Semiclassical Model Research Articles

Universal crossover in quantum circuits governed by a proximate classical error correction transition

We formulate a semi-classical circuit model to clarify the role of quantum entanglement in the recently discovered encoding phase transitions in quantum circuits with measurements. As a starting point we define a random circuit model with nearest neighbor classical gates interrupted by erasure errors. In analogy with the quantum setting, this system undergoes a purification transition at a critical error rate above which the classical information entropy in the output state vanishes. We show that this phase transition is in the directed percolation universality class, consistent with the fact that having zero entropy is an absorbing state of the dynamics; this classical circuit cannot generate entropy. Adding an arbitrarily small density of quantum gates in the presence of errors eliminates the transition by destroying the absorbing state: the quantum gates generate internal entanglement, which can be effectively converted to classical entropy by the errors. We describe the universal properties of this instability in an effective model of the semi-classical circuit. Our model highlights the crucial differences between information dynamics in classical and quantum circuits.

Fine Tuning the Intermolecular Interactions of Water Clusters Using the Dispersion-Corrected Density Functional Theory.

Dispersion-inclusive density functional theory (DFT) methods have unequivocally demonstrated improved performances with respect to standard DFT approximations for modeling large and extended molecular systems at the quantum mechanical level. Yet, in some cases, disagreements with highly accurate reference calculations, such as CCSD(T) and quantum Monte Carlo (MC) calculations, still remain. Furthermore, the application of general-purpose corrections, such as the popular Grimme's semi-classical models (DFT-D), to different Kohn-Sham exchange-correlation functionals sometimes leads to variable and inconsistent results, which recommend a careful prior evaluation. In a recent study, we proposed a simple optimization protocol for enhancing the accuracy of these DFT-D methods by following an alternative and system-specific approach. Here, adopting the same computational strategy, we show how the accurate MC intermolecular interactions of a large set of water clusters of variable sizes (i.e., 300 (H2O)n structures, n = 9, 15, 27) can be reproduced remarkably well by dispersion-corrected DFT models (i.e., B3LYP-D4, PBE-D4, revPBE(0)-D4) upon re-optimization, reaching a mean absolute error per monomer of ~0.1 kcal/mol. Hence, the obtained results support the use of this procedure for fine-tuning tailored DFT-D models for the accurate description of targeted molecular systems.

Spectral Properties of Exact Polarobreathers in Semiclassical Systems

In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born–Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency–momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable.

The Catalytic Role of Electrons and Positrons in the Synthesis of Chemicals and of Hadrons

We discuss the similarities and differences between catalysis/electrocatalysis of chemical processes, such as ammonia synthesis or H2O electrolysis on one hand, and of nuclear catalytic processes, commonly called baryosynthesis, such as the synthesis of neutrons and protons from quarks, on the other. In chemical synthesis the underlying forces are well known to be electrostatic in nature while in the synthesis of hadrons or nuclei from quarks (known as hadronization or nucleosynthesis) the underlying forces are known as the Strong nuclear forces, whereas if electrons are also involved, as Weak nuclear forces. Here we discuss for the first time from a catalytic viewpoint the importance of some recent developments in our understanding of the structure and synthesis of hadrons via a model entitled Rotating Lepton Model (RLM), which is quite similar to the Bohr model of the H atom used in Chemistry but which has shown that the Strong Force is a gravitational force between three very fast (relativistic) neutrinos, rotating symmetrically on a circular orbit, whose gravitational masses and gravitational attraction increases dramatically with increasing rotational speed, according to the theory of Special Relativity (SR), thus reaching the masses of quarks and the value of the Strong Force respectively. We show that, interestingly, positrons and electrons, which quite often play a very important and well established catalytic role in chemical synthesis due to their electrical charge, also play an equally important and central catalytic role in nuclear synthesis due to their enormous mass, relative to the mass of the neutrinos, and the concomitant dramatic acceleration of neutrinos to ultrarelativistic speeds and huge mass increase, resulting to enhanced very strong gravitational binding between them which reaches the value of the Strong Force. Consequently, electrons and positrons are the dual, electrostatic and gravitational, catalysts of our Universe for the production of chemicals and baryons.

