Many body theory of photoemission in the quadratic response formalism

Many body Green's function techniques are applied to show that the three current correlation function relating the one photon photoemission current to the applied external field may be expressed by one and two particle correlation properties only for arbitrary many body interactions. An analysis of the double time derivative of the three current correlation function leads to a generalization for arbitrary many body interaction of a formula frequently used for calculations of the photocurrent in the independent electron model. Implications are discussed for the case that only electrostatic electron-electron interactions are present.     

Long-range inverse two-spin correlations in one-dimensional Potts lattices

The inverse two-spin correlation function of a one-dimensional three-state Potts lattice with constant nearest-neighbor interactions in a uniform external field is derived exactly. It is shown that the external field induces long-range correlations. The inverse two-spin correlation function decays in a monotonie exponential fashion for a ferromagnetic lattice, while it decays in an oscillatory exponential fashion for an antiferromagnetic lattice. With no external field the inverse two-spin correlation function has a finite range equal to that of the interactions.     

The effects of electron–phonon interaction on anisotropic RKKY interaction in graphene nanoribbon

We study the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction in doped armchair graphene nanoribbon. The effects of both external magnetic field and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain both transverse and longitudinal static spin susceptibilities of armchair graphene nanoribbon in the presence of electron-phonon coupling and magnetic field. The spin susceptibility components are calculated using the spin dependent Green’s function approach for Holstein model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of magnetic field on the spatial behavior of in-plane and longitudinal RKKY interactions are different in the presence of magnetic field.     

Spatial correlation in the ambient core noise field of a turbofan engine

An acoustic transfer function relating combustion noise and turbine exit noise in the presence of enclosed ambient core noise is investigated using a dynamic system model and an acoustic system model for the particular turbofan engine studied and for a range of operating conditions. Measurements of cross-spectra magnitude and phase between the combustor and turbine exit and auto-spectra at the turbine exit and combustor are used to show the presence of indirect and direct combustion noise over the frequency range of 0-400 Hz. The procedure used evaluates the ratio of direct to indirect combustion noise. The procedure used also evaluates the post-combustion residence time in the combustor which is a factor in the formation of thermal NO(x) and soot in this region. These measurements are masked by the ambient core noise sound field in this frequency range which is observable since the transducers are situated within an acoustic wavelength of one another. An ambient core noise field model based on one and two dimensional spatial correlation functions is used to replicate the spatially correlated response of the pair of transducers. The spatial correlation function increases measured attenuation due to destructive interference and masks the true attenuation of the turbine.     

One-dimensional Ising model in arbitrary external field

The external potential needed to produce an arbitrary equilibrium density profile for a one-dimensional lattice gas with nearest neighbor interactions is solved exactly. The resulting sequence of direct correlation functions is shown to be of short range, and in the ferromagnetic case the even members alternate in sign at zero spin. The even Ursell distributions in this case likewise alternate in sign.Supported in part by U.S. ERDA under contract E(11-1)-3077.     

Direct coulomb and exchange interaction in artificial atoms

We determine contributions from the direct Coulomb and exchange interactions to the total interaction in artificial semiconductor atoms. We tune the relative strengths of the two interactions and measure them as a function of the number of confined electrons. The electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle-state degeneracy, and find that the spin configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states.     

The local pressure for one dimensional sticky rods

Thermodynamic properties of inhomogeneous one dimensional classical systems with nearest neighbor interactions are considered. In particular the partition function of a system of hard core particles with a zero range attractive interaction is determined in the presence of an arbitrary external potential. Different concepts of a local pressure are developed and compared with each other.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

One-dimensional inhomogeneous Ising model: A new approach

We present a new method for the study of a one-dimensional inhomogeneous Ising chain with nonconstant nearest neighbor interactions. The external field required to produce a given magnetization profile is derived exactly. Some properties of the pair direct correlation function are derived. Our findings generalize previous results of Percus.     

Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

Abstract

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet.     

Effects of Coulomb interactions on spin states in vertical semiconductor quantum dots

The effects of direct Coulomb and exchange interactions on spin states are studied for quantum dots contained in circular and rectangular mesas. For a circular mesa a spin-triplet favored by these interactions is observed at zero and nonzero magnetic fields. We tune and measure the relative strengths of these interactions as a function of the number of confined electrons. We find that electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle state degeneracy, and find that the spin-configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states. For a rectangular mesa we observe no signatures of the spin-triplet at zero magnetic field. Due to the anisotropy in the lateral confinement single-particle state degeneracy present in the circular mesa is lifted, and Coulomb interactions become weak. We evaluate the degree of the anisotropy by measuring the magnetic field dependence of the energy spectrum for the ground and excited states, and find that at zero magnetic field the spin-singlet is more significantly favored by the lifting of level degeneracy than by the reduction in the Coulomb interaction. We also find that the spin-triplet is recovered by adjusting the level degeneracy with magnetic field. Received: 14 April 2000 / Accepted: 17 April 2000 / Published online: 6 September 2000     

Short distance propagators in a background field

We derive an operator expansion of the scalar, the spinor and the vector propagators in the presence of an arbitrary long range background field, using the Schwinger-DeWitt ‘proper time’ formalism. This has the advantage of keeping the expansion gauge covariant at all stages. These results may be used to calculate the leading background effects in the one-loop correlation functions.     

Indirect RKKY interaction in doped armchair nanotube due to electron phonon interaction effects

We study the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in doped armchair nanotube in the presence of gap parameter. The effects of both next nearest neighbor hopping parameter and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments have been analyzed. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain the transverse static spin susceptibility of armchair graphene nanoribbon in the presence of electron-phonon coupling and gap parameter. The spin susceptibility components are calculated using Green’s function approach for Holstein model Hamiltonian. The effects of electron doping on dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of next nearest neighbor hopping parameter on the spatial behavior of RKKY interactions are different in the presence of electron phonon coupling.     

