Equation Of Motion Approach Research Articles

Fano and Dicke Effects in Parallel-Triple Quantum Dots Embedded Between Two Leads

This article explores electronic transport in a triple quantum dot system connected in parallel to metallic leads while subjected to an external magnetic flux. The Green-function formalism and the equation of motion approach were employed to derive a comprehensive formula for conductance. The study reveals the presence and modulation of Fano and Dicke effects in the conductance spectra of the Triple quantum dot system (TQD). These effects are controlled by adjusting the interdot coupling energy ( ), the coupling (Γ) of the three dots to the right and left leads, and manipulating the external magnetic flux.

Fano and Dicke Effects in Parallel-Coupled Quantum Dots Embedded Between Two Leads

In this article, electronic transport through a double quantum dot attached in parallel to a metal lead and with the presence of a magnetic flux is studied with the help of the Green-function formalism and the equation of motion approach. A detail formula is obtained for the density of states and the conductance. The Fano and Dicke effects in the conductance spectra of the double quantum dots system DQD is found and controlled by tuning the coupling (Γ) of the two dots to right (left) Leads and by changing the external magnetic flux.

Lyapunov equation in open quantum systems and non-Hermitian physics

The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic Hamiltonian, linear equations of motion) open quantum systems, typically from quantum master equations. Despite this, the Lyapunov equation is seldom considered a fundamental formalism for linear open quantum systems. In this work we aim to change that. We establish the Lyapunov equation as a fundamental and efficient formalism for linear open quantum systems that can go beyond the limitations of various standard quantum master equation descriptions, while remaining of much less complexity than general exact formalisms. This also provides valuable insights for non-Hermitian quantum physics. In particular, we derive the Lyapunov equation for the most general number conserving linear system in a lattice of arbitrary dimension and geometry, connected to an arbitrary number of baths at different temperatures and chemical potentials. Three slightly different forms of the Lyapunov equation are derived via an equation of motion approach, by making increasing levels of controlled approximations, without reference to any quantum master equation. Then we discuss their relation with quantum master equations, positivity, accuracy and additivity issues, the possibility of describing dark states, general perturbative solutions in terms of single-particle eigenvectors and eigenvalues of the system, and quantum regression formulas. Our derivation gives a clear understanding of the origin of the non-Hermitian Hamiltonian describing the dynamics and separates it from the effects of quantum and thermal fluctuations. Many of these results would have been hard to obtain via standard quantum master equation approaches.

Functional-integral approach to Gaussian fluctuations in Eliashberg theory

The Eliashberg theory of superconductivity is based on a dynamical electron-phonon interaction as opposed to a static interaction present in BCS theory. The standard derivation of Eliashberg theory is based on an equation of motion approach, which incorporates certain approximations such as Migdal's approximation for the pairing vertex. In this paper we provide a functional-integral-based derivation of Eliashberg theory and we also consider its Gaussian-fluctuation extension. The functional approach enables a self-consistent method of computing the mean-field equations, which arise as saddle-point conditions, and here we observe that the conventional Eliashberg self energy and pairing function both appear as Hubbard-Stratonovich transformations. An important consequence of this fact is that it provides a systematic derivation of the Cooper and density-channel interactions in the Gaussian fluctuation response. We also investigate the strong-coupling fluctuation diamagnetic susceptibility near the critical temperature.

Survival of quantum features in the dynamics of a dissipative quantum system and their effect on the state purity.

Destruction of the quantum mechanical features of matter by decoherence restricts the applicability of quantum technologies. The limited information of the quantum features (such as coherence) in the basis-dependent observations urges the use of a basis-independent quantity for a better understanding. In this context, the state purity of a quantum system (composed of quantized pigments immersed in a noisy protein environment) is studied with a numerically exact hierarchical equations of motion approach over the wide range of the parameter domain (with the main focus on the nonzero-energy gradient). It is noted that the state purity does not necessarily reflect any significant information about the persistence of quantum features (in the dissipative environment), even when the quantum coherence survives at the steady state in both the localized and the eigenstate basis.

