Equation Of Motion Method Research Articles

Effect of van-Hove singularities in single-walled carbon nanotube leads on transport through T-shaped double quantum dot system

The T-shaped double quantum dot system with single-walled metallic armchair carbon nanotube leads has been studied using Green functions obtained by the equation of motion method. The effect of relative spacing between the energy levels of the dots, interdot tunneling matrix-element, interdot Coulomb interaction, and van-Hove singularities in density of states characteristics of quasi-one-dimensional carbon nanotube leads on the conductance of the double quantum dot system has been studied. The conductance and dot occupancies are calculated at finite temperatures. The density of states of the carbon nanotube leads is observed to play a significant role in determining the conductance profile. In particular, whenever the chemical potential of the isolated double quantum dot system is aligned with the position of a van-Hove singularity in the density of states of armchair carbon nanotube leads, the height of the corresponding conductance peak falls considerably. It is further observed that the suppression in the heights of the alternate peaks depends on the relative positions of the energy levels of the dots and their magnitude of separation.

Introducing the Random Phase Approximation Theory

Random Phase Approximation (RPA) is the theory most commonly used to describe the excitations of many-body systems. In this article, the secular equations of the theory are obtained by using three different approaches: the equation of motion method, the Green function perturbation theory and the time-dependent Hartree–Fock theory. Each approach emphasizes specific aspects of the theory overlooked by the other methods. Extensions of the RPA secular equations to treat the continuum part of the excitation spectrum and also the pairing between the particles composing the system are presented. Theoretical approaches which overcome the intrinsic approximations of RPA are outlined.

Nuclear structure studies in mirror nuclei

The nuclear structure of the A=31 and A=47 mirror couples produced by two fusion evaporation reactions has been elaborated, utilizing the Doppler-shift attenuation method. Excited states in 31P and 31S were populated using the 1p and 1n exit channels, respectively, of the reaction 20Ne + 12C, while in 47Cr and 47V couple excited states were populated based on 28Si + 28Si reaction, as products of 2αn and 2αp exit channels. The A=31 mirror couple was studied utilizing Piave-Alpi accelerator of the Laboratori Nazionali di Legnaro with GASP multidetector array and for A=47 one - with the EUROBALL array using XTU Tandem also in Legnaro. In both cases the lifetime measurements in mirror couples at the same experiment open possibilities for investigations of isospin symmetry. Determined B(E1) strengths in the mirror nuclei 31P and 31S allow to extract the isoscalar component, which can reach up to 24% of the isovector one. The B(E1) values can be modeled by the Equation of motion method. In the case of A=47 mirror couple, the quadrupole moments can be described by shell-model calculations.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals.

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Magneto-optical properties of gapped-graphene

We theoretically study the optical properties of single-layer graphene placed on hexagonal boron nitride in the presence of a magnetic field. Analytical expressions for the longitudinal χxx(ω) and Hall χyx(ω) susceptibilities are derived from the equation of motion method. The χxx(ω) and χyx(ω) are evaluated as functions of photon energy for both undoped and doped graphenes for different values of electron densities, temperatures, and magnetic fields. The intra-band transitions induce only one peak while the inter-band ones cause a series of peaks that show oscillations with photon energy. The electron density is one of the main factors controlling the threshold energy in the doped regime. The contribution to the susceptibilities of the right polarized light is always dominant in the left polarized one.

Charge and spin currents in mesoscopic rings: Role of next nearest-neighbors Rashba spin–orbit coupling using the Green’s functions equation of motion technique

The electronic states of a mesoscopic ring are assessed using the Green functions approach and the equation of motion method. We put forward the Green’s function formalism to evaluate precisely persistent charge and spin currents in a ring exhibiting nearest-neighbors (NN) and next-nearest (NNN) neighbors Rashba spin–orbit interactions. Our present scheme circumvents direct diagonalization of the Hamiltonian, allowing to determine numerically persistent currents with both spin–orbit interactions simultaneously. Our results for the spin currents show that the NN Rashba interaction breaks the spin degeneracy producing a square-like shape; while the NNN Rashba interaction creates an energy-dependent splitting of the levels that generates a pattern of small peaks. The merging of both interactions rises a periodic squared-peaked pattern at half integer values of the quantum flux, which suggests the possibility of controlling the spin current magnitude and polarization by modulating the NNN Rashba parameter.

