International Journal of Modern Physics B

The experimental and theoretical investigation of the lifetime of excited electrons is of great importance for a variety of different fields in condensed matter physics. In this review two distinct classes of processes are discussed, which determine the lifetime of excited electrons in crystalline systems. One class is single-particle processes, which in many cases is able to describe the decay of excited electrons. For systems with weakly correlated electrons the state-of-the-art method is the solution of the Dyson equation using the GW approximation for the electronic self-energy. If applicable this approach leads to very good results. However, many of the experimental studies about the lifetime of excited electrons have been done using time-resolved two-photon photoemission spectroscopy utilizing ultrashort laser pulses. This technique, applied to materials with localized d electrons, can lead to the creation of bound, excitonic-like states in metals on a very short time scale, which are beyond the physics described in the single-particle approach. In this review the experimental evidence for both mechanisms is given and the theoretical tools to describe them are discussed. Furthermore, theoretical results are presented and compared to experimentally available data.

Model of superconductivity in the metallic phase of strongly correlated electrons in a half-filled narrow band forming a paramagnetic spin liquid is presented. A qualitatively new ground state and other eigenstates for the superconducting phase are found. Thermodynamic functions are derived within the Bogolubov method. Analytical formulae for the free energy as well as the gap equation and the equation for the chemical potential are presented. It is shown that the energy gap and the chemical potential are mutually correlated functions which must be simultaneously derived in a self-consistent manner. The gap equation and the equation for the chemical potential are numerically solved. The energy gap is doubly-valued in the subcritical temperature region, however only for the higher values of the gap the superconducting phase is stable. The phase transition between the superconducting and the normal phase is found to be of the first order with a conspicuous discontinuity in the entropy. Moreover it is shown that the derivation of the superconducting specific heat from the thermodynamic potential difference requires to include a chemical potential contribution.

We proposed Atomic Schwinger–Dyson method (ASD method) in previous paper, which was a nonperturbative and relativistic quantum field theory for a finite baryon density. We think it is important to show the significance of renormarization in order to get real physical predictions. Moreover, the real value of physical mass, electric charge and wave function are completely different from those of the non-renormalized electron and photon in mean field theory, since there are many of the particle-antiparticle creations and annihilations, particle-hole excitation, and Pauli blocking, which give an effect on bare mass, electric charge, polarization of vacuum, and self-energy. In this paper, we shows that ASD method is renormalizable theory, and that photon condensation of ASD method gave rise to Coulomb's potential and the mass shift of electron. The interacting photon and electron fields, which have physical mass and electric charge, are expressed as generalized free field equations by using the mass shift and the self-energy of those particles. We obtain the expression of an exact solution of these particles on the basis of the Green functional method.

Metal–Insulator transition using exact quasi dielectric functions is investigated for a shallow donor in an isolated well of GaAs/Ga_1-xAl_sAs superlattice system within the effective mass approximation. Vanishing of the donor ionization energy as a function of well width and the donor concentration suggests that no transition is possible below a well width of 50 Å supporting the scaling theory of localization. The effects of Anderson localization, exchange and correlation in the Hubbard model are included in a simple way. The relationship between the present model and the Mott criterion in terms of Hubbard model is also brought out. The critical concentration is enhanced when a random distribution of impurities is considered. Results are compared with the existing data available and discussed in the light of existing literature.

Based on the observation that for an entangled-particles system, the physical meaning of the Wigner distribution function should lie in that its marginal distributions would give the probability of finding the particles in an entangled way, we establish a tomography theory for the Wigner function of tripartite entangled systems. The newly constructed tripartite entangled state representation of the three-mode Wigner operator plays a central role in realizing this goal.

The shortcomings and advantages of the generalized self-consistent field (GSCF) approach, which includes the electron–hole order parameter and the average spin s within the one-dimensional repulsive Hubbard model, are analyzed by comparison of the ground state properties with the corresponding Bethe ansatz results in an entire parameter space of interaction strength U/t ≥ 0, magnetic field h ≥ 0 and electron concentration 0 ≤ n ≤ 1. The GSCF spectral characteristics are derived and criteria are found for the stability of incommensurate magnetic phase with the wave number 0 < q < π. The GSCF theory displays a simple relationship for the double occupancy D⁽⁺⁾ in terms of n, s and , where D⁽⁺⁾ underestimates electron correlations at weak and intermediate ranges and overestimates correlations at large interaction strengths. Beyond some critical U/t and n≠1 the GSCF D⁽⁺⁾ for spatially homogeneous state vanishes, while the exact D for all n at h=0 decreases gradually as U/t increases. At n ≠ 1 the GSCF chemical potential μ⁽⁺⁾ overestimates electron correlations everywhere and variation μ⁽⁺⁾versusn displays electron instability toward the phase separation in the vicinity of n=1. Exactly at n=1 the GSCF μ⁽⁺⁾versusU/t always underestimates electron correlation and as U/t → ∞ at h=0 we have μ⁽⁺⁾ → 0, while the Bethe ansatz result gives μ → 2t. In the limiting cases U/t → 0 and U/t → ∞ for all h ≥ 0 and 0 ≤ n ≤ 1 the GSCF ground state energy is exact, which is necessary for formulation of converging perturbation procedure about mean field solution in the entire parameter space.

The effect of the hopping term in the formation of excitons is studied in semiconductor nanostructures where electrons and holes are spatially separated by a potential barrier. We use the lattice gas model where electron–hole system is divided into unit cells with the effective lattice constant being of the order of the exciton size. The exciton density is calculated as a function of the disorder for several fixed values of the hopping integral. It is found that as the value of the hopping integral increases the exciton density decreases rapidly both for weak and strong disorder. Electronic correlation is treated explicitly by introducing repulsion between equally charged carriers and attraction between an electron and a hole from neighboring cells.

We consider one-dimensional models of classical statistical physics and prove that at each fixed value of the temperature for all realizations of additional sufficiently strong random external field the limiting Gibbs state is unique.

We study the dynamics and quantum characteristics of a single two-level atom interacting with a single mode cavity field undergoing a multi-photon processes in the presence of a nonlinear Kerr-like medium. The wavefunctions of the multi-photon system are obtained when the atom starts in the excited and in the ground state. The atomic inversion, the squeezing of the radiation field and the quasiprobability distribution Q-function of the field are discussed. Numerical results for these characteristics are presented when the atom starts in the excited state and the field mode in a coherent state. The influence of the presence and absence of the number operator and the Kerr medium for the one- and two-photon processes on the evolution of these characteristics are analyzed.

The temperature dependent binding energy of some low lying excited states for a compositional Quantum Well have been calculated for various impurity locations by extending the investigation of Elabsy.⁴ It has been observed that the temperature plays an important role in the binding energy of low lying excited states also.