Effects of charge ordering in electronic subsystem of quasi-2D BEDT-TTF conductors

The interplay of the inter-site Coulomb repulsion which induces charge ordering, and the correlated hopping of electrons, which causes peculiar dependence of energy characteristics on a doping, is studied in a model of BEDT-TTF organic conductor electronic subsystem. By applying the projection method in the Green function equation of motion approach the single-particle energy spectrum, sublattice magnetization in charge-ordered phase, and the transition temperature have been calculated. Dependence of Verwey temperature on the band filling shows that inter-site Coulomb correlation significantly influences the width of the concentration interval in which a charge order stabilizes. The correlated hopping causes the decrease of the critical value of electron concentration and increase of Verwey temperature in whole concentration interval of charge ordering stability.

A new density for transition properties within the similarity transformed equation of motion approach

ABSTRACT Similarity transformed equation of motion coupled cluster theory offers an efficient way of computing excited state energies by decoupling the space of singles from higher excitations. However, when computing properties with this method, one is left with a choice between an expensive method involving a transformation into the space of the singles and the doubles, or methods that approximate the full density. In this paper, we present a rigorous expectation value formulation of the density to compute transition properties and discuss its relation to other existing techniques. We confirm that the configuration interaction singles approximation we used in earlier studies oscillator strength values is a reliable one, but also that the current formulation provides a cost efficient improvement on it.

Sustained charge-echo entanglement in a two charge qubits under random telegraph noise

The echo signal influence in restoring the coherence lost due to a random telegraph noise (RTN) in a double quantum dot has been theoretically investigated. In this paper, we discuss the RTN effects according to two different protocols manipulations: free induction and echo signal. The time evolution of the coherence factor for both protocols is evaluated employing the equation of motion approach. The time dependence of both fidelity and purity is numerically assessed as well. Our results unveil an enhancement in the entangled states lifetime and how the effects of the RTN, ubiquitous to the solid-state devises, can be counteracted. Furthermore, applying charge-echo stretches the coherence time. Our results exhibit an improvement by 4 times of the coherence time, proving the echo signal efficiency. It is worth mentioning that our analysis is also applicable to other solid-state devices and helpful for further understanding the open quantum systems dynamics.

An equation of motion approach for the vibrational transition energies in the effective harmonic oscillator formalism: the Random phase approximation

A theory for calculating vibrational energy levels and infrared intensities is developed in the equation of motion framework at the random phase approximation level. The vibrational Hamiltonian is expanded in the harmonic oscillator ladder operators making a Hamiltonian a bosonic Hamiltonian. The excitation operator is expanded to include at most two creations and two annihilation operators making it equivalent to the random phase approximation. The method is applied for the calculation of vibrational spectral properties of two molecules. The results are found to be satisfactory, making this approach a viable option for large molecular systems. A theory for calculating vibrational energy levels and infrared intensities is developed in the equation of motion framework at the random phase approximation level. The vibrational Hamiltonian is expressed in bosonic representation. The excitation operator is expanded to include at most two creation and annihilation operators.

Monolayer transition metal dichalcogenides in strong magnetic fields: Validating the Wannier model using a microscopic calculation

Using an equation of motion (EOM) approach, we calculate excitonic properties of monolayer transition metal dichalcogenides (TMDs) perturbed by an external magnetic field. We compare our findings to the widely used Wannier model for excitons in two-dimensional materials and to recent experimental results. We find good agreement between the calculated excitonic transition energies and the experimental results. In addition, we find that the exciton energies calculated using the EOM approach are slightly lower than the ones calculated using the Wannier model. Finally, we also show that the effect of the dielectric environment on the magnetoexciton transition energy is minimal due to counteracting changes in the exciton energy and the exchange self-energy correction.