Singularity in the electron-core potential as a gateway to accurate multielectron ionization spectra in strongly driven atoms

We demonstrate a general three-dimensional semiclassical model as a powerful technique for the study of correlated multi-electron escape in atoms driven by infrared laser pulses at intensities where electron-electron correlation prevails. We do so in the context of triple ionization of strongly driven Ne. We show that a drawback of other current quantum mechanical and classical models of triple ionization is that they soften the Coulomb potential of each electron with the core. The model we employ fully accounts for the singularity in the Coulomb potentials of a recolliding electron with the core and a bound electron with the core as well as for the interaction of a recolliding with a bound electron. Our model treats approximately only the interaction between bound electrons through the use of effective potentials. These effective potentials ensure that no artificial autoionization takes place as a result of the full treatment of the electron-core potential. We demonstrate the accuracy of our model by obtaining triple ionization distributions of the sum of the final electron momenta which we find to be in very good agreement with experiments. Also, we explain the main features of these momenta distributions in terms of the prevalent pathways of correlated three-electron escape in Ne. We also show that the different ionization pathways prevailing in three-electron escape in strongly driven Ne versus Ar give rise to different momenta distributions in these two atoms.

Universal anomaly of dynamics at phase transition points induced by Pancharatnam-Berry phase

Dynamical anomalies are often observed near both the continuous and first-order phase transition points. We propose that the universal anomalies could originate from the geometric phase effects. A Pancharatnam-Berry phase is accumulated continuously in quantum states with the variation of tuning parameters. Phase transitions are supposed to induce an abrupt shift of the geometric phase. In our multi-level quantum model, the quantum interference induced by the geometric phase could prolong or shorten the relaxation times of excited states at phase transition points, which agrees with the experiments, models under sudden quenches and our semi-classical model. Furthermore, we find that by setting a phase shift of π, the excited state could be decoupled from the ground state by quantum cancellation so that the relaxation time even could diverge to infinity. Our work introduces the geometric phase to the study of conventional phase transitions as well as quantum phase transition, and could substantially extend the dephasing time of qubits for quantum computing.

Andreev processes in mesoscopic multiterminal graphene Josephson junctions

There is growing interest in using multi-terminal Josephson junctions (MTJJs) as a platform to artificially emulate topological phases and to investigate complex superconducting mechanisms such as quartet and multiplet Cooper pairings. Current experimental signatures in MTJJs have led to conflicting interpretations of the salient features. In this work, we report a collaborative experimental and theoretical investigation of graphene-based four-terminal Josephson junctions. We observe resonant features in the differential resistance maps that resemble those ascribed to multiplet Cooper pairings. To understand these features, we model our junctions using a circuit network of coupled two-terminal resistively and capacitively shunted junctions (RCSJs). Under appropriate bias current, the model predicts that a current flowing between two diagonal terminals in a four-terminal geometry may be represented as a sinusoidal function of a weighted sum of the superconducting phases. We show that starting from a semi-classical model with diffusive current-phase relations, the MTJJ effectively emulates a general form of the expected current-phase relation for multiplet Cooper pairings. Our study therefore suggests that differential resistance measurements alone are insufficient to conclusively distinguish resonant Andreev reflection processes from semi-classical circuit-network effects.

Fluorescence in quantum dynamics: Accurate spectra require post-mean-field approaches.

Real time modeling of fluorescence with vibronic resolution entails the representation of the light-matter interaction coupled to a quantum-mechanical description of the phonons and is therefore a challenging problem. In this work, taking advantage of the difference in timescales characterizing internal conversion and radiative relaxation-which allows us to decouple these two phenomena by sequentially modeling one after the other-we simulate the electron dynamics of fluorescence through a master equation derived from the Redfield formalism. Moreover, we explore the use of a recent semiclassical dissipative equation of motion [C. M. Bustamante et al., Phys. Rev. Lett. 126, 087401 (2021)], termed coherent electron electric-field dynamics (CEED), to describe the radiative stage. By comparing the results with those from the full quantum-electrodynamics treatment, we find that the semiclassical model does not reproduce the right amplitudes in the emission spectra when the radiative process involves the de-excitation to a manifold of closely lying states. We argue that this flaw is inherent to any mean-field approach and is the case with CEED. This effect is critical for the study of light-matter interaction, and this work is, to our knowledge, the first one to report this problem. We note that CEED reproduces the correct frequencies in agreement with quantum electrodynamics. This is a major asset of the semiclassical model, since the emission peak positions will be predicted correctly without any prior assumption about the nature of the molecular Hamiltonian. This is not so for the quantum electrodynamics approach, where access to the spectral information relies on knowledge of the Hamiltonian eigenvalues.

