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In this article, we analyse the Dyson equation for the density–density response function (DDRF) that plays a central role in linear response time-dependent density functional theory (LR-TDDFT). First, we present a functional analytic setting that allows for a unified treatment of the Dyson equation with general adiabatic approximations for discrete (finite and infinite) and continuum systems. In this setting, we derive a representation formula for the solution of the Dyson equation in terms of an operator version of the Casida matrix. While the Casida matrix is well-known in the physics literature, its general formulation as an (unbounded) operator in the N -body wavefunction space appears to be new. Moreover, we derive several consequences of the solution formula obtained here; in particular, we discuss the stability of the solution and characterise the maximal meromorphic extension of its Fourier transform. We then show that for adiabatic approximations satisfying a suitable compactness condition, the maximal domains of meromorphic continuation of the initial DDRF and the solution of the Dyson equation are the same. The results derived here apply to widely used adiabatic approximations such as (but not limited to) the random phase approximation and the adiabatic local density approximation. In particular, these results show that neither of these approximations can shift the ionisation threshold of the Kohn–Sham system. [ABSTRACT FROM AUTHOR]

Using adiabatic and one-electron approximations, the rate of multiphonon relaxation of the 1s(T2) triplet of neutral magnesium donors in silicon is estimated. The dominant scattering processes associated with interaction with LO and LA phonons are taken into account. According to calculations, the rate of multiphonon relaxation at zero temperature is of the order of 1011 s–1. [ABSTRACT FROM AUTHOR]

Let O (3) denote the group of orthogonal 3 × 3 real matrices, and M the 5-dimensional real vector space of all 3 × 3 real symmetric matrices with trace zero. Let λ 1 (A) ≤ λ 2 (A) ≤ λ 3 (A) be the eigenvalues of A ∈ M and Ξ - = { A ∈ M ∣ λ 1 (A) = λ 2 (A) } . M is an inner product space with the inner product ⟨ A , B ⟩ = trace (A B) . Let G 3 (M) be the set of all 3-dimensional subspaces of M , a 6-dimensional Grassman manifold. O (3) acts on M on the left by conjugation via inner product preserving linear isomorphisms, which map any 3-dimensional subspace into another 3-dimensional subspace; thus G 3 (M) also has a left action of O (3) . G 3 (M) becomes a category, an action groupoid, with morphisms (V , M , W) ∈ G 3 (M) × O (3) × G 3 (M) , where W = M V M T . Composition of morphisms is (V 1 , N , V 2) ∘ (V 0 , M , V 1) = (V 0 , N M , V 2) . Let C be a category whose objects (V, S) consist of a real inner product space V and S ⊂ V , and whose arrows (V , S) → (W , T) consist of f : V → W , an inner product preserving real linear mapping such that f (S) ⊂ T . We have the functor V ↓ (V , M , W) W G 3 (M) ⟶ F - (V , Ξ - ∩ V) ↓ F - (M) (W , Ξ - ∩ W) C where F - (M) : V → W : A ↦ M A M T . Suppose further that S 3 denotes the group of permutations of { 1 , 2 , 3 } , and ρ : S 3 → O (3) denotes a group homomorphism which is isomorphic as a group representation to the natural representation of S 3 on R 3 (which permutes the coordinates). Let Obj (L S) denote the set of all V ∈ G 3 (M) whose isotropy subgroup contains S = ρ (S 3) as a subgroup. This paper completely describes the full subcategory L S of G 3 (M) with object set Obj (L S) , as well as the details of the above functor restricted to L S . Thus all the members V ∈ Obj (L S) are determined, as well as the smooth manifold structure on Obj (L S) ; it is embedded as a one-dimensional submanifold of G 3 (M) . The isotropy subgroups of all V ∈ Obj (L S) are computed and all pairs V , W ∈ Obj (L S) which are isomorphic via some M ∈ O (3) are determined. The sets Ξ - ∩ V are all determined, and the functorial mappings on morphism sets are computed. However, L S is not a Lie groupoid. The image of Obj (L S) under the functor π 1 F - is the collection of fibres of the smooth manifold ∐ V ∈ Obj (L S) V , which is the total space of the canonical vector bundle over the base manifold Obj (L S) . The bifurcation points of the family of subsets Ξ - ∩ V as V ranges over Obj (L S) (within this total space) are seen to be the points of Obj (L S) with infinite isotropy subgroups. We also show how this mathematical problem arises naturally from a problem in mathematical chemistry. Hence certain features of numerical calculations of energy eigenvalue intersection patterns of the simple chemical system H3 are rationalized through linearization about the triple intersection point. [ABSTRACT FROM AUTHOR]

Galperin introduced an interesting method to learn the digits of π by counting the collisions of two billiard balls and a hard wall. This paper studies two quantum versions of the Galperin billiards. It is shown that the digits of π can be observed in the phase shifts of the quantum models. [ABSTRACT FROM AUTHOR]

Spectral lines in the optical spectra of atoms, molecules, and other quantum systems are characterized by a range of frequencies ω or a range of wavelengths λ=2πc/ω, where c is the speed of light. Such a frequency or wavelength range is called the width of the spectral lines (linewidth). It is influenced by many specific factors. Thermal motion of the molecules results in broadening of the lines as a result of the Doppler effect (thermal broadening) and by their collisions (pressure broadening). The electric fields of neighboring molecules lead to Stark broadening. The linewidth to be considered here is the so-called parametric broadening (PB) of spectral lines in the optical spectrum. PB can be considered the fundamental type of broadening of the electronic vibrational–rotational (rovibronic) transitions in a molecule, which is the direct manifestation of the basic concept of the collapse of a wavefunction that is postulated by the Copenhagen interpretation of quantum mechanics. Thus, that concept appears to be not only valid but is also useful for predicting physically observable phenomena.