Bound states in the continuum in a two-channel Fano-Anderson model

In this article, we study the formation of the bound states in the continuum (BICs) in a two-channel Fano-Anderson model. We employ the Green's function formalism, together with the equation of motion method, to analyze the relevant observables, such as the transmission coefficient and the density of states. Most importantly, our results show that the system hosts true BICs for the case of a symmetric configuration with degenerate impurity levels, and a complete transmission channel is then suppressed. Finally, we argue that the proposed mechanism could be relevant for the realization of BICs in electronic and photonic systems.

Anderson localization in the Anderson–Hubbard model with site-dependent interactions

We consider Anderson localization in the half-filled Anderson–Hubbard model in the presence of either random on-site interactions or spatially alternating interactions in the lattice. By using dynamical mean field theory with the equation of motion method as an impurity solver, we calculate the arithmetically and geometrically averaged local density of states and derive the equations determining the critical value for the phase transition between metallic, Anderson and Mott insulating phases. The nonmagnetic ground state phase diagrams are constructed numerically. We figure out that the presence of Coulomb disorder drives the system toward the Anderson localized phase that can occur even in the absence of Anderson structural disorder. For the spatially alternating interactions, we find that the metallic region is reduced and the Anderson insulator one is enlarged with increasing interaction modulation. Our obtained results are relevant to current research in ultracold atoms in disordered optical lattices where metal–insulator transition can be observed experimentally by using ultracold atom techniques.

Theory of Non-Equilibrium Heat Transport in Anharmonic Multiprobe Systems at High Temperatures.

We consider the problem of heat transport by vibrational modes between Langevin thermostats connected by a central device. The latter is anharmonic and can be subject to large temperature difference and thus be out of equilibrium. We develop a classical formalism based on the equation of motion method, the fluctuation–dissipation theorem and the Novikov theorem to describe heat flow in a multi-terminal geometry. We show that it is imperative to include a quartic term in the potential energy to insure stability and to properly describe thermal expansion. The latter also contributes to leading order in the thermal resistance, while the usually adopted cubic term appears in the second order. This formalism paves the way for accurate modeling of thermal transport across interfaces in highly non-equilibrium situations beyond perturbation theory.

An excited state coupled-cluster study on indigo dyes

In the present study, the domain-based pair natural orbital implementation of the similarity-transformed equation of motion method is employed to reproduce the vibrationally resolved absorption spectra of indigo dyes. After an initial investigation of multireference, basis set and implicit solvent effects, our calculated 0–0 transition energies are compared to a benchmark set of experimental absorption band maxima. It is established that the agreement between our method and experimental results is well below the desired 0.1 eV threshold in virtually all cases and that the shift in excitation energies upon chemical substitution is also well reproduced. Finally, the entire spectra of some of the main components of the Tyrian purple dye mixture are reproduced and it is found that our computed spectra match the experimental ones without an empirical shift.

Metal–insulator transitions of fermionic mixtures with mass imbalance in disordered optical lattice

We study the metal–insulator transitions in the half-filled Anderson–Hubbard model with mass imbalance by the typical medium theory using the equation of motion method as an impurity solver. The nonmagnetic ground state phase diagram of the system with mass imbalance is constructed numerically. In addition to the three phases showed up in the balanced case, the phase diagram of the mass imbalanced case contains a spin-selective localized phase, where one spin component is metallic while the other spin component is insulating. We find that if one increases the mass imbalance the metal region in the phase diagram is reduced, while both Anderson and Mott insulator regions are enlarged.