Valley-optical absorption in planar transition metal dichalcogenide superlattices

In this study, we investigate the optical absorption of a planar superlattice comprising alternatively arranged two-dimensional Transition Metal DiChalcogenide semiconductors. Within a semi-classical model and using the Dirac-like equation in the presence of light interaction as a perturbation, we obtained the governing Hamiltonian. Using this Hamiltonian, we derived a fully analytical relationship for the absorption coefficient of the structure. By calculating the effective mass for different bands and using the Drude-Lorentz model, our approach is able to determine the oscillator strength and the effective refractive index of the structure. We found that the spin–orbit coupling has important effect on the absorption coefficient and energy bands where it reduces the absorption coefficient of the structure from typical value of 11.54 ({10}^{5}{mathrm{cm}}^{-1})–5.937({10}^{5}{mathrm{cm}}^{-1}), also the valence band experiences a significant blue shift, while the conduction band shows minor changes due to spin orbit coupling. Moreover, the role of incident light angle and light polarization were studied in details at different valleys of K and {K}^{^{prime}}. The most important finding is that by changing the polarization of incident light, it is possible to increase the absorption coefficients of K and {K}^{^{prime}} valleys by up to 30 times. For light propagation direction close to perpendicular to the plane of the superlattice, the right-circular polarization is absorbed only by K valley in contrast to the left-circular polarization, which is absorbed by the {K}^{^{prime}} valley. Our model might be used to design newly developed 2D optovalleytronic devices.

“Bound luminosity” state in the extended Dicke model

The extended Dicke model describes interaction of the single-mode electromagnetic resonator with an ensemble of interacting two-level systems. In this paper we obtain quasiclassical equations of motion of the extended Dicke model. For certain initial conditions and range of parameters the equations of motion can be solved analytically via Jacobi elliptic functions. The solution is a “bound luminosity” state, which was described by the authors previously for ordinary Dicke model and now is generalized for the case of the extended Dicke model. In this state the periodic beatings of the electromagnetic field occur in the microwave cavity filled with the ensemble of two-level systems. At the beginning of the time period the energy is stored in the electromagnetic field in the cavity, then it is absorbed by the ensemble of two-level systems, being afterwards released back to the cavity in the end of the period. Also the chaotic properties of the semiclassical model are investigated numerically.

Anderson Localization in Dissipative Lattices

AbstractAnderson localization predicts that wave spreading in disordered lattices can come to a complete halt, providing a universal mechanism for dynamical localization. In the one‐dimensional Hermitian Anderson model with uncorrelated diagonal disorder, there is a one‐to‐one correspondence between dynamical localization and spectral localization, that is, the exponential localization of all the Hamiltonian eigenfunctions. This correspondence can be broken when dealing with disordered dissipative lattices. When the system exchanges particles with the surrounding environment and random fluctuations of the dissipation are introduced, spectral localization is observed but without dynamical localization. Previous studies consider lattices with mixed conservative (Hamiltonian) and dissipative dynamics and are restricted to a semiclassical analysis. However, Anderson localization in purely dissipative lattices, displaying an entirely Lindbladian dynamics, remains largely unexplored. Here the purely‐dissipative Anderson model in the framework of a Lindblad master equation is considered, and it is shown that, akin to the semiclassical models with conservative hopping and random dissipation, one observes dynamical delocalization in spite of strong spectral localization of the Liouvillian superoperator. This result is very distinct from delocalization observed in the Anderson model with dephasing, where dynamical delocalization arises from the delocalization of the stationary state of the Liouvillian.

THE RADIATIVE CORRECTIONS TO THE COULOMB LAW

Photon can exist in the intermediate state with electron and positron as virtual particles. The photon propagation function based on such process with electron-positron pair is determined from the effective emission and absorption sources. The Schwinger source methods of quantum field theory is applied. Then, the Coulomb potential and Bohr energy with radiative corrections is determined.