Background. Quantum dots (QDs) have unique optical properties that have found wide applications in optoelectronics, biology and medicine. The problem of controlling the spectral – luminescent properties of QDs initiated studies of the mechanisms of interaction of QDs with each other and with the surrounding matrix. Such interactions, under certain conditions, can significantly modify the radiative properties of QDs, which will affect the characteristics of laser structures and biosensors based on them. The purpose of this work is to study the effect of 2D dissipative tunneling in the QDs - surrounding matrix system, as well as the paired electrostatic interaction of QDs with (А+ + е) impurity complexes, on recombination radiation associated with the optical transition of an electron from the ground state of QDs to a quasi-stationary A+ state in the external electric field. Materials and methods. The interaction of an electron in the ground state of the QDs and a hole localized at the A+ center was considered in the framework of the adiabatic approximation. The dispersion equations determining the dependence of the binding energy of a hole in an impurity complex (А+ + е) in a spherically symmetric QDs on the magnitude of the external electric field and the parameters of dissipative tunneling are obtained within the framework of the zero radius potential model, in the approximation of the effective mass. The spectral intensity of recombination radiation (SIRI) in QDs with an impurity complex (А+ + е) in an external electric field is calculated in the dipole approximation. The effect of the electric field on the ground state of the electron in the QDs was taken into account in the second order of the perturbation theory. Numerical calculations and plotting of graphs were carried out for InSb-based semiconductor quantum dots using symbolic mathematics Mathcad 14 and Wolfram Mathematica 9. The probability of 2D dissipative tunneling was calculated with exponential accuracy for a model 2D oscillatory potential at a finite temperature, taking into account linear interaction with phonon modes of the environment at one time instanton quasi-classical approximation. Results. It is shown that the field dependence of the binding energy of the quasi-stationary A+ state has an oscillating character associated with quantum beats that occur during parallel 2D tunneling transfer. It is found that the SIRI curves have a characteristic fracture corresponding to the 2D bifurcation point that occurs when the tunneling modes in the interacting QDs pair change from synchronous to asynchronous. It is established that in the vicinity of the 2D bifurcation point there are irregular oscillations in SIRI associated with the modes of quantum beats when competing trajectories of tunnel transport appear. It is found that the parameters of dissipative tunneling: temperature, frequency of the phonon mode, the constant of interaction with the contact medium, the constant of interaction of QDs, have a significant effect on the amplitude of quantum beats and the position of the 2D bifurcation point in SIRI. Conclusions. Taking into account the interaction of QDs with the surrounding matrix leads to a significant modification of SIRI, which manifests itself in the form of bifurcation points and quantum beats depending on the parameters of dissipative tunneling. Taking into account the paired interaction of QDs with each other by means of hole pushing in (А+ + е) complexes leads to the suppression of recombination radiation with an increase in the constant interaction.

Background. At present, much attention is paid to the dielectric engineering of the material of the surrounding matrix and low-dimensional structures, which makes it possible to purposefully change their properties and optimize the characteristics of semiconductor devices. The purpose of this work is a theoretical study of the influence of the pair interacting quantum dots (QDs), as well as their interaction with the surrounding matrix through 2D - dissipative tunneling, on the photodielectric effect (PDE) associated with the excitation of an impurity complex (А+ + е) in a QD system in an external electric field. Materials and methods. Interaction of an electron with a hole in an impurity complex (А+ + е)in a QD has been considered in the adiabatic approximation. The dispersion equations for a hole in an impurity complex (А+ + е) in the presence of an external electric field and 2Ddissipative tunneling for the s- and p-states of an electron in a QD are obtained within the framework of the zero-range potential model in the effective mass approximation. The influence of the electric field on the ground state of an electron in a QD has been taken into account in the second order of the perturbation theory. The probability of 2D - dissipative tunneling is calculated in the one-instanton semiclassical approximation. The relative change in dielectric permittivity has been calculated in the dipole approximation. PDE field dependence curves have been plotted for InSb QDs. Results. It is shown that the PDE field dependence at a certain value of the strength of an external electric field and the parameters of 2D - dissipative tunneling has a characteristic kink associated with the effect of 2D - bifurcation, when under the action of an electric field the double-well oscillatory potential simulating the "QD - surrounding matrix" system is transformed and the tunnel transfer mode changes from synchronous to asynchronous. It has been established that there are irregular oscillations on the PDE curves in the vicinity of the 2D bifurcation point, which are associated with the regime of quantum beats. It is shown that the amplitude of the oscillations increases with increasing phonon mode frequency and temperature, and the break point shifts towards weaker fields. It has been found that an increase in the constant of interaction with the contact medium, as well as with the constant of the pair interaction of QDs, leads to the suppression of the PDE. Conclusions. The theoretically studied PDE at a wavelength of λ=6.2 μm in a QD with an impurity complex (А+ + е) in the presence of interactionwith the surround ng matrix through 2D - dissipative tunneling of a hole localized at the А+- center can be used in photosensor applications, for example, as a sensor, the structural component of which can detect the presence of IR - radiation due to a change in electrical capacitance.

