Unperturbed Ground State Research Articles

Questioning the Administrative Accountability of the ITU on the QUESS Oversight

In accordance with the SI unit of the unperturbed ground-state hyperfine transition frequency of the cesium 133 atom, Eutelsat has secured the safety procedures of telecommunication decays in the development of quantum communication technology. As observers of the International Atomic Energy Agency (IAEA), the International Telecommunication Union (ITU) is bound for intergovernmental observers with specialized agencies of the United Nations and IAEA based on reciprocity. The apparent overpowered photon beam of the Quantum Experiment at Space Scale (QUESS) military intelligence purposed telecommunication encryption designs launched around 2016, along with a German photon experiment directed at earth, were neither intervened by the ITU nor the IAEA. According to Article 10 63. 1. of the International Telecommunication Convention, the ITU is responsible with International Frequency Registration Board for the administrative accountability, however, Article 8 54. (3) gives rent to the administrative powers of the organization for agenda settings by the Secretary-General. The article analyzes and questions the administrative accountability of the ITU in the oversight of the high energy photon applications in the telecommunications and if the IAEA was informed by the International Frequency Registration Board on this matter. Correlated behaviors in the cyber-based criminology, with significant impact on public health and biological integrity from such operations, is supplemented for the alteration of financial & economic incentives in the democratic systems, which constituted the liberal International institutionalism. The research contends that criminal liabilities ought to be sought for in the criminological chain.

Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics.

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

On adiabatic theory for extended fermionic lattice systems

We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite and infinite systems, assuming either a uniform gap or a gap in the bulk above the unperturbed ground state. The goal of this Review is to provide an overview of these adiabatic theorems and briefly outline the main ideas and techniques required in their proofs.

An electron turnstile for frequency-to-power conversion.

Single-electron transport relates an operation frequency f to the emitted current I through the electron charge e as I = ef (refs. 1-5). Similarly, direct frequency-to-power conversion (FPC) links both quantities through a known energy. FPC is a natural candidate for a power standard resorting to the most basic definition of the watt: energy emitted per unit of time. The energy is traceable to Planck's constant and the time is in turn traceable to the unperturbed ground state hyperfine transition frequency of the caesium 133 atom. Hence, FPC comprises a simple and elegant way to realize the watt6. In this spirit, single-photon emission7,8 and detection9 at known rates have been proposed as radiometric standards and experimentally realized10-14. However, power standards are so far only traceable to electrical units, that is, to the volt and the ohm6,15-17. In this Letter, we demonstrate an alternative proposal based on solid-state direct FPC using a hybrid single-electron transistor (SET). The SET injects n (integer) quasi-particles (QPs) per cycle into the two superconducting leads with discrete energies close to their superconducting gap Δ, even at zero source-drain voltage. Furthermore, the application of a bias voltage can vary the distribution of the power among the two leads, allowing for an almost equal power injection nΔf into the two. While in single-electron transport current is related to a fixed universal constant (e), in our approach Δ is a material-dependent quantity. We estimate that under optimized conditions errors can be well below 1%.

Generation of quantum vortices in photodetachment: The role of the ground-state wave function

Formation of quantum vortices in laser-induced photodetachment from negative ions is analyzed. The driving laser field consists of a single ultrashort pulse of circular polarization and the unperturbed ground-state wave function of the anion is found in either the $s$ or $p$ state. In particular, numerical illustrations for the photodetachment from ${\mathrm{H}}^{\ensuremath{-}},$ ${\mathrm{O}}^{\ensuremath{-}},$ ${\mathrm{K}}^{\ensuremath{-}},$ and a model ${\mathrm{A}}^{\ensuremath{-}}$ anion are presented. Special attention is paid to the symmetry of the ground-state wave function and ionization potential over the final vortex pattern. It is shown that the two-dimensional spectra of photoelectrons in momentum space comprise three well-defined regions: The low-energy (central) region, multiphotonlike zone, and supercontinuum. While the supercontinuum does not contribute to vorticity and the multiphoton zone depends only on the laser field characteristics, vortices in the low-energy region strongly depend on the bound-state wave function and its ionization potential.