The ellipticity dependence of Rydberg state excitation of noble gas atoms subject to strong laser fields

In this work, we theoretically investigate the ellipticity dependence of the Rydberg state excitation (RSE) and ionization of noble gas atoms subject to strong laser fields at a series of intensities and wavelengthes by a semiclassical model, where the nonadiabtic effect is considered or ignored. Our results demonstrate that, if the nonadiabatic effect has been ignored, the ratio between RSE and ionization yields exhibits an anomalous maximum at a nonzero ellipticity. On the other hand, if the nonadiabatic effect has been considered, this anomalous behavior disappears. The analysis indicates that the absence of this anomalous behavior can be attributed to the nonadiabatic corrections of instantaneous ionization rate and the initial photoelectron momentum distribution at the tunnel exit.

Atomic photoionization by spatiotemporal optical vortex pulses

Electromagnetic waves with a helical-like wavefront are known as optical vortices. One of their main characteristics is a phase structure that has a circulation around a singularity and that they carry orbital angular momentum (OAM). OAM is a fundamental property that governs the interaction of these sources with matter. In the present paper, we study the electron dynamics driven by a so-called spatiotemporal optical vortex (STOV). Contrary to the conventional optical vortices, a STOV carries transverse OAM. By designing a streakinglike technique, we aim to fully characterize the OAM of the STOV. Using both quantum mechanical and semiclassical models, we are able to dissect the spatially resolved photoelectron energy spectra and accurately retrieve the OAM. Our approach paves the way toward a complete understanding of the interaction of complex spatiotemporal light fields with atomic targets.

Stochastic Nature and Intramolecular Coupling in Optical Response Profiles: Critical Analysis through Semiclassical Models.

We have studied the nonlinear absorptive and dispersive responses considering a molecular system consisting of two-levels, where aspects of the vibrational internal structure and intramolecular coupling are inserted, in addition to the considerations of interaction with the thermal reservoir. The Born-Oppenheimer electronic energy curve for this molecular model consists of two-intercrossing harmonic oscillator potentials with minima displaced in energy and nuclear coordinate. The results obtained show how these optical responses are sensitive to explicit considerations of both intramolecular coupling and the presence of the solvent through their stochastic interaction. Our study shows that the permanent dipoles of the system and the transition dipoles induced by electromagnetic field effects represent critical quantities for the analysis. The solvent action in our model is treated through the natural Bohr frequency shift to a time-dependent function, with explicit manifestations in its comparison as if the upper state were broadened. Significant variations in the nonlinear optical properties for cases of perturbative and saturative treatments, relaxation times, and optical propagation, mainly due to changes in the probe and pump intensities, are studied. Our studies relating the intramolecular effects with those generated by the presence of the solvent and its stochastic interaction with the solute of study, have allowed not only to analyze the influence of these in the profile of the optical responses, but they could also provide some insights into the analysis and characterization of molecular systems through nonlinear optical properties.

Mass-energy equation and the theory of photon emission derived from Bohr's theory

The Einstein's relativistic mass-energy equation ε = mc2 is also obtained from Bohr's theory. The Schrödinger equation (SE) is modified using this equation. In the hydrogenlike atom, the modified SE is solved for consistency with the eigenvalues of electron's energy derived from the Dirac equation. Based on the consistency of their eigenvalues, the theory of photon emission is expressed. From this theory, an emission process different from bremsstrahlung is expressed. X-ray and gamma-ray bursts associated with thunderclouds and lightning are discussed by this process.

Investigation of charged-particle induced reactions on 27Al up to 100 MeV leading to the formation of 22Na and 24Na

Abstract Studies using theoretical models are of great importance for understanding of reaction process and its nature. In this study, nuclear level density model calculations of the cross sections of 27Al are investigated by using TALYS 1.96 computer code. The cross section calculations of 27Al(α,x)22Na, 27Al(α,x)24Na, 27Al(3He,x)22Na, 27Al(3He,x)24Na, 27Al(p,x)22Na and 27Al(p,x)24Na reactions were carried out for incident particle energy up to 100 MeV. In these calculations, four nuclear level density models, namely constant temperature model (CTM), back-shifted Fermi gas model (BSFGM), generalized superfluid model (GSM) and recently proposed semi-classical Fermi gas model (CSCFGM) are used. This model is developed using the simplest model BSFGM. The most obvious difference between CSCFGM and other models is the inclusion of the collective effects in the base of the formulation. The predicted results are discussed and compared with each other and the available experimental data taken from EXFOR library. In order to better evaluate the model results, chi-squared values are calculated and compared with each other for all analyzed reactions. According to the chi-squared results, CSCFGM gives closer predictions to the experimental data compared with the other models in 4 of the 6 analyzed reactions. Therefore, in this study, it is presented that this model can be reliably used in the reaction cross section calculations.

