Equations For Green Functions Research Articles

Josephson current across a Double Quantum Dot Josephson junction in T-Shape Configuration

By implementing the Keldysh non-equilibrium Green's function equation of motion approach, Josephson current has been examined across a T-shaped uncorrelated double quantum dot Josephson junction. The behavior of the Josephson current as a function of the main quantum dot energy level for varied interdot tunneling and different dot-lead coupling strengths is examined. With this configuration, we illustrate that the side-attached quantum dot offers an alternative route for electron transmission, which modifies the Josephson current by varying interdot tunneling. Further, we also investigate how the dot-lead coupling strengths affect the Josephson current.

The dilute interacting Bose gas: comparisons between Feynman diagrammatic expansion and the hierarchy equations for the imaginary time Green functions

We analyze the correspondence between two formalisms describing an interacting Bose gas, namely the standard Feynman diagrammatic expansion on the one hand, and the hierarchy equations for the imaginary-time Green functions on the other hand. We show that the Hartree–Fock approximation, as well as its first corrections at low density derived by Baym et al (2001 Eur. Phys. J. B 24 107–24), can be equivalently formulated in both formalisms. Within the hierarchy approach, the two-body correlations are expressed at lowest order in the interactions in terms of the full one-body Green function. This sheds light on the physical content of the corrections to the Hartree–Fock theory. Moreover, this representation of can be extended to higher orders, opening the way to systematic calculations of further corrections to the ideal critical temperature when the density increases.

Phase and Thermal-Driven Transport Across T-Shaped Double Quantum Dot Josephson Junction

The phase and thermal driven transport properties of the T-shaped uncorrelated double quantum dot Josephson junction are analyzed by using Keldysh non-equilibrium Green's function equation of motion technique. In this setup, we have shown that the side-attached quantum dot provides an additional route for electron transmission which is affecting the transport properties by adjusting the interdot hopping between the main dot and the side dot. We began with investigating the impact of interdot hopping on Andreev bound states and Josephson supercurrent. When a small thermal bias is applied across the superconducting leads, the system exhibits a finite thermal response which is primarily due to the, thermally induced, quasi-particle current. The behavior of the Josephson supercurrent and the quasi-particle current flowing through the quantum dots is examined for various interdot hopping and thermal biasing. Finally, the system is considered in an open circuit configuration where the thermally driven quasi-particle current is compensated by the phase-driven Josephson supercurrent and the thermophase effect is observed. The effect of interdot hopping and the position of quantum dot energy level on the thermophase Seebeck coefficient is investigated

Projective-truncation-approximation study of the one-dimensional ϕ^{4} lattice model.

In this paper, we first develop the projective truncation approximation (PTA) in the Green's function equationof motion (EOM) formalism for classical statistical models. To implement PTA for a given Hamiltonian, we choose a set of basis variables and projectively truncate the hierarchical EOM. We apply PTA to the one-dimensional ϕ^{4} lattice model. Phonon dispersion and static correlation functions are studied in detail. Using one- and two-dimensional bases, we obtain results identical to and beyond the quadratic variational approximation, respectively. In particular, we analyze the power-law temperature dependence of the static averages in the low- and high-temperature limits, and we give exact exponents.

Advanced workflow for multi-well tracer test analysis in a geothermal reservoir

Interpretation of tracer tests in geothermal reservoirs is carried out by fitting the measured data either with simplified two-dimensional (2-D) analytical solutions or with complex numerical models. Available analytical solutions commonly only describe isotropic conditions in 1-D or 2-D, which is generally unsatisfactory to construct realistic reservoir models. Moreover, due to the large spatial and temporal scale of a tracer test in deep reservoirs, the concentration levels measured in the field are relatively low due to dispersion that complicates the assessment of breakthrough curve tailing and residence time. Fitting tracer data with fully resolving 3-D numerical models thus may be more appropriate, but even with a rich set of field data, reliable calibration is often compromised by the high computational effort and data hunger of such models. In this study, an advanced workflow is presented for evaluating tracer test data. Firstly, a 3-D analytical model in which solute transport is considered in anisotropic porous media is developed. Green's function method is applied to obtain a moving line source solution of the convection-dispersion-diffusion equation for solute transport in a 3-D porous medium. In addition, Green's function equation is analytically convoluted with a rectangular pulse function, which represents tracer injection. Secondly, the analytical model results are fitted to the tracer test data by Monte-Carlo simulations to obtain feasible ranges of flow velocities, as well as longitudinal and transversal dispersivities. Finally, the derived parameter values are implemented in a 3-D numerical model to evaluate the solute residence time in a large-scale reservoir. The results applied to field data from the Kızıldere field in Turkey demonstrate that the workflow provides robust estimates of effective parameters from well-to-well data in complex reservoir systems with anisotropic flow paths. Thus, despite the higher effort of applying convolution and stochastic parameter estimation, the preceding analytical step of the workflow substantially eases numerical model set-up.

Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity

We investigate the phase diagram of spinless fermions on a square lattice with nearest-neighbor interaction, using the recently developed projective truncation approximation in Green's function equation of motion. For attractive interaction, the ground state is in an homogeneous p + ip superconducting (SC) phase at high or low electron densities. Near half filling is a phase separation (PS) between the SC phases. Allowing inhomogeneous solution, we obtain p-wave SC domains with positive interface energy. As temperature increases, the SC phases transit into normal phases above Tsc, generating an homogeneous normal phase (far away from n = 1/2), or a PS between normal phases with different densities (close to n = 1/2). Further increasing temperature to Tps, the PS disappears and the particle-hole symmetry of the Hamiltonian is recovered. For repulsive interaction, depending on electron filling, the ground state is in charge-ordered phase (half filling), charge-disordered phase (large hole/electron doping), or PS between them (weak doping). At finite temperature, the regime of charge order phase moves to finite V and extends to finite doping regime.

Differential conductance and spin current in hybrid quantum dot-topological superconducting nanowire

Majorana bound states (MBSs) are topologically protected and follow the non-abelian rather than the usual Fermi–Dirac statistical rule, and then are ideal choice for the preparation of quantum bits in topologically fault-tolerant quantum computing. The MBSs also have significant influences on the electron transport processes in mesoscopic systems and have been studied in the field of fabricating efficient and energy-saving quantum devices. In this study, we investigated electron transport through a hybridized system composed of a topological superconducting nanowire and quantum dot (QD). Effects of MBSs prepared at the nanowire on differential conductance are calculated and analyzed. It is proved that the differential conductance peak near the superconducting nanowires at zero bias reflects the existence of Majorana fermions. By using the Green's function equation of motion method, we found that a pure spin current without the accompany of charge current can be generated by changing the coupling strength between the QD and MBSs, as well as the accumulation of spin heat in the leads. In the presence of Coulomb interaction in the QD, the direction of pure spin current can be changed by modulating the dot energy level and the coupling strength between dot and MBSs.

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.

GW/BSE nonadiabatic dynamics simulations on excited-state relaxation processes of zinc phthalocyanine-fullerene dyads: Roles of bridging chemical bonds

In this work, we employ electronic structure calculations and nonadiabatic dynamics simulations based on many-body Green function and Bethe-Salpeter equation (GW/BSE) methods to study excited-state properties of a zinc phthalocyanine-fullerene (ZnPc-C60) dyad with 6-6 and 5-6 configurations. In the former, the initially populated locally excited (LE) state of ZnPc is the lowest S1 state and thus, its subsequent charge separation is relatively slow. In contrast, in the latter, the S1 state is the LE state of C60 while the LE state of ZnPc is much higher in energy. There also exist several charge-transfer (CT) states between the LE states of ZnPc and C60. Thus, one can see apparent charge separation dynamics during excited-state relaxation dynamics from the LE state of ZnPc to that of C60. These points are verified in dynamics simulations. In the first 200 fs, there is a rapid excitation energy transfer from ZnPc to C60, followed by an ultrafast charge separation to form a CT intermediate state. This process is mainly driven by hole transfer from C60 to ZnPc. The present work demonstrates that different bonding patterns (i.e. 5-6 and 6-6) of the C−N linker can be used to tune excited-state properties and thereto optoelectronic properties of covalently bonded ZnPc-C60 dyads. Methodologically, it is proven that combined GW/BSE nonadiabatic dynamics method is a practical and reliable tool for exploring photoinduced dynamics of nonperiodic dyads, organometallic molecules, quantum dots, nanoclusters, etc.

