Semiclassical Approach Research Articles

Semiclassical Scattering by Edge Imperfections in Topological Insulators Under Magnetic Field

We study the scattering of edge states of 2D topological insulator in the uniform external magnetic field due to edge imperfections, common in realistic 2D topological insulator samples. The external magnetic field breaks time-reversal symmetry, opening the possibility of the scattering of otherwise topologically protected fermionic edge states. The scattering happens to be always an over-barrier event, irrespective of the shape of the edge deformation and magnitude of the magnetic field. We use the advanced Pokrovsky–Khalatnikov semiclassical approach, which allows us to obtain analytically both the main exponential and pre- exponential factors of the scattering amplitude for wide classes of analytic deformation profiles.

Resonant transport in a double-barrier heterostructure AlxGa1−xAs/GaAs and mass discontinuity: a semiclassical path integral approach

In this paper, we investigate the dependence of the resonant carrier transport in an AlGaAs/GaAs double-barrier heterostructure on the electron’s effective mass discontinuity between the well and the barrier layer. We use a one-dimensional model for the effective potential and consider the activation of the resonant tunneling mechanism when a bias is applied between the emitter and the collector. We calculate the system’s Green’s function through semiclassical path integration to obtain the complex spectrum. Electron’s effective mass discontinuity affects our calculations through the contributions of the various propagations inside the heterostructure and the multiple reflections from the turning points. Our findings show that the lowest resonance energy decreases linearly with increasing bias, while the real energy shift of the resonance decreases in a non-linear manner with the mass discontinuity. We also observe that the resonant transport time increases nearly linearly with the mass discontinuity. These results demonstrate the impact of the carrier’s inertia enhancement on the resonance characteristics and are consistent with established concepts in quantum mechanics and previously published works. Furthermore, we identify a critical bias value that distinguishes the behavior of the symmetric and asymmetric heterostructure. Additionally, the derivative of the transport time with respect to mass discontinuity is found to be independent of the applied bias. Our results provide concise analytical relationships involving parameters such as barrier and well thickness and shape, enabling the prediction and optimization of various nanoscale devices’ performance.

Model and Energy Bounds for a Two-Dimensional System of Electrons Localized in Concentric Rings.

We study a two-dimensional system of interacting electrons confined in equidistant planar circular rings. The electrons are considered spinless and each of them is localized in one ring. While confined to such ring orbits, each electron interacts with the remaining ones by means of a standard Coulomb interaction potential. The classical version of this two-dimensional quantum model can be viewed as representing a system of electrons orbiting planar equidistant concentric rings where the kinetic energy may be discarded when one is searching for the lowest possible energy. Within this framework, the lowest possible energy of the system is the one that minimizes the total Coulomb interaction energy. This is the equilibrium energy that is numerically determined with high accuracy by using the simulated annealing method. This process allows us to obtain both the equilibrium energy and position configuration for different system sizes. The adopted semi-classical approach allows us to provide reliable approximations for the quantum ground state energy of the corresponding quantum system. The model considered in this work represents an interesting problem for studies of low-dimensional systems, with echoes that resonate with developments in nanoscience and nanomaterials.

Randomized SearchRank: A semiclassical approach to a quantum search engine

The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the N/M ratio between the network size N and the number of marked nodes M is sufficiently large. We propose a modification of the algorithm, replacing the underlying Szegedy quantum walk with a semiclassical walk. To maintain the same time complexity as the quantum SearchRank algorithm we propose a simplification of the algorithm. This new algorithm is called randomized SearchRank, since it corresponds to a quantum walk over a randomized mixed state. The performance of the SearchRank algorithms is first analyzed on an example network and then statistically on a set of different networks of increasing size and different number of marked nodes. On the one hand, to test the search ability of the algorithms, it is computed how the probability of measuring the marked nodes decreases with N/M for the quantum SearchRank, but remarkably it remains at a high value around 0.9 for our semiclassical algorithms, solving the quantum SearchRank problem. The time complexity of the algorithms is also analyzed, obtaining a quadratic speedup with respect to the classical ones. On the other hand, the ranking functionality of the algorithms has been investigated, obtaining a good agreement with the classical PageRank distribution. Finally, the dependence of these algorithms on the intrinsic PageRank damping parameter has been clarified. Our results suggest that this parameter should be below a threshold so that the execution time does not increase drastically. Published by the American Physical Society 2024

Inverse spectral Love problem via Weyl–Titchmarsh function

In this paper, we prove an inverse resonance theorem for the half-solid with vanishing stresses on the surface via Weyl–Titchmarsh function. Using a semi-classical approach, it is possible to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schrödinger equation with Robin boundary conditions on the half-line. The goal of the paper is to establish a method to recover the potential from eigenvalues and resonances through the Weyl–Titchmarsh function for non-self-adjoint problems and to establish a one-to-one and onto map between suitable function spaces. Moreover, we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances, via the spectral data.