Empirical relations for the sensitivities of solar-like oscillations to magnetic perturbations

ABSTRACT Oscillation mode frequencies of stars are typically treated as static for a given stellar model. However, in reality they can be perturbed by time-varying sources such as magnetic fields and flows. We calculate the sensitivities of radial p-mode oscillations of a set of models for masses between 0.7 and 3.0 M⊙ from the main sequence to the early asymptotic giant branch. We fit these mode sensitivities with polynomials in fundamental stellar parameters for six stages of stellar evolution. We find that the best-fitting relations differ from those proposed in the literature and change between stages of stellar evolution. Together with a measure of the strength of the perturbation, e.g. of the level of magnetic activity, the presented relations can be used for assessing whether a star’s observed oscillation frequencies are likely to be close to the unperturbed ground state or whether they should be adjusted.

Self-polarization effects in spherical inverted core–shell quantum dot

Single electron in spherical shell in infinite potential barrier is investigated. Schrodinger equation in effective mass approximation for this spherical heterosystem is solved to get eigenenergies and corresponding wave functions. In case of infinite potential barrier the ground state energy depends only on the shell width. Self-polarization potential is obtained by solving Poisson equation in three concentric spherical regions: core, shell and surrounding medium. Shell self-polarization energy depends on geometry (core and shell radius) and the dielectric mismatch at the quantum dot boundaries. Self-polarization energy is used as perturbation. One electron ground state energy results are presented in this paper. CdSe is placed in the shell. Surrounding medium is dielectric of smaller permittivity (vacuum or water), that is the most realistic case. The core dielectric permittivity influence on ground state energy is analysed. The self-polarization corrections to the ground state energy for different compositions, i.e. core and shell radius, are presented. For smaller core radius and the same shell thickness (which imply the same unperturbed ground state energy) bigger is the energy correction, i.e. perturbed energy state, for fixed value of the core dielectric permittivity. Increase of core dielectric permittivity produces decrease of energy correction.

Entanglement spectrum of the degenerative ground state of Heisenberg ladders in a time-dependent magnetic field

We investigate the relationship between the entanglement and subsystem Hamiltonians in the perturbative regime of strong coupling between subsystems. One of the two conditions that guarantees the proportionality between these Hamiltonians obtained by using the nondegenerate perturbation theory within the first order is that the unperturbed ground state has a trivial entanglement Hamiltonian. Furthermore, we study the entanglement Hamiltonian of the Heisenberg ladders in a time-dependent magnetic field using the degenerate perturbation theory, where couplings between legs are considered as a perturbation. In this case, when the ground state is twofold degenerate, and the entanglement Hamiltonian is proportional to the Hamiltonian of a chain within first-order perturbation theory, even then also the unperturbed ground state has a nontrivial entanglement spectrum.

Dalgarno–Lewis perturbation theory for nonlinear optics

We apply the quadrature-based perturbation method of Dalgarno and Lewis to the evaluation of the nonlinear optical response of quantum systems. This general operator method for perturbation theory allows us to derive exact expressions for the first three electronic polarizabilities which require only a good estimate of the ground state wave function, makes no explicit reference to the underlying potential, and avoids complexities arising from excited state degeneracies. We apply this method to simple examples in 1D quantum mechanics for illustration, exploring the sensitivity of this method to variational solutions as well as poor numerical sampling. Finally, to the best of our knowledge, we extend the Dalgarno-Lewis method for for the first time to time-harmonic perturbations, allowing dispersion characteristics to be determined from the unperturbed ground state wave function alone.