Spin excitations in the Kitaev-Heisenberg model: Popov-Fedotov fermionization

We study a Kitaev-Heisenberg model of spin 1/2 using the Popov-Fedotov fermionization proccedure. We derive the free energy of the quantum spin system on a Bravais lattice within one-loop approximation with exact on-site constraint. We discuss the obtained magnetic excitation spectrum for a particular case of square lattice in relation to the data derived by the equation of motion method and with the result of the linear spin wave theory in Holstein - Primakoff representation.

Thermal rectification through a nonlinear quantum resonator

We present a comprehensive and systematic study of thermal rectification in a prototypical low-dimensional quantum system -- a non-linear resonator: we identify necessary conditions to observe thermal rectification and we discuss strategies to maximize it. We focus, in particular, on the case where anharmonicity is very strong and the system reduces to a qubit. In the latter case, we derive general upper bounds on rectification which hold in the weak system-bath coupling regime, and we show how the Lamb shift can be exploited to enhance rectification. We then go beyond the weak-coupling regime by employing different methods: i) including co-tunneling processes, ii) using the non-equilibrium Green's function formalism and iii) using the Feynman-Vernon path integral approach. We find that the strong coupling regime allows us to violate the bounds derived in the weak-coupling regime, providing us with clear signatures of high order coherent processes visible in the thermal rectification. In the general case, where many levels participate to the system dynamics, we compare the heat rectification calculated with the equation of motion method and with a mean-field approximation. We find that the former method predicts, for a small or intermediate anharmonicity, a larger rectification coefficient.

Majorana–Kondo interplay in a Majorana wire-quantum dot system with ferromagnetic contacts* *Project supported by the Science Foundation of Civil Aviation Flight University of China (Grant No. JG2019-19).

We consider a single-level quantum dot (QD) and a topological superconducting wire hosting Majorana bound states at its ends. By the equation of motion method, we give the analytical Green's function of the QD in the noninteracting and the infinite interacting case. We study the effects of QD energy level and the spin polarization on the density of states (DOS) and linear conductance of the system. In the noninteracting case, the DOS resonance shifts with the change of energy level and it shows bimodal structure at large spin polarization strength. In the infinite interacting case, the up-spin linear conductance first increases and then decreases with the increase of spin polarization strength, but the down-spin is stable. However, the DOS shows a splitting phenomenon in the large energy level with the increase of spin polarization strength. This provides an interesting way to explore the physical properties of such spin dependent effect in the hybrid Majorana QD systems.

Phase- and spin-dependent manipulation of leakage of Majorana mode into double quantum dot* *Project supported by the Science Foundation of Civil Aviation Flight University of China (Grant No. JG2019-19).

We present a phase- and spin-dependent manipulation of leakage of a Majorana mode into a double quantum dot. We study the density of states (DOS) to show the effect of phase change factor on the Majorana leakage into (out) of a double quantum dot. The DOS is derived from the Green’s function of the quantum dot by the equation of motion method, and exhibits a formant structure when ϕ = 0,2π and a resonance shape when ϕ = 0.5π and 1.5π. Also, it changes more strongly under the spin-polarized coefficient than the non-polarized lead. Such a theoretical model can be modified to explore the spin-dependent effect in the hybrid Majorana quantum dot system.

Symmetry-adapted formulation of the hybrid treatment resulting from the G-particle-hole Hypervirial equation and equations of motion methods: a procedure for modeling solids

Highly accurate electron affinities and ionization potentials of chemical systems were described by means of the procedure called GHV-EOM (Valdemoro et al, in Int J Quantum Chem 112:2965, 2012), which combines the G-particle-hole hypervirial (GHV) equation method (Alcoba et al, in Int J Quantum Chem 109:3178, 2009) and that of the equations-of-motion (EOM), by Simons and Smith (Simons and Smith, in J Chem Phys 58:4899, 1973). The present work improves that hybrid method by introducing the point group symmetry within its framework, providing a higher computational efficiency. We report results which show the achievements attained by using the symmetry-adapted methodology. The new formulation turns out to be particularly suitable for characterizing solid models, as cyclic one-dimensional chains.