Definition: Spectral lines in the optical spectra of atoms, molecules, and other quantum systems are characterized by a range of frequencies ω or a range of wavelengths λ = 2 π c / ω , where c is the speed of light. Such a frequency or wavelength range is called the width of the spectral lines (linewidth). It is influenced by many specific factors. Thermal motion of the molecules results in broadening of the lines as a result of the Doppler effect (thermal broadening) and by their collisions (pressure broadening). The electric fields of neighboring molecules lead to Stark broadening. The linewidth to be considered here is the so-called parametric broadening (PB) of spectral lines in the optical spectrum. PB can be considered the fundamental type of broadening of the electronic vibrational–rotational (rovibronic) transitions in a molecule, which is the direct manifestation of the basic concept of the collapse of a wavefunction that is postulated by the Copenhagen interpretation of quantum mechanics. Thus, that concept appears to be not only valid but is also useful for predicting physically observable phenomena. [ABSTRACT FROM AUTHOR]

Abstract Electronic and excitonic states in an InSb strongly flattened ellipsoidal quantum dot (QD) with complicated dispersion law are theoretically investigated within the framework of the geometric adiabatic approximation in the strong, intermediate, and weak quantum confinement regimes. For the lower levels of the spectrum, the square root dependence of energy on QD sizes is revealed in the case of Kane’s dispersion law. The obtained results are compared to the case of a parabolic (standard) dispersion law of charge carriers. The possibility of the accidental exciton instability is revealed for the intermediate quantum confinement regime. For the weak quantum confinement regime, the motion of the exciton's center-of-gravity is quantized, which leads to the appearance of additional Coulomb-like sub-levels. It is revealed that in the case of the Kane dispersion law, the Coulomb levels shift into the depth of the forbidden band gap, moving away from the quantum confined level, whereas in the case of the parabolic dispersion law, the opposite picture is observed. The corresponding selection rules of quantum transitions for the interband absorption of light are obtained. New selection rules of quantum transitions between levels conditioned by 2D exciton center of mass vertical motion quantization in a QD are revealed. The absorption threshold behavior characteristics depending on the QDs geometrical sizes are also revealed.

At present, much attention is paid to the dielectric engineering of the material of the surrounding matrix and low-dimensional structures, which makes it possible to purposefully change their properties and optimize the characteristics of semiconductor devices. The aim of this work is a theoretical study of the influence of the pair interaction of quantum dots (QDs), as well as their interaction with the surrounding matrix through 2D dissipative tunneling, on the photodielectric effect (PDE) associated with the excitation of an impurity complex A+ + e in a QD system in an external electric field. Interaction of an electron with a hole in an impurity complex A+ + e in a QD has been considered in the adiabatic approximation. The dispersion equations for a hole in an impurity complex A+ + e in the presence of an external electric field and 2D dissipative tunneling for the s- and p-states of an electron in a QD are obtained within the framework of the zero-range potential model in the effective mass approximation. The influence of the electric field on the ground state of an electron in a QD has been taken into account in the second order of the perturbation theory. The probability of 2D dissipative tunneling is calculated in the one-instanton semiclassical approximation. The relative change in dielectric permittivity has been calculated in the dipole approximation. PDE field-dependence curves have been plotted for InSb QDs. It is shown that the PDE field dependence at a certain value of the strength of an external electric field and the parameters of 2D dissipative tunneling has a characteristic kink associated with the effect of 2D bifurcation, when, under the action of an electric field, the double-well oscillatory potential simulating the "QD–surrounding matrix" system is transformed and the tunnel transfer mode changes from synchronous to asynchronous. It has been established that there are irregular oscillations on the PDE curves in the vicinity of the 2D bifurcation point, which are associated with the regime of quantum beats. It is shown that the amplitude of the oscillations increases with increasing phonon mode frequency and temperature, while the break point shifts towards weaker fields. It has been found that an increase in the constant of interaction with the contact medium, as well as with the constant of the pair interaction of QDs, leads to the suppression of the PDE. [ABSTRACT FROM AUTHOR]

Quantum dots (QDs) have unique optical properties that are widely used in optoelectronics, biology, and medicine. The problem of controlling the spectral and luminescent properties of QDs has initiated studies of the mechanisms by which QDs interact with each other and with the surrounding matrix. Such interactions can, under certain conditions, significantly modify the radiative properties of QDs, which will affect the characteristics of laser structures and biosensors based on them. The aim of this work is a theoretical study of the 2D dissipative tunneling effect in the "QD–surrounding matrix" system, as well as the pair electrostatic interaction of QDs with A++ e impurity complexes, on recombination radiation associated with the optical transition of an electron from the QD ground state to the quasi-stationary A+ state in an external electric field. The interaction of an electron, which is in the ground state of a QD, and a hole that is localized at the A+ center has been considered within the framework of the adiabatic approximation. The dispersion equations that determine dependence of the hole binding energy in the A++ e impurity complex in a spherically symmetric QD on the external electric field and dissipative tunneling parameters have been obtained within the zero range potential model, in the effective mass approximation. Calculation of the spectral intensity of recombination radiation (SIRR) in QDs with an A++e impurity complex in an external electric field has been performed in the dipole approximation. Influence of the electric field on the ground state of an electron in a QD has been taken into account in the second order of the perturbation theory. Numerical calculations and plotting were carried out for a semiconductor quantum dot based on InSb using the symbolic mathematics of Mathcad 14 and Wolfram Mathematica 9. The 2D dissipative tunneling probability has been calculated with exponential accuracy for the 2D oscillatory potential model at a finite temperature, taking into account the linear interaction with the phonon modes of the environment media (or a heat bath) in the one-instanton semiclassical approximation. It is shown that the field dependence of the binding energy for the quasi-stationary A+ state has an oscillating character, associated with quantum beats that occur during parallel 2D tunneling transfer. It is found that the SIRR curves have a characteristic kink corresponding to the 2D bifurcation point that occurs when the tunneling regimes in the interacting pair of QDs change from synchronous to asynchronous. It has been established that, in the vicinity of the 2D bifurcation point, there are irregular oscillations in the SIRR associated with the modes of quantum beats, in the course of which competing trajectories of tunneling appear. It is found that the parameters of dissipative tunneling—the temperature, frequency of the phonon mode, constant of interaction with the contact medium, constant of the QDs interaction—have a significant effect on the amplitude of quantum beats and the position of the 2D bifurcation point in the SIRR. Taking into account the interaction of the QD with the surrounding matrix leads to a significant modification of the SIRR, which manifests itself in the form of bifurcation points and quantum beats that depend on the dissipative tunneling parameters. Accounting for the pairwise interaction of QDs with each other via hole repulsion in A++ e complexes leads to suppression of recombination radiation with an increase in the interaction constant. [ABSTRACT FROM AUTHOR]