Numerical Study on a Multibuoy-Type Wave Energy Converter With Hydraulic PTO System Under Real Sea Conditions

This study aims to investigate the power takeoff (PTO) performance of a two-buoy-type wave energy converter (WEC) with a PTO system under real sea conditions. The two-buoy-type WEC is composed of two hemispherical heaving buoys with a hydraulic PTO system. The hydrodynamic analysis considering two-body interaction is carried out based on the wave green function and Cummins equation. In addition, a hydraulic PTO system is described as an approximate Coulomb damping force and applied to the equation of motion for a WEC. First, by comparing the extraction power on various irregular wave conditions, the PTO performance of an isolated-buoy WEC, and the two-buoy-type WEC is estimated. Through this, it is found that the maximum extraction power occurred when the wave peak period is 1.2 times longer than the heave natural period of a WEC. By comparing the external force and wave elevations near the WEC, three incident wave directions are applied for the maximum or minimum extraction power. Based on these results, the two-buoy-type WEC is applied to the Korean coastal area (Uljin). The PTO force is calculated from the polynomial regression analysis to produce maximum extraction power on various irregular wave conditions. Finally, the annual extraction power and capture width of the WEC in Uljin are calculated. The relation between the design wave period and heave natural period of the WEC is investigated. The annual extraction power is maximum when the design wave period is 20% longer than the WEC's heave natural period and the incident wave is 90°.

Electronic and Cooper pair tunneling signatures in the electronic spectra of superconductors coupled to quantum dot nano-junction

We present here calculations on electronic spectra of a system consisting of a quantum dot connected to superconducting leads on its either side. In these calculations the generated spectra has contributions from both, the single particle tunneling, and from the tunneling Cooper pair of electrons. In this, the Anderson model is used for the theoretical construct, and hence, the single particle tunneling, the Josephson tunneling, the energy states of the quantum dot and the super conducting order parameter for BCS superconductors are principally considered. The Green's function equation of motion technique is used to obtain the single particle spectral function. Our results from the numerical computations in the present work indicate, under certain conditions, the occurrence of breaking of Cooper pairs at the junctions between the superconducting leads and the quantum dot. These are seen to be, understandably, depending on the interaction terms included in our model. Our present work suggests a way to understand the interplay of single particle and the ‘Cooper pairs tunneling’ in the resultant electronic spectra in the light of extended Anderson model applicable to the system. It thus presents a theoretical understanding on the transmission of supercurrents through nanoscopic junctions, such as that considered here.

Study of inter-band pair transfer and density of states on isotope effect in TTF[Ni (dmit)2]2 organic superconductor

The present work deals with the influence of the inter-band pair transfer process and density of states on the isotope effect in layered TTF[Ni(dmit)2]2 organic superconductors. The model Hamiltonian is based on two chains tight binding Hubbard model that includes the electron coupled intra and intermolecular vibrations in the presence of electron Coulomb energy and the electron transfer energy between the chains. The expressions for superconducting order parameter, transition temperature and finally the isotope effect coefficient (α) are calculated in the BCS-framework of Green's function equations of motion approach. The numerical computation predicts that pair transfer processes and density of states controls the isotope effect coefficient in a significant way. More rigorous experimental investigations are needed to understand the microscopic origin of superconductivity and isotope effect in these organic superconductors.

Phase transitions in a model of BEDT-TTF compound electron subsystem

Model of electronic subsystem of (BEDT-TTF)2X family is studied theoretically within Green function equation of motion approach. The configurational representation of the model Hamiltonian which allows analytical calculation of the energy spectrum is developed. Effective Hamiltonian of the model takes into account the strong intra-site Coulomb, intersite exchange interaction of electrons and correlated hopping of electrons both within the conducting plane and in transversal direction. With rise of intraatomic Coulomb repulsion in the energy spectrum a gap opens and the transition to antiferromagnetic state is realized. At the external pressure and decreasing temperature the transition from insulator to metallic phase occurs. The experimental phase diagrams for quasi-twodimensional organic conductors with strong electron correlations and correlated hopping are discussed.

A simplified derivation of the ordinary differential equations for the free-surface Green functions

Ordinary differential equations (ODEs) are derived for the free-surface Green functions and their gradients, in a fluid of infinite depth. The cases of harmonic time-dependence in the frequency domain and impulsive motion in the time domain are considered separately. These ODEs were derived originally by Clément, starting with fourth-oder equations in the time domain and using Fourier transforms to derive a second-order ODE in the frequency domain. In the present work a simpler procedure is followed independently in each domain, transforming the governing Laplace equation to an ordinary differential equation. The results are consistent with the ODEs derived using Clément’s method.