Radiation damage in X-ray crystallography: a quantum-mechanical study of photoinduced defect formation in beeswax-analogue n-eicosane crystals

We study the nuclear dynamics of n-eicosane ( $$\hbox {C}_{20}\hbox {H}_{42}$$ ) in the crystalline state after photoirradation at room temperature using adiabatic ab initio excited-state dynamics based on hybrid time-dependent density-functional theory. We consider the weak perturbation (absorption) limit, in which an excited electron and a hole are simultaneously created in the system, and the strong perturbation (photoemission) regime, in which one electron is removed. We examine the changes in the carbon chain conformation occurring over timescales of the order of ca. 5 ps relative to the unperturbed (ground state) crystal structure at room temperature, which we simulate using standard ab initio molecular dynamics based on hybrid density-functional theory. Whereas the system retains its ground-state structure in the photoemission limit, the formation of structural defects, in the form of local distortions of the chain geometry, is observed in the absorption limit. We attribute the formation of these defects to the nuclear screening of the electron–hole pair created by photoexcitation. We discuss these findings in the context of radiation damage in organic/biological macromolecules and X-ray diffraction techniques.

High-energy anomalies in covalent high-Tc cuprates with large Hubbard Ud on copper

A large Ud theory is constructed for the metallic state of high-Tc cuprates. The Emery three-band model, extended with Ox–Oy hopping tpp, and with Ud→∞, is mapped on slave fermions. The Dyson time-dependent diagrammatic theory in terms of the Cu–O hopping tpd, starting from the nondegenerate unperturbed ground state, is translationally and asymptotically locally gauge invariant. The small parameter of the theory is the average hole occupation of Cu sites nd. The lowest order of the theory generates the single particle propagators of the hybridized pdp- and dpd-fermions with the exact covalent three band structure. The leading many-body effect is band narrowing, accompanied by Landau-like damping of the single particle propagation, due to incoherent local charge Cu–O fluctuations. The corresponding continuum is found below and above the Fermi level.

Entanglement spectra of Heisenberg ladders of higher spin

We study the entanglement spectrum of Heisenberg spin ladders of arbitrary spin length S in the perturbative regime of strong rung coupling. For isotropic spin coupling the entanglement spectrum is, within first-order perturbation theory, always proportional to the energy spectrum of the single chain with a proportionality factor that is also independent of S. In particular, although the spin ladder possesses an excitation gap over its ground state for any spin length, the entanglement spectrum is gapless for half-integer S and gapful otherwise. A more complicated situation arises for anisotropic ladders of higher spin S ≥ 1 since here even the unperturbed ground state has a nontrivial entanglement spectrum. Finally we discuss related issues in dimerized spin chains.

Concurrent multiple-state analytic perturbation theory via supersymmetry

Conventional nondegenerate perturbation theory for some nth state starts with the corresponding unperturbed state. The present formulation yields recursively perturbation expansions for any bound state using the sole information of the unperturbed ground state. Logarithmic perturbation theory is exploited along with supersymmetric quantum mechanics to achieve this end. As the method involves ground-state perturbations of a series of supersymmetric Hamiltonians, concern about nodal shifts of targeted excited states arises only at the ultimate step, thus, minimizing considerably the labor of clumsy computations involved in dealing with excited states.

Scaling Property of the F–AF Spin Chain Near the Exactly Solvable Point

We investigate the ground state of the J 1 – J 2 spin-1/2 chain with J 1 <0 and J 2 >0 in the case that the nearest-neighbor J 1 interaction in the z -direction has a weak anisotropy as J 1 (1-α). We perform a perturbational analysis for small α and λ≡ J 2 -| J 1 |/4 with the exact solution of the unperturbed ground state for α=λ=0. The scaling property of the ground-state energy is examined in detail. By the numerical diagonalization analysis of finite-size systems, we found the phase boundary equation between the spin fluid and dimer phases as α c =14λ c 4/3 .