Quantum entanglement of parallel-coupled double quantum dots: A theoretical study using the hierarchical equations of motion approach

Quantum dots comprise a type of quantum impurity system. The entanglement and coherence of quantum states are significantly influenced by the strong electron-electron interactions among impurities and their dissipative coupling with the surrounding environment. Competition between many-body effects and transfer couplings plays an important role in determining the entanglement among localized impurity spins. In this work, we employ the hierarchical-equations-of-motion approach to explore the entanglement of a strongly correlated double quantum dots system. The relation between the total system entropy and those of subsystems is also investigated.

Constructing Electronic Phase Diagram for the Half-filled Hubbard Model with Disorder

The electronic phase diagram of strongly correlated systems with disorder is constructed using the typical-medium theory. For half-filled system, the combination of the linearized dynamical mean field theory and equation of motion approach allows to derive the explicit equations determining the boundary between the correlated metal, Mott insulator, and Anderson insulator phases. Our phase diagram is consistent with those obtained by the more sophisticated methods.

Linearization of a warpedf(R)theory in the higher-order frame. II. The equation of motion approach

Without using conformal transformation, a simple type of five-dimensional $f(R)-$brane model is linearized directly in its higher-order frame. In this paper, the linearization is conducted in the equation of motion approach. We first derive all the linear perturbation equations without specifying a gauge condition. Then by taking the curvature gauge we derive the master equations of the linear perturbations. We show that these equations are equivalent to those obtained in the quadratical action approach [Phys. Rev. D 95 (2017) 104060], except the vector sector, in which a constraint equation can be obtained in the equation of motion approach but absent in the quadratical action approach. Our work sets an example on how to linearize higher-order theories without using conformal transformation, and might be useful for studying more complicated theories.

Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss

We present an algorithm which combines the quantum trajectory approach to open quantum systems with a density-matrix renormalization group scheme for infinite one-dimensional lattice systems. We apply this method to investigate the long-time dynamics in the Bose-Hubbard model with local particle loss starting from a Mott-insulating initial state with one boson per site. While the short-time dynamics can be described even quantitatively by an equation of motion (EOM) approach at the mean-field level, many-body interactions lead to unexpected effects at intermediate and long times: local particle currents far away from the dissipative site start to reverse direction ultimately leading to a metastable state with a total particle current pointing away from the lossy site. An alternative EOM approach based on an effective fermion model shows that the reversal of currents can be understood qualitatively by the creation of holon-doublon pairs at the edge of the region of reduced particle density. The doublons are then able to escape while the holes move towards the dissipative site, a process reminiscent---in a loose sense---of Hawking radiation.

Understanding the Different Exciton–Plasmon Coupling Regimes in Two-Dimensional Semiconductors Coupled with Plasmonic Lattices: A Combined Experimental and Unified Equation of Motion Approach

We study exciton–plasmon coupling in two-dimensional semiconductors coupled with Ag plasmonic lattices via angle-resolved reflectance spectroscopy and by solving the equations of motion (EOM) in a coupled oscillator model accounting for all the resonances of the system. Five resonances are considered in the EOM model: semiconductor A and B excitons, localized surface plasmon resonances (LSPRs) of plasmonic nanostructures, and the lattice diffraction modes of the plasmonic array. We investigated the exciton–plasmon coupling in different 2D semiconductors and plasmonic lattice geometries, including monolayer MoS2 and WS2 coupled with Ag nanodisk and bowtie arrays and examined the dispersion and line shape evolution in the coupled systems via the EOM model with different exciton–plasmon coupling parameters. The EOM approach provides a unified description of the exciton–plasmon interaction in the weak, intermediate, and strong coupling cases with correctly explaining the dispersion and lineshapes of the complex system. This study provides a much deeper understanding of light–matter interactions in multilevel systems in general and will be useful to instruct the design of novel two-dimensional exciton–plasmonic devices for a variety of optoelectronic applications with precisely tailored responses.