Aeroacoustic noise calculation of noncompact bodies with time-domain scattered green’s function

In view of the scattering effect induced by non-compact bodies, and the growing time cost of the noise calculation with high-order methods, tailored green function methods gradually become effective means to study acoustic noise of noncompact bodies. With the help of free-space green function and convective wave equation, time-domain integral method is presented to calculate scattered green function under arbitrary boundary condition. In order to verify the present method, the cylinder noise under solid wall condition is firstly calculated with stationary point source. The scattered green functions are in good agreement with Gloerfelt’s analytical solution and Takaishi’s frequency method. The pressure distribution demonstrates that the pressure appears as circle shape at low frequency but petal-like pattern at high frequency. Furthermore, point sources in parabolic moving form is chosen to study the influence of scattering effect to far field noise. Numerical results illustrate that the scattering effect is closely related to cylinder radius and the location of sound sources, large body size and sound sources adjacent closely to body surface could lead to serious scattered noise. Besides, time-domain method overcomes the limit that noise calculations have to be performed in relative coordinate system, and it can calculate scattered noise accurately and instantaneous.

Nonequilibrium Green function simulation of coupled electron–phonon transport in one-dimensional nanostructures

Phonon thermal-conductance of a one-dimensional semiconductor nanostructure has been calculated by self-consistently solving coupled nonequilibrium Green function equations for electrons and phonons. The channel length, N, dependence of the phonon thermal-conductance change, ΔKp, due to the electron–phonon interaction is found to obey a simple relation of with a constant proportionality factor β for the calculated N range up to N = 100 (Ge is the electrical conductance). The phonon thermal-conductance change in the isotopically disordered system is found to be hardly affected by the presence of the isotope impurities.

The diffusion equation in multilayered rectangular biological tissue with finite thickness

In biomedical optics, the diffusion model of biological tissue plays an important role. In the biological tissue of any multi-layer rectangular non-matching slab medium, under the rectangular boundary condition, based on the diffusion equation of light propagation in the biological medium, using the extrapolation boundary condition, the exact solution of the diffusion equation Green function of the light in any multi-layer rectangular medium of finite thickness is established and given, and the spatial resolution diffuse reflectivity and transmittance and time resolved diffuse reflectivity and transmittance are calculated in this paper. Different formulas for calculating transmittance are given. We use Monte Carlo to verify our model. The results show that our equation is in good agreement with Monte Carlo simulation. The equation can not only solve the problem of medium which is rectangular laterally, but also solve the problem that the x axis and y axis are infinite in transverse direction, and the medium is semi-infinite in longitudinal direction, and it can also solve the problem that the x, y and z coordinate axes are finite in size. So it's more universal.

Multiscale Modeling of Electromagnetic Telemetry in Layered Transverse Isotropic Formation

Electromagnetic telemetry (EMT) systems are utilized for measurement while drilling to transmit data from borehole to the ground surface during drilling or vice versa. To help predict the successful deployment of the EMT system within complex formation and environmental noise, a reliable numerical algorithm is developed and applied to model the EMT system for directional drilling in layered transverse isotropic (TI) formation. In the telemetry system, the long and thin drill string having three-dimensional trajectory acts as an underground antenna that can be modeled as a thin wire excited by a delta gap voltage/current source near the drill bit. Using the thin wire assumption, the developed algorithm calculates the thin wire kernel in homogeneous uniaxial media with high accuracy to reduce the dimension and complexity of the problem. The mixed-potential form of layered media Green's function and electric field integral equation are used to model the electromagnetic interaction of the drill string and layered TI media. The effect of drilling fluid outside the pipe is modeled using the volumetric equivalence principle. The accuracy and efficiency of the new algorithm are demonstrated by several numerical examples.

Dzyaloshinskii-Moriya interaction of polar magnet Fe2Mo3O8 and its multiferroicity

We propose a theoretical model with Dzyaloshinskii-Moriya interaction for the polar magnet Fe2Mo3O8. Via Wigner-Jordan transformation, the electric polarization Px and the magnetization M formula are obtained. Combined with the Green's function equation of motion method, we show that the electric polarization can be induced by a magnetic ordering and manipulated by a magnetic field. There exist structural and metamagnetic transitions in the Fe2Mo3O8 system, which is in agreement with the experimental results.

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.