Theoretical Description of Pump-Probe Experiments in Charge-Density-Wave Materials out to Long Times

We describe coupled nonequilibrium electron-phonon systems semiclassically—Ehrenfest dynamics for the phonons and quantum mechanics for the electrons—using a classical Monte Carlo approach that determines the nonequilibrium response to a large pump field. The semiclassical approach is expected to be accurate, because the phonons are excited to average energies much higher than the phonon frequency, eliminating the need for a quantum description. The numerical efficiency of this method allows us to perform a self-consistent time evolution out to very long times (tens of picoseconds), enabling us to model pump-probe experiments of a charge-density-wave (CDW) material. Our system is a half-filled, one-dimensional (1D) Holstein chain that exhibits CDW ordering due to a Peierls transition. The chain is subjected to a time-dependent electromagnetic pump field that excites it out of equilibrium, and then a second probe pulse is applied after a time delay. By evolving the system to long times, we capture the complete process of lattice excitation and subsequent relaxation to a new equilibrium, due to an exchange of energy between the electrons and the lattice, leading to lattice relaxation at finite temperatures. We employ an indirect (impulsive) driving mechanism of the lattice by the pump pulse due to the direct driving of the electrons. We identify two driving regimes, where the pump can either cause small perturbations or completely invert the initial CDW order. Our work successfully describes the ringing of the amplitude mode in CDW systems that has long been seen in experiment but never successfully explained by microscopic theory. We also describe the fluence-dependent crossover that inverts the CDW order parameter and changes the phonon dynamics. Finally, we illustrate how this method can examine a number of different types of experiments including photoemission, x-ray diffraction, and two-dimensional (2D) spectroscopy. Published by the American Physical Society 2024

Schrödinger equation for the chiral geometry in atomic nuclei

The dynamical and spectral features of the chiral geometry in atomic nu clei are described by means of a triaxial rigid rotor Hamiltonian cranked by quasiparticle alignments. The problem is treated alternatively in the space of angular momentum states and using a Schr¨odinger equation for a continuous variable associated with an angular momentum projection. The later is con structed using a semiclassical approach. Numerical applications performed for various deformation and alignment conditions with both methods are compared in terms of energy levels and wave functions.

GPU-accelerated on-the-fly nonadiabatic semiclassical dynamics.

GPU-accelerated on-the-fly nonadiabatic dynamics is enabled by interfacing the linearized semiclassical dynamics approach with the TeraChem electronic structure program. We describe the computational workflow of the "PySCES" code interface, a Python code for semiclassical dynamics with on-the-fly electronic structure, including parallelization over multiple GPU nodes. We showcase the abilities of this code and present timings for two benchmark systems: fulvene solvated in acetonitrile and a charge transfer system in which a photoexcited zinc-phthalocyanine donor transfers charge to a fullerene acceptor through multiple electronic states on an ultrafast timescale. Our implementation paves the way for an efficient semiclassical approach to model the nonadiabatic excited state dynamics of complex molecules, materials, and condensed phase systems.

Computational insights into the multifunctional properties of Li2AgBiX6 (X=Cl, Br, I) double perovskite materials

We investigate the potential of Li2AgBiX6 (X = Cl, Br, I) double perovskites for optoelectronic and transport applications using density functional theory. Structural stability is confirmed through lattice constant, tolerance factor, and formation enthalpy calculations. Using the HSE-06 functional, we determine indirect bandgaps of 1.78, 1.76, and 0.92 eV for Cl, Br, and I compositions, respectively. Maximum optical absorption occurs in the visible region, supporting their potential in optoelectronic devices. Spectroscopic limited maximum efficiency calculations reveal Li2AgBiI6 as the most efficient (29.3 %) due to higher absorbance. We evaluate thermoelectric properties using the Boltzmann semi-classical approach and assess mechanical stability through elastic constants. Thermodynamic properties, including Debye temperature and melting point, are calculated. Magnetic property calculations indicate zero magnetic moment. The comprehensive analysis of structural, electronic, optical, transport, elastic, thermodynamic, and magnetic properties provide valuable insights into these promising double perovskite materials for various applications.