Theoretical Prediction of Mobility Improvement in GaN-Based HEMTs at High Carrier Densities

In this article, we use a semiclassical low-field mobility modeling framework, which includes all relevant scattering mechanisms, to examine the dependence of electron mobility on 2-D electron gas (2DEG) density in previously characterized high Al-content AlGaN/gallium nitride (GaN) high electron mobility transistors (HEMTs) with and without an AlN spacer layer. Polar optical phonon (POP) scattering has previously been identified as the dominant scattering mechanism in GaN-based HEMTs at room temperature, so the analysis of POP scattering rates is of particular importance. We find that the POP-limited mobility in both structures decreases with increasing 2DEG density up to a critical density of around <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${10}^{{13}}$ </tex-math></inline-formula> cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{-{2}}$ </tex-math></inline-formula> , above which we observe a significant improvement of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${46}\%$ </tex-math></inline-formula> , contrary to the behavior typically reported for GaN HEMT structures. The POP-limited mobility increase is explained by the interplay of ground-state energy and quasi-Fermi energy within the channel, by which intrasubband POP emission within the ground state is suppressed at high 2DEG densities. This provides a universal guideline for the design and operation of GaN-based HEMTs to achieve a minimum ON-resistance in switching applications at room temperature and above.

Interlocking Toy Bricks Help Nursing Students “Handle” Valence Electrons, Molarity, Solubility, and More!

For decades, chemical modeling sets have allowed the user to manipulate atoms and bonds using plastic/wooden ball and stick materials. Here is a design for an interlocking toy brick modeling set in which the undergraduate nursing student can manipulate electrons during the simulated chemical bonding exercise. The author presents a teaching and learning activity/demonstration designed to help undergraduate nursing (BSN) students both visualize and physically manipulate (“handle”) abstract chemical education topics such as valence shell electrons and molarity (with manipulatives for solubility rules) of salts, acids, and bases in a chemistry for health professions didactic course, as an effort to increase comprehension of these chemical education topics. This learning tool was one in a series of newly coined “PERCEIVE” (Preparing Engaging Real-time Chemical Education Interactive and Visual Examples) chemical education demonstrations, where BSN students prepare engaging demonstrations, while working in groups. The preparation (building) step allows students to get a “handle” on how the chemistry concept works. Afterward the newly prepared demonstrations are utilized as examples for chemical education and chemistry in health topics─hence, the “PERCEIVE” acronym. This publication outlines: (i) Connections between Molarity and Solubility in modern healthcare practices, (ii) The method and materials for using interlocking toy bricks selected according to CPK color-scheme for modeling valence shell electrons (based on Bohr models), (iii) Solubility rules, (iv) Molarity (and calculations), and (v) Results from anonymous pre- and postqualitative student questionnaires. Student responses indicated a marked increase in the ability to calculate molarity in different volumes (1 L vs 500 mL) postdemonstration. Additional qualitative surveys were conducted, and the results highlighted more than 90% of 152 respondents endorsed the continued implementation of this demo in subsequent chemistry for health professions courses.

Revealing the band structure of ZrTe5 using multicarrier transport

The layered material ZrTe$_5$ appears to exhibit several exotic behaviors which resulted in significant interest recently, although the exact properties are still highly debated. Among these we find a Dirac/Weyl semimetallic behavior, nontrivial spin textures revealed by low temperature transport, and a potential weak or strong topological phase. The anomalous behavior of resistivity has been recently elucidated as originating from band shifting in the electronic structure. Our work examines magnetotransport behavior in ZrTe$_5$ samples in the context of multicarrier transport. The results, in conjunction with ab-initio band structure calculations, indicate that many of the transport features of ZrTe$_5$ across the majority of the temperature range can be adequately explained by the semiclassical multicarrier transport model originating from a complex Fermi surface.