A theoretical scenario for the generation of coherent π‐electron angular momentum in a low‐symmetry aromatic molecule using two nonresonant shift‐up lasers is presented. The effects of vibrational modes on coherent π‐electron angular momentum are considered in the adiabatic approximation. In this scenario, two electronic excited states are irradiated with two linearly polarized nonresonant lasers. This causes a consistent up‐shift in the vibronic energy levels of each electronically excited state toward higher energy as a result of the dynamic Stark effect. For the weak coupling case of the electronic‐vibrational interactions, the lowest vibronic states in the two electronic excited states are designed to be degenerate by varying the parameters (frequency and intensity) of each laser. The resultant degenerate state, called the dynamic Stark‐induced degenerate vibronic state (DSIDVS), is the origin of the coherent π‐electron angular momentum generation. An optimal laser parameter set is determined under conditions in which the lowest two vibronic states form the DSIDVS. The DSIDVS was formulated by the method of Laplace transformations. An analytical expression for the coherent π‐electron angular momentum was derived in the displaced harmonic oscillator model. We examined the dependence of the time‐averaged z‐component of the coherent angular momentum L¯z on the ratio of the two detunings and potential displacements of toluene, a typical low‐symmetry aromatic ring molecule, which belongs to the weak coupling case and is adopted to demonstrate the theoretical scenario. The inclusion of potential displacements in the angular momentum generation was found to reduce the value of L¯z by half, compared with that in the frozen nuclear approximation. [ABSTRACT FROM AUTHOR]

We examine the applicability of the adiabatic approximation in the case of proton scattering off statically deformed actinide and rare-earth nuclei. This is achieved by deforming a global spherical potential to allow coupling of the elastic channel to inelastic rotational excitation states. Only the radius of volume term of the spherical potential is deformed. The rest of the potential parameters are used unaltered. The model reproduced the scattering observables well. The results are congruent to those of a global model in the literature that determines the potential parameters by fitting the experimental data within a channel coupling formalism. A necessary requirement for the adiabatic approximation to hold is that the speed of the proton should be much larger than the angular speed of the deformed target nucleus. The fact that our calculated angular distributions and total cross sections agree well with experiment indicates that this condition is still valid despite the possibility of the proton being decelerated by the coulomb force as it approaches the deformed nucleus.

The temporal evolution of pandemics described by the susceptible-infectious-recovered (SIR)-compartment model is sensitively determined by the time dependence of the infection (a(t)) and recovery (μ(t)) rates regulating the transitions from the susceptible to the infected and from the infected to the recovered compartment, respectively. Here, approximated SIR solutions for different time dependencies of the infection and recovery rates are derived which are based on the adiabatic approximation assuming time-dependent ratios, k(t)=μ(t)/a(t), varying slowly in comparison with the typical time characteristics of the pandemic wave. For such slow variations, the available analytical approximations from the KSSIR-model, developed by us and valid for a stationary value of the ratio k, are used to insert a posteriori the adopted time-dependent ratio of the two rates. Instead of investigating endless different combinations of the time dependencies of the two rates a(t) and μ(t), a suitably parameterized reduced time, τ, dependence of the ratio k(τ) is adopted. Together with the definition of the reduced time, this parameterized ratio k(τ) allows us to cover a great variety of different time dependencies of the infection and recovery rates. The agreement between the solutions from the adiabatic approximation in its four different studied variants and the exact numerical solutions of the SIR-equations is tolerable providing confidence in the accuracy of the proposed adiabatic approximation.

In this paper, we consider a system driven by a controlled Schrödinger equation with two external control inputs. Motivated by applications to the control of quantum systems having conical or semi-conical eigenvalue intersections, we propose to study the singularities and the parametric bifurcations of the associated non-mixing field, along whose integral curves in the space of controls the adiabatic approximation holds with higher precision. Our results can be applied to optimize the adiabatic control strategies of well known quantum systems such as Qubit systems, Stirap Processes and Eberly-Law models. [ABSTRACT FROM AUTHOR]

Within the framework of the available theories, the initiation of plastic shear and nucleation cracks in perfect crystals is possible only at a deforming stress close to the theoretical strength. It is shown that a perfect crystal, treated as an open system of nuclei and electrons, loses its stability at applied stresses that are orders of magnitude smaller than the theoretical strength. This helps avoiding the use of the concept of various types of defects present in the bulk and in the surface layer of the crystal. The physical reason for the instability is the excitation of dynamic displacements determined by nonadiabatic transitions of Landau-Zener atoms between the intersecting potential energy surfaces in open nonequilibrium systems. A qualitative explanation of the experimentally observed results is given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the applicability of different theories on the intensity-dependent ionization rate for C2+ atomic targets at different laser wavelengths (frequency) and at linear polarization. We use the analytical formulas and draw conclusions, from numerical comparison with the results from ab initio 'two-state model' R-matrix Floquet calculation, on their correct predictions of the ionization rate. The single-photon ionization has been studied in the vicinity of the 1s2 (2Po)2pns (1Po), n = 5–12 autoionizing resonances at non-perturbative laser intensity. The results obtained from Perelomov–Popov–Terent'ev and Ammosov–Delone–Krainov models are compared in a region away from resonance where the two-state model description is not as good. To quantify the deviation between theoretical models, we analyze the ratio between different data sets as functions of the Keldysh parameter. We conclude that the results obtained with the model of Perelemov–Popov–Terent'ev are the closest to the ab initio R-matrix Floquet calculation. [ABSTRACT FROM AUTHOR]

Lutosław Wolniewicz, one of prominent quantum chemists, known for his seminal works on the structure and spectra of the hydrogen molecule and its isotopomers, passed away in December 2020. This paper presents his life and works. [ABSTRACT FROM AUTHOR]

