact results from a Kubo formalism that complement the semiclassical approach.

Lorentzian vacuum transitions with a generalized uncertainty principle

The vacuum transition probabilities between to minima of a scalar field potential in the presence of gravity are studied using the Wentzel–Kramers–Brillouin approximation. First we propose a method to compute these transition probabilities by solving the Wheeler–DeWitt equation in a semi-classical approach for any model of superspace that contains terms of squared as well as linear momenta in the Hamiltonian constraint generalizing in this way previous results. Then we apply this method to compute the transition probabilities for a Friedmann–Lemaitre–Robertson–Walker (FLRW) metric with positive and null curvature and for the Bianchi III metric when the coordinates of minisuperspace obey a Standard Uncertainty Principle and when a Generalized Uncertainty Principle (GUP) is taken into account. In all cases we compare the results and found that the effect of considering a GUP is that the probability is enhanced at first but it decays faster so when the corresponding scale factor is big enough the probability is reduced. We also consider the effect of anisotropy and compare the result of the Bianchi III metric with the flat FLRW metric which corresponds to its isotropy limit and comment the differences with previous works.

Correlating stimulated emission phase to the gain spectra in semiconductor lasers

In laser physics, the incident electric field and the stimulated field are assumed to have the same frequency, direction of propagation, polarization, and phase —same state. However, no formal proof of the phase identity (zero phase shift) was reported. The existing theories on the phase shift are in conflict with each other and with the phase identity. The phase shift in three semiconductor active media (GaAs, In0.15Ga0.85As, and In0.48Ga0.58As0.9P0.1) has been studied using a semiclassical approach. Contrary to the conventional belief, it has been found that the phase shift is not zero. The phase shift is not even a single value but rather a spectrum corresponding to the gain spectrum. At a carrier concentration of 2.5 × 1024 m −3, the minima of the phase shift spectra are 1.5597, 1.509, and 1.399 radians for GaAs, In0.15Ga0.85As, and In0.48Ga0.58As0.9P0.1, respectively. Stimulated emission is shown to occur whenever the phase shift is positive and lies in the interval between 0 and π/2. Because of radiation reaction of the radiating source and the finite lifetime of excited states, stimulated emission cannot attain the same phase as the incident field —no zero-phase shift. These results reveal that the conventional picture of phase identity is incorrect, and phase matching between the incident field and stimulated is not a necessary condition for stimulated radiation. Despite the fundamentality of the concept of stimulated emission phase, such outcomes are not reported nor discussed in the literature.