Inertia from radiation: A semiclassical approach

Starting from a thought experiment based on an accelerated reflecting cavity containing a radiation bath, the cavity-radiation dynamical interaction is evaluated. The radiation is considered as a monochromatic flux of photons that bounces forwards and backwards in the direction of acceleration. In this case, in each reflection, the delay originating from the time of flight of photons causes a difference in velocity between the receiving and emitting reflecting faces at the opposite ends of the cavity, and consequently, a Doppler shift. Despite the ends of the cavity being at rest relative to each other, this phenomenon generates a difference of radiation pressure between both ends, which acts as the inertia of the radiation bath and verifies Newton’s 2nd Law for non-relativistic conditions. This result has interesting implications for the current theoretical pictures of dynamical properties of photons.

Semiclassical approach for nuclear Coulomb excitation

Semiclassical approach for nuclear Coulomb excitation

Semiclassics for the QCD vacuum structure through T2-compactification with the baryon-’t Hooft flux

We study QCD vacuum structure with the topological θ angle using a recently proposed semiclassical approach on ℝ2 × T2 with the ’t Hooft and baryon magnetic fluxes. Under the assumption of adiabatic continuity in this setup, the confining vacuum can be described by the dilute gas of center vortices. With this semiclassical approach, we derive the 2d effective description at small T2 and successfully explain the reasonable theta dependence of the QCD vacuum: in the one-flavor QCD at θ = π, the CP symmetry is spontaneously broken for quark mass above a critical value and restored for a subcritical mass, while the CP symmetry is always spontaneously broken in the multi-flavor QCD at θ = π. From our semiclassical description, we discuss implications to the 4d chiral Lagrangian and propose how the η′ meson should be incorporated in consistent with known global structures: the periodicity of the η′ should be extended from the naive one 2π to 2πN. Additionally, we revisit the phase diagram of Nf = 1 + 1 and Nf = 1 + 1 + 1 QCD on the up and down quark mass plane, confirming and refining the existence of the CP-broken Dashen phase.

A Perspective on the Investigation of Spectroscopy and Kinetics of Complex Molecular Systems with Semiclassical Approaches.

In this Perspective we show that semiclassical methods provide a rigorous hierarchical way to study the vibrational spectroscopy and kinetics of complex molecular systems. The time averaged approach to spectroscopy and the semiclassical transition state theory for kinetics, which have been first adopted and then further developed in our group, provide accurate quantum results on rigorous physical grounds and can be applied even when dealing with a large number of degrees of freedom. In spectroscopy, the multiple coherent, divide-and-conquer, and adiabatically switched semiclassical approaches have practically permitted overcoming issues related to the convergence of results. In this Perspective we demonstrate the possibility of studying the semiclassical vibrational spectroscopy of a molecule adsorbed on an anatase (101) surface, a system made of 51 atoms. In kinetics, the semiclassical transition state theory is able to account for anharmonicity and the coupling between the reactive and bound modes. Our group has developed this technique for practical applications involving the study of phenomena like kinetic isotope effect, heavy atom tunneling, and elusive conformer lifetimes. Here, we show that our multidimensional anharmonic quantum approach is able to tackle on-the-fly the thermal kinetic rate constant of a 135 degree-of-freedom system. Overall, semiclassical methods open up the possibility to describe at the quantum mechanical level systems characterized by hundreds of degrees of freedom leading to the accurate spectroscopic and kinetic description of biomolecules and complex molecular systems.

Extended calculations of nitrogen-induced line broadening coefficients in the [formula omitted] band of ethylene

Computations of room-temperature N2-broadening coefficients are performed for 3546 lines in the ν7 infrared absorption band of ethylene to provide data required for atmospheric studies but missing in spectroscopic databases. The calculations are done in the framework of a semi-classical exact-trajectory approach developed previously (Buldyreva and Nguyen, 2008). The active molecule is rigorously treated as an asymmetric top and the perturber is traditionally considered to be in its ground vibrational state. The data are provided for the P,RP-, P,RQ- and P,RR-subbranches (lines with ΔKa=±1 having observable intensities) for (initial) rotational quantum numbers J up to 22, limited by the available numerical energies for the excited vibrational level. Moreover, potentially detectable lines with ΔKa=±3 are also considered for J≤13, limited by high computational cost. Being validated by comparison with existing experimental results, these data can replace unavailable measurements and will be useful for atmospheric/industrial applications.