Electronic and excitonic states in an InSb strongly flattened ellipsoidal quantum dot (QD) with complicated dispersion law are theoretically investigated within the framework of the geometric adiabatic approximation in the strong, intermediate, and weak quantum confinement regimes. For the lower levels of the spectrum, the square root dependence of energy on QD sizes is revealed in the case of Kane's dispersion law. The obtained results are compared to the case of a parabolic (standard) dispersion law of charge carriers. The possibility of the accidental exciton instability is revealed for the intermediate quantum confinement regime. For the weak quantum confinement regime, the motion of the exciton's center-of-gravity is quantized, which leads to the appearance of additional Coulomb-like sub-levels. It is revealed that in the case of the Kane dispersion law, the Coulomb levels shift into the depth of the forbidden band gap, moving away from the quantum confined level, whereas in the case of the parabolic dispersion law, the opposite picture is observed. The corresponding selection rules of quantum transitions for the interband absorption of light are obtained. New selection rules of quantum transitions between levels conditioned by 2D exciton center of mass vertical motion quantization in a QD are revealed. The absorption threshold behavior characteristics depending on the QDs geometrical sizes are also revealed. [ABSTRACT FROM AUTHOR]

Semiconductor quantum dots, due to their unique optical properties, are promising materials for the design of optoelectronic devices. At the same time, the parameters of instruments significantly depend both on the band structure and the impurity energy levels in quantum dots. In this regard, the electron–phonon interaction acts as the most important mechanism of temperature shift in energy levels. The aim of the present work was to theoretically study how the electron–phonon interaction influences the temperature dependence of radiative recombination in an impurity complex in a semiconductor quasi-zero-dimensional structure. The effect of temperature on the energy levels in a semiconductor quantum dot was theoretically considered by the statistics method assuming that the electron–phonon interaction makes the main contribution to the temperature dependence. The dispersion equation defining the hole binding energy in the impurity complex in a spherically symmetric quantum dot was obtained in terms of the adiabatic approximation in the zero-range potential model. The spectral intensity of recombination radiation in the quasi-zero-dimensional structure with impurity complexes was calculated in the dipole approximation taking into account the radius dispersion of quantum dots. Temperature curves were plotted for the case of InSb-based quantum dots. The temperature dependence of the binding energy in the complex was calculated for different values of the quantum-dot radius. The hole binding energy was shown to decrease with an increase in temperature, which was due to a temperature spreading of the wave function of a quasi-steady A+ state under the conditions of electron–phonon and hole–phonon interactions. The bond energy of the A+ state was found to increase with a decrease in the quantum-dot radius due to an increase in the ground state energy of the adiabatic electron potential. The spectral intensity of recombination radiation was calculated as a function of the transition energy for different temperature values. It was found that, with an increase in temperature, the threshold transition energy shifts to the short-wave spectral region and thermal quenching of the recombination radiation occurs. This was due to a decrease in the overlap integral of the wave functions of initial and final electron states because of the transition energy increase. The effect of the electron–phonon interaction on recombination processes in the impurity complex in spherically symmetric quantum dot is manifested in temperature quenching of the recombination radiation spectral intensity. The effect of coming to a plateau appears to be common for different mechanisms of photoluminescence. [ABSTRACT FROM AUTHOR]

There has been an increasing interest in the study of the effect of electric field on the properties of semiconductor quantum dots. This is due to the fact that such systems provide a high degree of freedom in the control of the band structure and the binding energy of impurity states, which is important for instrumental applications. Of particular interest is the study of the effect of electric field on the A+ impurity states, which can form long-lived complexes with nonequilibrium electrons. Variations in the magnitude of the external electric field can be used to control the binding energy of the A+ state, concentration of charge carriers, and optical properties of quasi-zero-dimensional structures. The purpose of this work is to theoretically study the effect of external electric field on the binding energy of a hole in the impurity complex in a spherically symmetric quantum dot. The interaction of an electron in the ground state of a quantum dot and a hole localized at the A+ center is considered in the framework of the adiabatic approximation. The dispersion relation that determines the dependence of the binding energy of a hole in the impurity complex in a spherically symmetric quantum dot on the magnitude of the external electric field is obtained in the model of the zero-radius potential in the approximation of effective mass. All curves are plotted for quantum dots based on InSb. An analytical solution of the problem of bound states of a hole in the complex in a spherically symmetric quantum dot is obtained in the presence of an external electric field in the zero-radius-potential model in the adiabatic approximation. The centered and uncentered locations of the A+ center in a quantum dot are considered. It is shown that the curve of the field dependence of the binding energy of the A+ center has a characteristic maximum, the position of which is related to the dynamics of the adiabatic potential in the presence of an external electric field. It is shown that there is a threshold value of the external electric field at which the existence of the bound A+ state becomes impossible. The monotonic behavior of the dependence of the binding energy of the A+ state on the radius of the QD is violated for the uncentered A+ center. For certain values of the QD radius, the binding energy reaches maximum, which is due to coincidence of the position of the center and the minimum of the adiabatic potential. [ABSTRACT FROM AUTHOR]

The temporal evolution of pandemics described by the susceptible-infectious-recovered (SIR)-compartment model is sensitively determined by the time dependence of the infection ( a (t) ) and recovery ( μ (t)) rates regulating the transitions from the susceptible to the infected and from the infected to the recovered compartment, respectively. Here, approximated SIR solutions for different time dependencies of the infection and recovery rates are derived which are based on the adiabatic approximation assuming time-dependent ratios, k (t) = μ (t) / a (t) , varying slowly in comparison with the typical time characteristics of the pandemic wave. For such slow variations, the available analytical approximations from the KSSIR-model, developed by us and valid for a stationary value of the ratio k, are used to insert a posteriori the adopted time-dependent ratio of the two rates. Instead of investigating endless different combinations of the time dependencies of the two rates a (t) and μ (t) , a suitably parameterized reduced time, τ , dependence of the ratio k (τ) is adopted. Together with the definition of the reduced time, this parameterized ratio k (τ) allows us to cover a great variety of different time dependencies of the infection and recovery rates. The agreement between the solutions from the adiabatic approximation in its four different studied variants and the exact numerical solutions of the SIR-equations is tolerable providing confidence in the accuracy of the proposed adiabatic approximation. [ABSTRACT FROM AUTHOR]

