Narrow Results

This paper is concerned with the discrete spectrum of the self-adjoint realization of the semi-classical Schrödinger operator with constant magnetic field and associated with the de Gennes (Fourier/Robin) boundary condition. We derive an asymptotic expansion of the number of eigenvalues below the essential spectrum (Weyl-type asymptotics). The methods of proof rely on results concerning the asymptotic behavior of the first eigenvalue obtained in a previous work [10].

We have derived an expression for the physical mass and width of the ρ-meson in vacuum from its spectral function, calculated in the vector meson dominance model when a ρ⁰ meson couples to two virtual pions π⁺–π^-. The propagator is computed after evaluating the ρ-meson self-energy. The real part of the ρ-meson self-energy is given by a divergent integral and needs to be regularized; the regularization is done by using a double subtracted dispersion relation. The result leads to a closed analytical expression which allow us to evaluate the spectral function in a closed way. The physical mass, defined as the magnitude of the four-momentum |k| for which the spectral function S(k²) attains its maximum value, is obtained, and it gives a value of 770 MeV, which is in total agreement with the reported experimental value of the ρ-meson mass.

We show how to compute the spectral function for a scalar theory in two different scenarios: one which disregards backreaction, i.e. the response of the environment to the external particle, and the other one where backreaction is considered. The calculation was performed using the Kadanoff–Baym equation through the Keldysh formalism. When backreaction is neglected, the spectral function is equal to the equilibrium one, which can be represented as a Breit–Wigner distribution. When backreaction is introduced we observed a damping in the spectral function of the thermal bath. Such behavior modifies the damping rate for particles created within the bath.

The temperature behavior of the pion width in the hadronic phase is investigated in the framework of the Nambu–Jona–Lasinio (NJL) model. The contribution to the width from the pion–pion collision is considered with a scalar sigma-meson as an intermediate state. It is shown that the pion width significantly broadens at $T>0.1$GeV. Using the two-step iteration method, suggested by Kadanoff and Baym, the pion spectral function in a hot pion gas is calculated at different temperatures.

Recent angle-resolved photoemission (ARPES) studies of the La_2-xSr_xCuO₄ (LSCO) compound provide a new piece of information on the evolution of the electronic structure in cuprate systems with doping. Our aim is to analyze that evolution by means of the spin polaron approach based on the string picture. We study the motion of a single mobile hole in the stripe phase of a doped antiferromagnet. Holes within the stripes are taken to be static, undoped antiferromagnetic domains between hole stripes are assumed to have an alternating staggered magnetization, as it has been suggested by neutron scattering experiments. The system is described by the t-t′-t′′-J model with realistic parameters and we compute the single particle spectral density. In this paper we concentrate on the filling level 1/12. Theoretical spectra and results of measurements performed at that hole concentration show reasonable agreement. In both cases we observe, along the direction (0,0)→(π,0), "splitting" of the spectrum and formation of new low energy states around (π,0). This splitting is also observed in the direction (0,π)→ (π,π). The spectra along the direction (π,0)→ (π,π) are much broader. That hinders us in assignment of any band for some range of k points in that direction. Finally, the spectra along the direction (0,0)→ (π,π) are very broad and it is also practically impossible to distinguish any sharp band.

In this contribution, the peak position of the spectral function in the ARPES spectrum has been calculated for several gap symmetries and electronic band structures. As a result, the d–wave, s + id and s* + id symmetries appear to be consistent with ARPES results. An additional comparison with previous calculations of the specific heat in normal and superconducting states as well as the single particle tunnelling current, reveals the existence of two characteristic temperatures, intrinsically associated with the Van Hove Singularity.

This work investigates a d-p Hubbard model by the n-pole approximation in the hole-doped regime. In particular, the spectral function A(ω, k) is analyzed varying the filling, the local Coulomb interaction and the d-p hybridization. It should be remarked that the original n-pole approximation (Phys. Rev.184, 451 1969) has been improved in order to include adequately the k-dependence of the important correlation function 〈S_j·S_i〉 present in the poles of the Green's functions. It has been verified that the topology of the Fermi surface (defined by A(ω = 0, k)) is deeply affected by the doping, the strength of the Coulomb interaction and also by the hybridization. Particularly, in the underdoped regime, the spectral function A(ω = 0, k) presents very low intensity close to the antinodal points (0, ±π) and (±π, 0). Such a behavior produces an anomalous Fermi surface (pockets) with pseudogaps in the region of the antinodal points. On the other hand, if the d-p hybridization is enhanced sufficiently, such pseudogaps vanish. It is precisely the correlation function 〈S_j·S_i〉, present in the poles of the Green's functions, plays an important role in the underdoped situation. In fact, antiferromagnetic correlations coming from 〈S_j·S_i〉 strongly modify the quasiparticle band structure. This is the ultimate source of anomalies in the Fermi surface in the present approach.