Recent Advances in Explicitly Correlated Coupled-Cluster Response Theory for Excited States and Optical Properties

Abstract The derivation of coupled-cluster response theory for explicitly correlated wavefunctions with terms linear in the interelectronic distance r 12 (CC-R12) or a function f 12 thereof (CC-F12) is reviewed and an implementation at the CCSD(R12) and CCSD(F12) for excitation energies and the linear, quadratic and cubic reponse functions is reported for ansätze 1 and 2. We discuss the results of first applications for vertical excitation energies, excited state equilibrium structures and vibrational frequencies, polarizabilities and first and second hyperpolarizabilities with focus on present limitations and future prospects of the approach. We show in particular that the standard choice of the geminal functions and wavefunction expansion can in certain cases lead to a bias towards the unperturbed ground state and how this can be avoided by extending the geminal space. If taken care of this, in particular CCSD(F12)/ansatz 2 shows for the potential energy curves of excited states and for optical properties a similar enhanced basis set convergence of the correlation contribution due to connected double excitations as for ground state energies. For diffuse excited states and hyperpolarizbilities the correlation contribution converges with CCSD(F12)/ansatz 2 often faster than orbital relaxation contributions. The convergence of the latter can be improved by allowing single excitations into a space spanned by a complementary auxiliary basis set.

Dynamic susceptibilities of the single-impurity Anderson model within an enhanced noncrossing approximation

The single-impurity Anderson model is studied within an enhanced noncrossing approximation (ENCA). This method is extended to the calculation of susceptibilities and thoroughly tested, also in order to prepare applications as a building block for the calculation of susceptibilities and phase transitions in correlated lattice systems. A wide range of model parameters, such as impurity occupancy, temperature, local Coulomb repulsion, and hybridization strength, are studied. Results for the spin and charge susceptibilities are presented. By comparing the static quantities to exact Bethe ansatz results, it is shown that the description of the magnetic excitations of the impurity within the ENCA is excellent, even in situations with large valence fluctuations or vanishing Coulomb repulsion. The description of the charge susceptibility is quite accurate in situations where the singly occupied ionic configuration is the unperturbed ground state; however, it seems to overestimate charge fluctuations in the asymmetric model at too low temperatures. The dynamic spin-excitation spectrum is dominated by the Kondo screening of the impurity spin through the conduction band, i.e., the formation of the local Kondo singlet. A finite local Coulomb interaction $U$ leads to a drastic reduction in the charge response as processes involving the doubly occupied impurity state are suppressed. In the asymmetric model, the charge susceptibility is enhanced for excitation energies smaller than the Kondo scale ${T}_{K}$ due to the influence of valence fluctuations.

Domain walls and chaos in the disordered SOS model

Domain walls, optimal droplets and disorder chaos at zero temperature are studied numericallyfor the solid-on-solid model on a random substrate. It is shown that the ensemble ofrandom curves represented by the domain walls obeys Schramm’s left passage formula withκ = 4 whereas theirfractal dimension is ds = 1.25, and therefore their behavior cannot be described as showing ‘Schramm– (orstochastic) Loewner evolution’ (SLE). Optimal droplets with a lateral size betweenL and2L have the same fractal dimension as domain walls but an energy that saturates at a value oforder for such that arbitrarily large excitations exist which cost only a small amount of energy.Finally it is demonstrated that the sensitivity of the ground state to small changes of orderδ in the disorder is subtle: beyond a crossover length scaleLδ∼δ−1 the correlations of the perturbed ground state with the unperturbed ground state, rescaledusing the roughness, are suppressed and approach zero logarithmically.

Simple Glass Models and Their Quantum Annealing

We study first-order quantum phase transitions in mean-field spin glasses. We solve the quantum random energy model using elementary methods and show that at the transition the eigenstate suddenly projects onto the unperturbed ground state and that the gap between the lowest states is exponentially small in the system size. We argue that this is a generic feature of all "random first-order" models, which includes benchmarks such as random satisfiability. We introduce a two-time instanton to calculate this gap in general, and discuss the consequences for quantum annealing.