Collision of protons with carbon atoms of a graphene surface in the presence of adsorbed potassium

In this work we study the frontal collision of protons with the carbon atoms of a graphene surface with a low coverage of adsorbed potassium. It is aimed at the analysis of the effect of the adsorbates in both charge exchange and electron emission processes, when the binary collision occurs between the proton and a carbon atom of the surface. The frontal collision with the K adsorbate, already analyzed and discussed in a previous work, is compared with the frontal collision with different carbon neighbors. In the present work we studied the signals, due to the localized structures in the density matrix of the composed graphene plus potassium surface, that can be distinguished when the collision occurs either with the adsorbate, a nearby carbon atom, or a carbon atom that does not feel the presence of the adsorbate. The interacting system is described by the Anderson Hamiltonian which takes into account the electronic repulsion on the projectile site; the charge fractions, the energy distribution of electrons in the solid, and the electron emission after the collision are calculated by using the nonequilibrium Green-Keldysh functions formalism solved by the equation of motion method. In the binary collision with a carbon atom, the extended features of the band structure of graphene smooth the dependence of the projectile charge fractions on the incoming energy and notably decrease the negative ions formation. The localized structures of the density of matrix caused by the presence of the adsorbate are perceptible for scattered carbon atoms close to K. The intense emission of low energy electrons obtained in the case of the scattering by potassium is fundamentally associated with the very localized K-$4s$ empty band. This characteristic, although less marked, remain in the scattering by nearby carbon atoms, due to both the interaction with K along the projectile trajectory and the perturbed local density of states on the carbon atoms due to the adsorbate presence. In addition, the extended nature of the electronic structure of graphene allows for the emission of more energetic electrons.

Quantitative comparison of Anderson impurity solvers applied to transport in quantum dots

We study the single impurity Anderson model (SIAM) using the equations of motion method (EOM), the non-crossing approximation (NCA), the one-crossing approximation (OCA), and Wilson’s numerical renormalization group (NRG). We calculate the density of states and the linear conductance focusing on their dependence on the chemical potential and on the temperature paying special attention to the Kondo and Coulomb blockade regimes for a large range of model parameters. We report that some standard approximations based on the EOM technique display a rather unexpected poor behavior in the Coulomb blockade regime even at high temperatures. Our study offers a critical comparison between the different methods as well as a detailed compilation of the shortcomings and limitations due the approximations involved in each technique, thus allowing for a cost-benefit analysis of the different solvers that considers both numerical precision and computational performance.

Coupled self-consistent random-phase approximation equations for even and odd particle numbers: Tests with solvable models

Coupled equations for even and odd particle number correlation functions are set up via the equation of motion method. For the even particle number case this leads to self-consistent RPA (SCRPA) equations already known from the literature. From the equations of the odd particle number case the single particle occupation probabilities are obtained in a self-consistent way. This is the essential new procedure of this work. Both, even and odd particle number cases are based on the same correlated vacuum and, thus, are coupled equations. Applications to the Lipkin model and the 1D Hubbard model give very good results.

Influence of weak measurement on uncertainty relations in a quantum dissipative system

We investigate the influence of weak measurement on the quantum-memory-assisted entropic uncertainty relation and quantum speed limit time in a quantum dissipative system by making use of the hierarchical equations of motion method. It is demonstrated that the weak measurement and measurement reversal can suppress the entropic uncertainty during the evolution of the system, and we find a periodical crossover of the quantum speed limit time for different weak measurement strengths, which disappears when increasing the coupling strength. Similar influence of the weak measurement on uncertainty relations is then explored at the finite temperature. We also consider the effect of the counter-rotating-wave term and show that the rotating-wave approximation is an applicable approximation when studying quantum speed limit time but not appropriate when investigating the quantum-memory-assisted entropic uncertainty relation.