In this paper, taking into account the effect of the induced interaction, we calculate the spectral function and hence density of states (DOS) of ultracold Fermi gases within the framework of non-self-consistent T-matrix approximation (nTMA) in the normal phase. The corresponding equations are calculated on the real-frequency axis directly with high accuracy. Our result shows that pseudogap phenomenon still exists in the spectral function and DOS.

Momentum density studies are the key tool in Fermiology in which electronic structure calculations have proven to be the integral underlying methodology. Agreements between experimental techniques such as Compton scattering experiments and conventional density functional calculations for late transition metal oxides (TMOs) prove elusive. In this work, we report improved momentum densities of late TMOs using the GW approximation (GWA) which appears to smear the momentum density creating occupancy above the Fermi break. The smearing is found to be largest for NiO and we will show that it is due to more spectra surrounding the NiO Fermi energy compared to the spectra around the Fermi energies of FeO and CoO. This highlights the importance of the positioning of the Fermi energy and the role played by the self-energy term to broaden the spectra and we elaborate on this point by comparing the GWA momentum densities to their LDA counterparts and conclude that the larger difference at the intermediate level shows that the self-energy has its largest effect in this region. We finally analyzed the quasiparticle renormalization factor and conclude that an increase of electrons in the $d$-orbital from FeO to NiO plays a vital role in changing the magnitude of electron correlation via the self-energy.

The influence of hole–hole propagation in addition to the conventional particle–particle propagation on the energy per nucleon and the momentum distribution is investigated. The results are compared to the Brueckner–Hartree–Fock (BHF) calculations with a continuous choice and a conventional choice for the single-particle spectrum. Also, the structure of nucleon self-energy in nuclear matter is evaluated. All the off-shell self-energies are calculated self-consistently. Using the self-consistent self-energy, the hole and particle self-consistent spectral functions including the particle–particle and hole–hole ladder contributions in nuclear matter are calculated using realistic NN interactions. We found that the hole–hole ladder brought about non-negligible contributions to the nuclear matter binding energy per nucleon.

The ambiguities proposed by Benhar et al., about the the different implementation of the impulse approximation for calculating the response function of many-fermion systems, are investigated theoretically in the frame work of simple harmonic oscillator shell model for the double closed shell nuclei, e.g. ⁴He, ¹⁶O and ⁴⁰Ca nuclei. For each nucleus as a finite system, we evaluate the response function by using its definition in terms of the one-body spectral function and the one-body momentum distribution. It is demonstrated analytically, that there exists a sizable shift between the two schemes for each nucleus, which increases as we switch to the heavier nuclei. So one can conclude that for the nuclei with atomic number less than 4, such as ²H, ³H or ³He, it is good approximation to ignore this discrepancy. This conclusion is important for theoretical explanation of the ongoing deep inelastic scattering (DIS) experiments of ³H or ³H in the Jefferson Laboratory. However present calculation confirms the work of Modarres and Younesizadeh (2010), in which they have shown that, the above shift can be removed by imposing the impulse approximation in the same footing in the many-fermion wave-function.

The ρ-meson spectral function in hot nuclear matter is studied by taking into account the pion and the nucleon loops within the quantum hadrodynamics (QHD) model as well as using an effective chiral SU(3) model. The effects of density and temperature on the spectral function of the ρ-meson are studied assuming the ρ-meson to be with a finite momentum. These investigations are performed using both the mean field approximation (MFA) and the relativistic Hartree (RHA) approximation. The inclusion of the nucleon loop is observed to considerably change the ρ-meson spectral function. Due to a larger mass drop of ρ-meson in the RHA, it is seen that the spectral function shifts towards the low invariant mass region, whereas in the MFA the spectral function is seen to be almost centered around the nominal ρ-pole, but develops a second peak due to the opening of the Nh-channel. Within both the Walecka and the chiral SU(3) models, it is observed that the ρ-meson spectral function has a strong dependence on the nucleon-ρ meson tensor coupling.

In this work, the response functions (RFs) of the ⁴He, ¹⁶O and ⁴⁰Ca nuclei are calculated in the harmonic oscillator shell model (HOSM) and the impulse approximation (IA). First, the one-body momentum distribution and the one-body spectral functions for these nuclei are written in the HOSM configuration. Then, their RFs are calculated, in the two frameworks, namely the spectral and the momentum distribution functions, within the IA. Unlike our previous work, no further assumption is made to reduce the analytical complications. For each nucleus, it is shown that the (RF) evaluated using the corresponding spectral function has a sizable shift, with respect to the one calculated in terms of the momentum distribution function. It is concluded that for the heavier nuclei, this shift increases and reaches nearly to a constant value (approximately 62 MeV), i.e., similar to that of nuclear matter. It is discussed that in the nuclei with the few nucleons, the above shift can approximately be ignored. This result reduces the theoretical complication for the explanation of the ongoing deep inelastic scattering (DIS) experiments of ³H or ³H nucleus target in the Jefferson Laboratory. On the other hand, it is observed that in the heavier nuclei, the RF heights (width) decrease (increase), i.e., the comparison between the theoretical and the experimental electron nucleus scattering cross-section is more sensible for heavy nuclei rather than the light ones.