In the physics literature it is common to use "in cascade" the rotating wave approximation and the adiabatic approximation for chirped pulses of two-level quantum systems driven by one external field, in particular when the resonance frequency is not known precisely. Both approximations need relatively long time and are based on averaging theory of dynamical systems. Unfortunately, the two approximations cannot be done independently since, in a sense, the two time scales interact. We study how the cascade of the two approximations can be justified, while preserving the robustness of the adiabatic strategy. Our first result, based on high-order averaging techniques, gives a precise quantification of the uncertainty interval of the resonance frequency for which the population inversion works. As a by-product, we prove controllability of an ensemble of spin systems by a single real-valued control, providing an extension of a celebrated result with two controls by Khaneja and Li. [ABSTRACT FROM AUTHOR]

Modeling three-dimensional (3D) underwater acoustic propagation is vital for underwater detection, localization, and navigation. This article introduces a novel model order reduction (MOR) technique to solve horizontal refraction equations (HREs) in the modeling of 3D underwater acoustic propagation. This approach relies on an adiabatic approximation of the 3D sound field, representing the field as a combination of local vertical modes with their modal coefficients governed by a system of two-dimensional (2D) HREs. Inspired by normal mode theory, the coefficients in the expansion over vertical modes are determined by projecting them onto a lower-dimensional, orthogonal space defined by their transverse eigenfunctions. By artificially truncating the horizontal domain in the transverse directions using two perfectly matched layers (PMLs), the eigenproblem associated with the transverse eigenfunctions of the modal coefficients is closed and thus can be solved through a modal projection method. The modal projection method enables fast computation of modal coefficients in a longitudinally invariant environment within seconds, offering a naturally wide-angle solution covering ± 90 °. The MOR method is extended to encompass fully 3D cases by introducing an admittance matrix, a memory-saving strategy that prevents numerical overflow when the longitudinal range is large. Moreover, the fact that the outer boundaries of the PMLs are range-independent allows the proposed MOR technique to perform well on a coarse grid when employing the Magnus scheme, significantly saving the numerical cost for the fully 3D simulation. Numerical simulations are provided for both longitudinally invariant and fully 3D scenarios, demonstrating the high accuracy and efficiency of the proposed MOR technique in solving HREs. • A model order reduction technique is designed to solve horizontal refraction equations. • Only a few seconds are required for longitudinally invariant environments. • The solution provided by the proposed model is naturally a wide-angle solution. • The proposed model enables efficient and accurate solutions on a coarse grid. • A full-order, benchmark model for solving horizontal refraction equations is developed. [ABSTRACT FROM AUTHOR]

Herein, we investigate the effects of the irreversible action of the medium on the theoretical elucidation of the IR spectrum of weakly H-bonded systems, a prototypical model which provides a rigorous treatment of the relaxation mechanisms impacts on the IR spectral density. The attention will be focused particularly on the effect of indirect damping on the IR υ S (X − H ⃗) spectrum beyond the harmonic and adiabatic approximations. The ultimate objective of the present investigation is the treatment of the action of the surrounding of the intermonomer modes of H-bonded systems, which must induce a broadening of the Dirac delta peaks, the nature of which, as shown by Maréchal and Witkowski theory, is a Franck–Condon progression. The quantum treatment of the IR absorption band reveals that quantum relaxation of the intermonomer mode of H-bonded complexes could be successfully approached by a non-Hermitian Hamiltonian formalism. Motivated by development of a second method that will be able to validate the first approach, a computationally efficient algorithm was proposed for elucidating the quantum indirect relaxation using Hermitean Hamiltonians. The real eigenvalues, corresponding to different energies of the system are considered to be complex by adjunction of the imaginary parts, which reflects the action of the indirect irreversible action of the medium. These two crude approaches may pave the way for the incorporation of the mechanism of indirect relaxation in more physical and complex situations dealing, particularly, with tunnelling effects in strong H-bonded species, Fermi resonances, and Davydov coupling for cyclic H-bonds dimers beyond the harmonic and adiabatic assumptions. • The effect of the medium on the IR spectra of H-bonded systems is elucidated. • Two crude methods are proposed. • Non-Hermitian Hamiltonian formalism is used to describe the Indirect relaxation. • The eigenvalues are considered to be complex by adjunction of imaginary parts. • The imaginary parts reflect the indirect irreversible action of the medium. [ABSTRACT FROM AUTHOR]

The adiabaticity assumption (AA) and the resulting concept of optical potential in the context of atom focusing with lasers were examined numerically for various experimentally controllable laser parameters. The Schrödinger equations for the atomic center‐of‐mass dynamics in a laser field were calculated using with or without the AA, and the results were compared. The validity of the AA was tested over a wide range of the Rabi frequency to detuning ratios and the optical potential depths. From the analysis, several specific guidelines were provided on choosing laser parameters that sustain the validity of the AA and improve atom focusing outcomes. [ABSTRACT FROM AUTHOR]

This paper investigates the waveguide propagation of polarized electromagnetic radiation in a thin-film integral optical waveguide. To describe this propagation, the adiabatic approximation of solutions of Maxwells equations is used. The construction of a reduced model for adiabatic waveguide modes that retains all the properties of the corresponding approximate solutions of the Maxwell system of equations was carried out by the author in a previous publication in DCM ACS, 2020, No 3. In this work, for a special case when the geometry of the waveguide and the electromagnetic field are invariant in the transverse direction. In this case, there are separate nontrivial TEand TM-polarized solutions of this reduced model. The paper describes the parametrically dependent on longitudinal coordinates solutions of problems for eigenvalues and eigenfunctions - adiabatic waveguide TE and TM polarizations. In this work, we present a statement of the problem of finding solutions to the model of adiabatic waveguide modes that describe the stationary propagation of electromagnetic radiation. The paper presents solutions for the single-mode propagation of TE and TM polarized adiabatic waveguide waves.