Excitonic effects in the optical properties of 2D materials:an equation of motion approach

We present a unified description of the excitonic properties of four monolayer transition-metal dichalcogenides (TMDC’s) using an equation of motion method for deriving the Bethe–Salpeter equation in momentum space. Our method is able to cope with both continuous and tight-binding Hamiltonians, and is less computational demanding than the traditional first-principles approach. We show that the role of the exchange energy is essential to obtain a good description of the binding energy of the excitons. The exchange energy at the point is also essential to obtain the correct position of the C-exciton peak. Using our model we obtain a good agreement between the Rydberg series measured for WS2. We discuss how the absorption and the Rydberg series depend on the doping. Choosing r0 and the doping we obtain a good qualitative agreement between the experimental absorption and our calculations for WS2. We also derive a semi-analytical version of Ellitot’s formula for TMDC’s.

Mass-imbalanced Hubbard model in optical lattice with site-dependent interactions

We study the half-filled mass-imbalanced Hubbard model with spatially alternating interactions on an optical bipartite lattice by means of the dynamical mean-field theory. The Mott transition is investigated via the spin-dependent density of states and double occupancies. The phase diagrams for the homogeneous phases at zero temperature are constructed numerically. The boundary between metallic and insulating phases at zero temperature is analytically derived within the dynamical mean field theory using the equation of motion approach as the impurity solver. We found that the metallic region is reduced with increasing interaction anisotropy or mass imbalance. Our results are closely relevant to current researches in ultracold fermion experiments and can be verified through experimental observations.

Antiferromagnetic ordering and pseudogap in a model of quasi-1D organic superconductor electronic subsystem

ABSTRACTModel of electronic subsystem of Fabre salts (TMTTF)2X and Bechgaard salts (TMTSF)2X has been studied theoretically within Green function equation of motion approach with special attention to microscopical mechanism for antiferromagnetic order stabilization and pseudogap formation in the electronic spectrum. Conditions for pseudogap opening in the spectrum and anomalies in dispersion of current carriers are determined. Next-nearest-neighbor hopping is shown to break the perfect nesting property and destabilize antiferromagnetic state. On the basis of these results, experimental phase diagrams for quasi-one-dimensional organic superconductors (TMTSF)2X and (TMTTF)2X are interpreted.

Irreducible Green Functions Method Applied to Nanoscopic Systems

The equation of motion method for the Green functions is one of the tools used in the analysis of quantum dot system coupled with the metallic and superconducting leads. We investigate modified equation of motion, based on dierentiation of double-time temperature dependent Green functions both over the primary time t and secondary time t 0 . Our equation of motion approach allows us to obtain the Abrikosov‐Suhl resonance in the particle‐hole symmetric case and also in the asymmetric cases. We will apply the irreducible Green functions technique to analyses of the equation of motion applied to the dot system. This method gives a workable decoupling scheme breaking the infinite set of the Green function equations. We apply this technique to calculate the density of the states and the dierential conductance of single-level quantum dot with the Coulomb repulsion attached to one metallic and one superconducting leads (N‐QD‐SC). Our results are compared with the previous calculations. DOI: 10.12693/APhysPolA.130.551 PACS/topics: 73.63.Kv, 73.23.Hk, 74.45.+c

Electron Pumping under Non-Markovian Dissipation: The Role of the Self-Consistent Field

Focusing on electron transport through a periodically driven resonant tunneling diode, we study the generation of a non-vanishing dc-current by applying symmetry breaking external ac fields with phase difference φ in a statically unbiased system. The effect of an environment is investigated using the system-bath Hamiltonian represented by the electron system coupled to harmonic oscillator modes with a Drude–Lorentz spectral density. To carry out simulations, we use the hierarchal equations of motion approach in the Wigner representation including a self-consistently constructed electric field that is determined from the electron distribution using the Poisson equation. We show that the maximal pumping current at a phase difference near φ = π/2 is strongly influenced by the system-bath coupling strength. The effect of dissipation is diminished if the self-consistent part of the potential is ignored.