Low-frequency atomic stabilization and dichotomy in superintense laser fields: Full Floquet results

In the preceding paper we have shown, based on the high-intensity, high-frequency Floquet theory (HIHFFT), that atomic quasistationary stabilization (QS) and dichotomy are not necessarily high-frequency phenomena as widely believed, but can occur also at photon energies small with respect to the unperturbed ground state binding energy, provided that the field is strong enough. In this paper we approach the issue from the point of view of accurate numerical Floquet computations. We have made a comprehensive determination of the Floquet quasienergies for a one-dimensional (1D) atomic model with a soft-core Coulomb potential (ground state energy ${W}_{0}=\ensuremath{-}0.500\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$) in a laser field of constant amplitude ${E}_{0}$ and frequency $\ensuremath{\omega}$. The excursion parameter ${\ensuremath{\alpha}}_{0}={E}_{0}∕{\ensuremath{\omega}}^{2}$ was varied over the range $0l{\ensuremath{\alpha}}_{0}l100$, at two low frequencies $\ensuremath{\omega}=0.12$ and $0.24\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ $(\ensuremath{\omega}l\ensuremath{\mid}{W}_{0}\ensuremath{\mid})$; the lowest-lying 18 states were computed. We present graphs for the ${\ensuremath{\alpha}}_{0}$ dependence of the energies of the states in the field, $W({\ensuremath{\alpha}}_{0})=\mathrm{Re}\phantom{\rule{0.2em}{0ex}}E$ (``Floquet maps''), and their ionization rates $\ensuremath{\Gamma}({\ensuremath{\alpha}}_{0})$. An intricate behavior of $W({\ensuremath{\alpha}}_{0})$ was revealed at low ${\ensuremath{\alpha}}_{0}$, with many crossings, avoided crossings (ACs), and Floquet states materializing or disappearing at multiples of $\ensuremath{\omega}$ energy thresholds. At large ${\ensuremath{\alpha}}_{0}$, however, the uneventful pattern encountered at high frequencies is regained, in which the levels tend monotonically to zero modulo $\ensuremath{\omega}$ (i.e., the binding energies of all states vanish). Also $\ensuremath{\Gamma}({\ensuremath{\alpha}}_{0})$ varies substantially at low ${\ensuremath{\alpha}}_{0}$, attaining sometimes large values, but at large ${\ensuremath{\alpha}}_{0}$ it decreases to zero in an oscillatory manner (QS). The form of the components of the Floquet wave function was also followed from low to large ${\ensuremath{\alpha}}_{0}$, and abrupt changes were found in most cases at ACs. The Floquet results were then compared to a computation of the HIHFFT formulas for the quasienergies and good agreement was found (to within the expected accuracy of HIHFFT). This confirms that HIHFFT is fully capable of describing the low-frequency regime at large enough ${\ensuremath{\alpha}}_{0}$, and in particular the existence of QS and dichotomy.

Does the classically chaotic Henon-Heiles oscillator exhibit quantum chaos under intense laser fields?

The quantum dynamics of an electron moving under the Henon-Heiles (HH) potential in the presence of external time-dependent (TD) laser fields of varying intensities have been studied by evolving in real time the unperturbed ground-state wave function φ (x, y, t) of the HH oscillator. The TD Schrodinger equation is solved numerically and the system is allowed to generate its own wave packet. Two kinds of sensitivities, namely, sensitivity to the initial quantum state and to the Hamiltonian, are examined. The threshold intensity of the laser field for an electron moving in the HH potential to reach its continuum is identified and in this region quantum chaos has been diagnosed through a combination of various dynamical signatures such as the autocorrelation function, quantum ‘phase-space’ volume, ‘phase-space’ trajectory, distance function and overlap integral (akin to quantum fidelity or Loschmidt echo), in terms of the sensitivity towards an initial state characterized by a mixture of quantum states (wave packet) brought about by small changes in the Hamiltonian, rather than a ‘pure’ quantum state (a single eigenstate). The similarity between the HH potential and atoms/molecules in intense laser fields is also analyzed.