Synergism in electron gas in crossed fields. II degenerate 3DEG—hall conductance

A microscopic many body correlation dynamics has been worked out for a 3DEG in degenerate state far removed from equilibrium, placed in crossed electric and magnetic fields of arbitrary strength. It is shown that linear electric field case gives only σ₁₂, even though the response function retains all the nonlinear effects in the system. The nonanalytic behaviour of the response function is explicitly shown. The quantisation of Hall current comes out as a direct consequence both for odd and even filling factors, and this is due to an exact evaluation of the dynamics in the self consistent field case. Radiated energy for this system is also calculated. A comparison of the present results with those obtained based on Kubo formalism has brought out the incompatability of using external fields as ordering parameters in any expansion scheme. A further new result is the nonanalytic property of the response function obtained in the present formulation.     

Nonexistence of Kirkwood's instability in a uniform fluid

Kirkwood's instability in the theory of fluid-solid transitions is proved to be impossible. Fluctuation of the one-particle distribution function in the first equation of the BGY hierarchy is investigated beyond Kunkin and Frisch's treatment. The second equation of the BGY hierarchy is utilized to eliminate the three-particle distribution function left in the Kunkin-Frisch result. The final expression for the first-order fluctuation of the one-particle distribution function under the presence of an external field is written in a form including only the pair correlation function and agrees identically with the one obtained from the direct expansion of the oneparticle distribution function in terms of the external field.     

Intensity Correlation of the Resonance Fluorescence Light in Quasi-monochromatic Chaotic Fields

The behaviour of the intensity correlation function of the resonance fluorescence light from a single atom is studied in the case of a quasi-monochromatic chaotic pump field of arbitrary mean intensity. In particular, it is found that the factorization of the intensity correlation function, which is impossible in the case of a narrow band chaotic pump field of low intensity, becomes a better approximation when the mean intensity of the pump field is enhanced.     

Field characterization of therapeutic ultrasound phased arrays through forward and backward planar projection

Spatial planar projection techniques propagate field measurements from a single plane in front of a transmitter to arbitrary new planes closer to or further away from the source. A linear wave vector frequency-domain projection algorithm is applied to the acoustic fields measured from several focused transducer arrays designed for ultrasound therapy. A polyvinylidene difluoride hydrophone is first scanned in a water tank over a plane using a three-dimensional positioning system to measure the complex pressure field as a function of position. The field is then projected to a series of new planes using the algorithm. Results of the projected fields are compared with direct measurements taken at corresponding distances. Excellent correlation is found between the projected and measured data. The method is shown to be accurate for use with phase-controlled field patterns, providing a rapid and accurate method for obtaining field information over a large spatial volume. This method can significantly simplify the characterization procedure required for phased-array application used for therapy. Most significantly, the wavefront propagated back to a phased array can be used to predict the field produced by different phase and amplitude settings of the array elements. A field back-projected to the source could be used as an improved source function in acoustic modeling.     

Spin-wave excitation by direct current in obliquely magnetized nanostructures

The magnetization dynamics of magnetic nanostructures magnetized at an arbitrary out-of-plane angle is investigated with the spin-wave formalism. The magnetic excitations driven by a spin-polarized direct current are considered to be standing spin-wave modes appropriate for nanopillar structures. The spin waves grow exponentially above a certain critical value of the current density and their post-threshold nonlinear dynamics leads to magnetization oscillations in the microwave range. Due to demagnetizing fields, the current-driven excitation strongly depends on the direction of the applied external magnetic field. In order to calculate the microwave oscillation frequency we derive an equation of motion for the spin-wave amplitude as a function of the out-of-plane angle of the applied field. The results are compared with recent experimental data as well as with another theoretical approach.     

On the properties of the Ising antiferromagnets in the maximum critical field

We demonstrate that all Ising antiferromagnets with general spin S and arbitrary many-neighbour interactions in the maximum critical field have highly degenerate ground states accompanied with nonzero residual entropies. For finite S, the residual entropies vanish when the range of interaction tends to infinity. The proof is realised by establishing bounds for residual entropies in the case of an Ising system situated on a lattice with arbitrary number of dimensions. In addition we estimate the ground-state entropies for a few two-dimensional lattices.     

Some static problems in a wave-guide of general cross-section

The electrostatic field created by electrically polarized matter of arbitrary shape placed in a direct wave-guide of general cross-section is derived by means of the electrostatic potential. Green's function method is used.     

Dead time correction of photon correlation functions

The dynamic range of single photon counting measurements in quasi elastic light scattering is restricted by detector and counter dead time effects. While distortions of single interval statistics have been treated at great length, only lowest order corrections or very special cases of dead time effects on temporal correlation functions were computed in the past.Dead times result in a direct distortion of correlograms on time scales comparable to the dead time. This effect exists even at low count-rates. It is independent of the count rate for paralyzable systems. Nonparalyzable systems show a count rate dependence with increasing correlation times at high count rates.Furthermore, counting saturation produces additional distortions extending to all lag times. These distortions are computed for the rather general case of -distributed intensities with arbitrary shape of the photon correlation function. Such signals are commonly found in multiparticle homodyne experiments with a finite size detector, i.e. arbitrary value of the intercept or contrast of the correlogram. Exact results are provided for the paralyzable system including the effect of fluctuating dead times. The latter case is then used to compute a useful approximation for nonparalyzable systems as well.