Complex-energy States Research Articles

Band dispersion, scattering rate, and carrier mobility using the poles of Green’s function for dilute nitride alloys

The band-anticrossing (BAC) model provides the basis for the self-consistent Green’s function method that we have previously developed to calculate the density of states of GaNxAs1−x dilute nitride alloys. In this paper, we extend this Green’s function method to include the complex energy states and to find the poles of the Green’s function, thereby allowing one to calculate the dispersion relation, group velocity, and the carrier decay rate in disordered dilute nitride alloys. Two different models of the N states have been studied to investigate the band structure of these materials: (1) the conventional two-band BAC model, which assumes that all N states are located at the same energy, and (2) a model which includes N states distributed over a range of energies, as expected in actual dilute nitride samples. Our results for the second model show a much shorter carrier mean-free path, and lower carrier mobility for GaNxAs1−x, with the magnitude of the calculated mobility in good agreement with the experimental data.

The Definition of Entropy for Quantum Unstable Systems: A View-Point Based on the Properties of Gamow States.

In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy states. After introducing a generalized basis of states which includes resonances, and working with amplitudes instead of probabilities, we found an expression for the entropy which exhibits real and imaginary components. We discuss the meaning of the imaginary part of the entropy on the basis of the similarities existing between thermal and time evolutions.

Richardson’s Solutions in the Real– and Complex–Energy Spectrum

The constant pairing Hamiltonian holds exact solutions worked out by Richardson in the early Sixties. This exact solution of the pairing Hamiltonian regained interest at the end of the Nineties. The discrete complex-energy states had been included in the Richardson’s solutions in [1]. In this contribution we reformulate the problem of determining the exact eigen-energies of the pairing Hamiltonian when the continuum is included through the single particle level density. The solutions with discrete complex-energy states is recovered by analytic continuation of the equations to the complex energy plane. This formulation may be applied to loosely bound system where the correlations with the continuum-spectrum of energy is really important. Some details are given to show how the many-body eigen-energy emerges as sum of the pair-energies.

Two-color photoionization of helium above theN=2ionization threshold

We study two-color photoionization of helium in the region of the 3s3d D-1 autoionizing state with resonant excitation of the intermediate 2s2p P-1 autoionizing state. We show that the corresponding time-dependent Schrodinger equation may be solved by expanding the total wave function on a few complex energy states. Perimetric coordinates are used to describe correlation effects accurately. Populations at the end of the interaction as well as photoionization probabilities are studied as a function of the laser pulse duration acid both frequencies. Our calculations show that many continua play a crucial role at high intensities. [S1050-2947(99)06308-8].

Complex dynamics variables for molecules and molecular clusters

We describe a method to analyse dynamic properties of molecules and molecular clusters. The model involves the change in lifetimes of collective, quasi-stationary excited states of the system under consideration by low energy electron local excitations. Probabilities of desorption-ionisation processes and cluster decomposition are also estimated. The model is based on the quantum multi-particle theory and the exciton or excimol theory for condensed matter and molecules. The energies of excitation have complex values which permit us to take into account the unharmonic character of bond vibrations and the relaxation process. We apply a perturbation theory for excitation analysis describing the possible deviation of molecules or molecular clusters from regular structures. The wave-functions can be taken in their asymptotic form and the dilatation method is used for the complex energy states.

R-matrix methods for studying nuclear effects in ?CF

Properties ofR-matrix theory that are useful for studying muon-catalyzed fusion reactions are reviewed, and applications to the dtμ system are discussed, using both “improved adiabatic” and non-adiabatic (variational) wave functions. We give complex eigenvalues and α-μ sticking fractions for the (L, v)=(0,0) and (0, 1) states of dtμ using variational Hamiltonian matrix elements that have been properly symmetrized by means of the Block operator. Expressions for the fusion rate and α-μ sticking fraction are developed from a time-dependent theory that uses the complex-energy states corresponding to the poles of the systemS-matrix. These are shown to reduce with the appropriate approximations to the expressions and values commonly used. Additional nuclear effects on these quantities can easily be studied within the framework developed, but they are not expected to be large.

Androgen Receptor Defects in Patients with Minimal and Partial Androgen Resistance Classified According to a Model of Androgen-Receptor Complex Energy States

We have characterized intracellularly the androgen-receptor (A-R) complexes formed by genital skin fibroblasts from 2 unrelated males with qualitative defects of the androgen receptor: one has a small nonhypospadic penis as part of a syndrome of mild androgen resistance; the other was born with ambiguous external genitalia. The dissociation rate constants of testosterone, methyltrienolone (MT), dihydrotestosterone (DHT) and mibolerone (MB) from normal androgen receptors were determined at various temperatures: when plotted by the method of Arrhenius, they yielded a linear hierarchy of dissociation states with energies of state IV greater than III greater than II greater than I, respectively. Relative to this hierarchy, patient A-R complexes were displaced to higher, androgen-inappropriate energies in a mutant-distinctive pattern. MB- or MT-R complexes of both patients were thermolabile; however, both up-regulated normally in response to prolonged incubation with either hormone. Apparent equilibrium affinity constants (Kd) of the DHT- and MB-R complexes formed by both patients were normal; however, the binding capacity (Bmax) for MB in 1 case was subnormal. The distinctive biochemical phenotypes of A-R complexes in these 2 patients with androgen resistance will facilitate the definition of structure-function relations in the androgen receptor, a classical DNA-binding, transcription-regulating protein.

Field ionization of Rydberg atoms: A semiclassical treatment of complex energy states in intense electric fields

The semiclassical treatment of energy levels and lifetimes of hydrogenic atoms in a homogeneous electric field is discussed. Particular attention is payed to the critical regime of intense fields or high quantum number (Rydberg) states of the atom, where the ionization is fast. An extension of the real-energy resonant-state treatment to a complex-valued (Siegert-type) semiclassical approximation is derived, which is both conceptually and computationally convenient.

On the virial of quasi-stationary molecular systems

For quasi-stationary complex-energy states, the fundamental quantum mechanical relationships are formulated: complex form of Heisenberg's equation of motion, hypervirial theorem, and Hellmann-Feynman theorems. Particular attention is focused on molecular dynamics of complex-energy states; at the equilibrium geometry on the Born-Oppenheimer adiabatic potential energy surface, it is found that the complex virial theorem is consonant with the theorem for the entire molecular system. Furthermore, the complex-coordinate method is developed particularly for the application to the molecular dynamics of complex-energy states. An example of the problem of molecular dynamics on complex potential energy surfaces is also given: 2σ u + transient H2 - ion formed as an intermediate species in a dissociative attachment reaction.

Complex energy eigenstates in quantum decay models

Properties of complex energy solutions to the Schrodinger equation are studied in a spectral representation of the type used in the Lee-Friedrichs model of unstable states. The construction of a complete, orthonormal set of complex energy states is first discussed for a general Hamiltonian and then illustrated in detail for a new solvable model. This model determines normalizable eigenvectors corresponding to resonant solutions to the eigenvalue equation for a simple potential scattering problem.