A semi-classical Floquet-NEGF approach to model photon-assisted tunneling in quantum well devices

A semi-classical Floquet-NEGF approach to model photon-assisted tunneling in quantum well devices

Multicritical dissipative phase transitions in the anisotropic open quantum Rabi model

We investigate the nonequilibrium steady state of the anisotropic open quantum Rabi model, which exhibits first-order and second-order dissipative phase transitions upon varying the degree of anisotropy between the coupling strengths of rotating and counter-rotating terms. Using both semiclassical and quantum approaches, we find a rich phase diagram resulting from the interplay between the anisotropy and the dissipation. First, there exists a bistable phase where both the normal and superradiant phases are stable. Second, there are multicritical points where the phase boundaries for the first- and second-order phase transitions meet. We show that a new set of critical exponents governs the scaling of the multicritical points. Finally, we discuss the feasibility of observing the multicritical transitions and bistability using a pair of trapped ions where the anisotropy can be tuned by controlling the intensity of the Raman transitions. Our study enlarges the scope of critical phenomena that may occur in finite-component quantum systems, which could be useful for applications in critical quantum sensing. Published by the American Physical Society 2024

Quantum gravity signatures in gravitational wave detectors placed inside a harmonic trap potential

In this work, we consider a general gravitational wave detector of gravitational waves interacting with an incoming gravitational wave carrying plus polarization only placed inside a harmonic trap. This model can be well acquainted with the description of a resonant detector of gravitational waves as well. The well-known detector-gravitational wave interaction scenario uses the method of a semiclassical approach where the detector is treated quantum mechanically but the gravitational wave is considered at a classical level. In our analysis, we use a discrete mode decomposition of the gravitational wave perturbation which results in a Hamiltonian involving the position and momentum operators corresponding to the gravitational wave and the harmonic oscillator. We have then calculated the transition probability for the harmonic oscillator-gravitational wave tensor product state for going from an initial state to some unknown final state. Using the energy flux relation of the gravitational waves, we observe that if we consider the total energy as a combination of the number of gravitons in the initial state of the detector then the transition probability for the resonant absorption case scenario takes the analytical form which is exactly similar to the semiclassical absorption case. In the case of the emission scenario, we observe a spontaneous emission of a single graviton which was completely absent in the semiclassical analog of this model. This therefore gives a direct signature of linearized quantum gravity. Published by the American Physical Society 2024

Non-supersymmetric duality cascade of QCD(BF) via semiclassics on ℝ2× T2 with the baryon-’t Hooft flux

We study the phase diagrams of the bifundamental QCD (QCD(BF)) of different ranks, which is the 4d SU(N1) × SU(N2) gauge theory coupled with a bifundamental Dirac fermion. After discussing the anomaly constraints on possible vacuum structures, we apply a novel semiclassical approach on ℝ2× T2 with the baryon-’t Hooft flux to obtain the concrete dynamics. The 2d effective theory is derived by the dilute gas approximation of center vortices, and it serves as the basis for determining the phase diagram of the model under the assumption of adiabatic continuity. As an application, we justify the non-supersymmetric duality cascade between different QCD(BF), which has been conjectured in the large-N argument. Combined with the semiclassics and the large-N1,2 limit, we construct the explicit duality map from the parent theory, SU(N1) × SU(N2) QCD(BF), to the daughter theory, SU(N1) × SU(N2− N1) QCD(BF), including the correspondence of the coupling constants. We numerically examine the validity of the duality also for finite N1,2 within our semiclassics, finding a remarkable agreement of the phase diagrams between the parent and daughter sides.

Behavior of Correlation Functions in the Dynamics of the Multiparticle Quantum Arnol'd Cat.

The multi-particle Arnol'd cat is a generalization of the Hamiltonian system, both classical and quantum, whose period evolution operator is the renowned map that bears its name. It is obtained following the Joos-Zeh prescription for decoherence by adding a number of scattering particles in the configuration space of the cat. Quantization follows swiftly if the Hamiltonian approach, rather than the semiclassical approach, is adopted. The author has studied this system in a series of previous works, focusing on the problem of quantum-classical correspondence. In this paper, the dynamics of this system are tested by two related yet different indicators: the time autocorrelation function of the canonical position and the out-of-time correlator of position and momentum.

Zigzag phase transition of electrons confined within a thin annulus region

We consider a semiclassical approach to study the possible stabilization of a zigzag phase for a system of interacting electrons confined within a thin annulus region with infinite inner/outer walls. The electrons are considered spinless and interact via the standard Coulomb interaction potential. The classical minimum energy configuration of the system due to the Coulomb repulsion between electrons is accurately determined by using the simulated annealing method. As the number of electrons increases we see the appearance and stabilization of a two-ring structure with zigzag patterns. Further increase of the number of electrons appears to eventually lead to the collapse of the two-ring zigzag structure. A simple quantum treatment of the nodal features of the free many-particle wave function shows the appearance of nodal domain patterns that are consistent with the zigzag features that were observed in the classical model.