Background. Recently, there has been growing interest in studying the influence of electric field effects on the properties of semiconductor quantum dots. This is due to the fact that in such systems there is a high degree of freedom in controlling the band structure and binding energy of impurity states, which is important from the point of view of instrumental applications. Of particular interest is the study of the effect of an electric field on impurity A+ states, which are capable of forming long-lived (A+ + e) complexes with nonequilibrium electrons. Varying the strength of the external electric field opens up possibilities for controlling the binding energy of the A+ state, the concentration of charge carriers, and also the optical properties of quasi-zero-dimensional structures. The purpose of this work is to theoretically study the effect of an external electric field on the binding energy of a hole in an (A+ + e) impurity complex in a spherically symmetric quantum dot (QD). Materials and methods. The interaction between an electron in the ground state of a quantum dot and a hole localized at the A+ center is considered within the framework of the adiabatic approximation. The dispersion equation that determines the dependence of the hole binding energy in the (A+ + e) impurity complex in a spherically symmetric quantum dot on the magnitude of the external electric field was obtained within the framework of the zero radius potential model, in the effective mass approximation. All curves are plotted for quantum dots based on InSb. Results. An analytical solution of the problem of bound states of a hole in the (A+ + e) omplex in a spherically symmetric quantum dot in the presence of an external electric field is obtained in the zero-radius potential model in the adiabatic approximation. The cases of centered and non-centered location of the A+ center in a quantum dot are considered. It is shown that the field dependence curve of the binding energy of the A+ center has a characteristic maximum, the position of which is related to the dynamics of the adiabatic potential in an external electric field. It is shown that there is a threshold value of the external electric field strength at which the existence of a bound A+ state becomes impossible. Conclusions. The monotonic behavior of the dependence of the binding energy of the A+ state on the QD radius is broken if the A+ center is not centered. For certain values of the QD radius, the binding energy reaches its maximum value, which is associated with the coincidence of the position of the A+ center and the minimum of the adiabatic potential.

Background. Interest in the optical properties of quantum dots (QD) with (A+ + e) impurity complexes is associated with the possibility of creating new elements of semiconductor optoelectronics based on such structures. In this case, the high sensitivity of the band structure and the energy of impurity states in QD to an external electric field opens up possibilities for controlling the spectra of recombination radiation in impurity complexes. The purpose of this research is to study the effect of an external electric field on radiative recombination in the (A+ + e) impurity complex in semiconductor QD. Materials and methods. The calculation of the spectral recombination radiation intensity (SRRI) in a quantum dot with (A+ + e) impurity complexes in an external electric field was performed in the dipole approximation. The influence of the electric field on the ground state of an electron in a QD was taken into account in the second order of the perturbation theory. The spectral curves of the SRRI, as well as the dependences of the SRRI on the strength of the external electric field, were plotted for QD based on InSb. Results. In the dipole approximation, the SRRI was calculated taking into account the Lorentz broadening of energy levels in QD with the (A+ + e) impurity complex. The calculation is based on the use of the adiabatic approximation to describe the interaction of a hole localized at the A+ center with an electron localized in the ground state of the QD. It is shown that a significant change in SRRI occurs due to a decrease in the overlap integral of the wave functions of an electron and a hole localized at the A+ center due to the electron-hole polarization. It is shown that the asymmetry of the adiabatic potential minimum position in an electric field leads to a nontrivial dependence of the SRRI on the coordinates of the A+ center: when the impurity center approaches the QD boundary, the SRRI maximum shifts to the short-wavelength region of the spectrum, and an increase in the electric field strength leads to a significant drop in the radiation intensity and a shift of its maximum to the long-wavelength region of the spectrum (quantum size Stark effect). Conclusions. In an electric field, efficient control of SIRI with the participation of the (A+ + e) impurity complexes is possible due to the modification of the electronic adiabatic potential.

Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than otherwise possible. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certain classes of approximations. Here I review the fundamental challenges the approximate functionals have in describing double excitations and charge-transfer excitations, which are two of the most common impediments for the theory to be applied in a black-box way. At the same time, I describe the progress made in recent decades in developing functional approximations that give useful predictions for these excitations. [ABSTRACT FROM AUTHOR]

Background. Semiconductor quantum dots, due to their unique optical properties, are a promising material for creating optoelectronic devices. At the same time, the devices’ parameters change significantly over a wide temperature range, which requires knowledge of the temperature dependence of both the band structure and the energy of impurity levels in quantum dots. In this case, the electron-phonon interaction acts as the most important mechanism for the temperature shift of energy levels. The purpose of this work is to theoretically study the effect of electron-phonon interaction on the temperature dependence of radiative recombination in an extrinsic complex ( A+ + e ) in a semiconductor quasi-zerodimensional structure. Materials and methods. The theoretical consideration of the temperature effect on the energy levels in a semiconductor quantum dot was carried out by a statistical method under the assumption that the main contribution to the temperature dependence comes from the electron-phonon interaction. The dispersion equation, which determines the binding energy of a hole in an extrinsic complex ( A+ + e ) in a spherically symmetric quantum dot, was obtained in the framework of the adiabatic approximation in the model of a zero-radius potential. The calculation of the spectral intensity of recombination radiation in a quasi-zero-dimensional structure with extrinsic complex ( A+ + e ) was performed in the dipole approximation taking into account the dispersion of the radius of quantum dots. The temperature dependence curves are plotted for the case of InSb-based quantum dots. Results. The temperature dependence of the binding energy in the complex ( A+ + e ) is calculated for various values of the quantum dot radius. It is shown that, with increasing temperature, the hole binding energy decreases, which is associated with the temperature “spreading” of the wave function of the quasistationary A+ -state under conditions of electron-phonon and hole-phonon interactions. It was found that with a decrease in the radius of a quantum dot, the binding energy of the A+ -state increases due to an increase in the energy of the ground state of the adiabatic potential of an electron. The dependence of the spectral intensity of the recombination radiation on the transition energy is calculated for various values of temperature. It was found that with increasing temperature, the threshold transition energy shifts to the short-wavelength region of the spectrum, and temperature quenching of the recombination radiation takes placeThis is due to a decrease in the overlap integral of the wave functions of the initial and final states of an electron due to an increase in the transition energy. Conclusions. The effect of electron-phonon interaction on recombination processes in extrinsic complexes ( A+ + e ) in a spherically symmetric quantum dot manifests itself in temperature reduction of the spectral intensity of the recombination radiation. The effect of reaching a “plateau” appears to be common to different photoluminescence mechanisms.

In this paper, we investigate the applicability of different theories on the intensity-dependent ionization rate for C2+ atomic targets at different laser wavelengths (frequency) and at linear polarization. We use the analytical formulas and draw conclusions, from numerical comparison with the results from ab initio ‘two-state model’ R-matrix Floquet calculation, on their correct predictions of the ionization rate. The single-photon ionization has been studied in the vicinity of the 1s2 (2Po)2pns (1Po), n = 5–12 autoionizing resonances at non-perturbative laser intensity. The results obtained from Perelomov–Popov–Terent’ev and Ammosov–Delone–Krainov models are compared in a region away from resonance where the two-state model description is not as good. To quantify the deviation between theoretical models, we analyze the ratio between different data sets as functions of the Keldysh parameter. We conclude that the results obtained with the model of Perelemov–Popov–Terent’ev are the closest to the ab initio R-matrix Floquet calculation.

The existence in the Born–Oppenheimer approximation of a fundamentally new type of broadening of the spectral line of the electronic vibrational–rotational (rovibronic) transition in a molecule, caused by zero-point vibrations and thermal fluctuations of atomic nuclei near their equilibrium positions during vibrational–rotational motion inside the molecule, is discovered. A quantitative description in the harmonic approximation is obtained to describe the shape and width of the electron transition line corresponding to this type of broadening, which is called parametric, since the energy of any rovibronic level and transition between levels depends parametrically on the current instantaneous position of nuclei, which move much more slowly than electrons. To take this effect into account, Franck-Condon diagrams with oblique (bent) levels of vibrational energy are proposed. From the point of view of the Copenhagen interpretation of quantum mechanics, the parametric broadening exists due to the difference between an open (i.e. experimentally measured) quantum system from an isolated (unobservable) one. The magnitude of this broadening is estimated on the example of the 0–0 transition in a series of polymethine dye monomers. The estimate showed that the magnitude of the parametric broadening of the indicated zero-phonon line is comparable with the broadening observed in the experiment. The existing quantum chemical methods for calculating molecular spectra do not take into account the parametric broadening. They smooth the quasi-continuum of closely spaced rovibronic transitions, approximately calculating their common envelope, but do not consider the broadening of a single transition. The creation of a theory of parametric broadening will contribute to the development of intramolecular converters of energy from nuclei to electrons and vice versa, sensing nanoprobes, and quantum radio, photoacoustic and acousto-optic, and transceiving or converting devices of molecular size. [ABSTRACT FROM AUTHOR]

In this paper, we address the adiabatic technique for quantum estimation of the azimuthal orientation of a magnetic field. Exactly solving a model consisting of a two-qubit system, where one of which is driven by a static magnetic field while the other is coupled with the magnetic field rotating adiabatically, we obtain the analytical expression of the quantum Fisher information (QFI). We investigate how the two-qubit system can be used to probe the azimuthal direction of the field and analyze the roles of the intensities of the magnetic fields, Dzyaloshinskii–Moriya (DM) interaction, spin–spin coupling coefficient, and the polar orientation of the rotating field on the precision of the estimation. In particular, it is illustrated that the QFI trapping or saturation may occur if the qubit is subjected to a strong rotating field. Moreover, we discuss how the azimuthal direction of the rotating field can be estimated using only the qubit not affected by that field and investigate the conditions under which this strategy is more efficient than use of the qubit locally interacting with the adiabatically rotating field. Interestingly, in the one-qubit scenario, it was found that when the rotating field is weak, the best estimation is achieved by subjecting the probe to a static magnetic field. [ABSTRACT FROM AUTHOR]

The gravitational Dirichlet problem - in which the induced metric is fixed on boundaries at finite distance from the bulk - is related to simple notions of UV cutoffs in gauge/gravity duality and appears in discussions relating the low-energy behavior of gravity to fluid dynamics. We study the Einstein-Maxwell version of this problem, in which the induced Maxwell potential on the wall is also fixed. For flat walls in otherwise asymptotically flat spacetimes, we identify a moduli space of Majumdar-Papapetrou-like static solutions parametrized by the location of an extreme black hole relative to the wall. Such solutions may be described as balancing gravitational repulsion from a negative-mass image source against electrostatic attraction to an oppositely signed image charge. Standard techniques for handling divergences yield a moduli space metric with an eigenvalue that becomes negative near the wall, indicating a region of negative kinetic energy and suggesting that the Hamiltonian may be unbounded below. One may also surround the black hole with an additional (roughly spherical) Dirichlet wall to impose a regulator whose physics is more clear. Negative kinetic energies remain, though new terms do appear in the moduli space metric. The regulator dependence indicates that the adiabatic approximation may be ill-defined for classical extreme black holes with Dirichlet walls.

This technical note introduces adiabatic dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity.