Petros N. Argyres's research while affiliated with Northeastern University and other places

Publications (42)

Article
The recently introduced projection technique in the theory of alloys is used to develop in a simple way the cluster expansions of the self-energy for an arbitrary reference medium. Three choices of the reference medium, self-consistent and non-self-consistent, are considered and pair site approximations (PSA) are developed. It is shown that the 'op...
Article
In connection with the controversial question about the interband matrix elements of a stair-function potential in a crystal, the authors show analytically that they are non-vanishing, in general, for an arbitrary band model for both an infinite and a finite crystal. This is in accord with numerical studies of specialised models, but in contradicti...
Article
A general theory is presented for the interband tunnelling probability of electrons in a crystal in the presence of phonons and a strong electric field, for both the phonon-assisted and the phonon-modified-Zener tunnelling. For the case of tunnelling from a fully occupied band the dependence of the tunnelling rate on the electric field is shown in...
Article
A general theory is presented for the one-electron density operator for electrons in strong and time-dependent electric fields in the presence of phonons, with full account of electron exchange. A quantum kinetic equation for the distribution function of electrons in one band is derived and discussed. Other applications are indicated.
Article
A general theory is presented for the intraband and interband processes of electrons in a crystal with static impurities in a strong electric field. The interband tunneling processes, both the impurity-assisted and the Zener tunneling (and its modification by the impurities), are examined in detail. For the case of tunneling from a fully occupied b...
Article
It is proven, contrary to a recently published claim, that the eigenvalues and eigenstates of an electron in a finite, 1-D, periodic potential and a constant electric field are given by a secular equation that does couple band indices. Implications for Wannier-Stark ladders are pointed out.
Article
It is shown that in the case of an infinite crystal the model of a Bloch electron in a rational step-like electric potential is not equivalent to a one-band approximation, in contradiction to reports in the literature. Instead, such a potential has effects similar to those of a uniform electric field, which it approaches as the steps become smaller...
Article
The recently proposed memory-function method for the calculation of transport coefficients is discussed and criticised in the context of a simple model. In the study of the frequency-dependent conductivity sigma ( omega ) of this model it is shown that this method yields a simple result for sigma (0) that is, however, different from the standard re...
Article
The recently proposed force-balance theory of resistivity is examined critically in the context of a simple model. It is shown that this theory's basic formula, when evaluated correctly, yields in general a vanishing resistivity. This renders this theory untenable.
Article
A theory of the coherent-potential and average t-matrix approximations for the low-temperature transport properties of alloys is given on the basis of a general Bethe-Salpeter equation derived by algebraic techniques with the use of a projection operator. Both approximations are studied, discussed, and applied to the standard one-band model of rand...
Article
An expression for the cyclotron-resonance power absorption by electrons interacting with phonons is derived with the help of a projection operator that takes into account the effects of exchange. It is shown that the correct evaluation of this expression requires the summation of an infinite number of terms in order to describe the effects of scatt...
Article
A recent claim by Choi, Yi and Chung that the Argyres-Sigel theory of cyclotron resonance line shape is invalid is proved to be wrong.
Article
A recent claim by Choi and Chung that the Argyres-Sigel theory of cyclotron resonance line shape is invalid is shown to be erroneous.
Article
The principal methods of formulating the single site approximations (both average t matrix and coherent potential approximations) for the equilibrium properties of disordered alloys are discussed. It is shown that the recent method based on the use of a projection operator can be used to derive the other formulations simply and more generally.
Article
A formulation of the average t-matrix approximation (ATA) for the electrical conductivity of a disordered binary alloy is presented on the basis of the method of kinetic equations, with the help of a projection operator to denote the configuration average. It is shown that this ATA preserves all qualitative properties of the exact average density o...
Article
We introduce a projection operator to denote the configuration average for an arbitrarily disordered system. This allows us to derive a formal, exact expression for the self-energy of the average propagator in terms of the disordered part of the Hamiltonian of the system. We use this expression to give a new formulation of the single-site approxima...
Article
Introducing the configuration averaging as a projection operator, we propose a new formulation of the average t-matrix and the coherent potential approximations that treats on equal footing both the equilibrium and the residual transport properties of disordered alloys.
Article
An approximation for systems of interacting fermions which goes beyond the standard thermal Hartree-Fock approximation (THFA) is developed on the basis of the variational principle of statistical mechanics. The new approximation consists of choosing the “best” trial Hamiltonian such that all its eigenstates are single determinants whose occupied st...
Article
We recently showed that under certain reasonable assumptions, localized atomiclike solutions to the Hartree-Fock equations for a crystal do not exist even for very widely separated atoms, in contradiction to a long-standing argument to the contrary due to Seitz. Brandow has claimed that our proof is logically unsound. We refute this claim, showing...
Article
It is argued that the measurement of absorption of electromagnetic radiation at optical frequencies induced by an electric field at a different frequency provides a valid and convenient way to obtain an absolute measure of the Raman scattering tensor of optical phonons in solids. Supported by the AFCRL Contract No. F19628-73-C-0132.
Article
An expression for the cyclotron-resonance power absorption is derived with the help of a projection operator. It is shown that the correct evaluation of this formula requires the summation of an infinite number of terms in order to describe the effects of the scattering interaction to second order. These results are in contradiction with those obta...
Article
A discussion is given of the details of our work, the results of which have recently been presented, in connection with the role of projection techniques in the theory of electrical resistivity. It is shown that, contrary to earlier claims, the correct evaluation of the resistivity to the lowest order in the strength of the scattering on the basis...
Article
Full-text available
It is shown that a large class of approximations in statistical thermodynamics that are based on the free-energy variational principle for the density operator yield expressions for the macroscopic quantities of the system that are consistent from both the statistical-mechanical and thermodynamical points of view. This corrects some erroneous state...
Article
A formula for the electrical resistivity expressed in terms of a projection operator is derived and discussed. It is argued that the correct evaluation of the resistivity to the lowest order in the strength of the scattering interaction on the basis of this formula requires, as do other formal expressions, the summation of an infinite number of ter...
Article
We calculate the magnetic field dependence of the cyclotron-resonance linewidth of a semiconductor in the quantum limit due to charged impurities, taking into account the anisotropic screening of the impurities due to the magnetic field. We find that the resonance line broadens and reaches a saturation value as the magnetic field increases.
Article
We have derived expressions for the cyclotron-resonance line-shape parameters by means of a new formalism. The formalism is based on a "damping iteration" for the exact expression of the conductivity tensor in the presence of static impurities. We have applied this theory to the case of a nondegenerate semiconductor in the quantum limit and have ob...
Article
We develop an algebraic technique for the evaluation of the coefficients of a general transport equation for dynamically independent electrons in the presence of random impurities. This method readily yields, for arbitrarily strong single center potentials, these coefficients in powers of the density of the impurities. There is no restriction, in t...
Article
We show that an electron-impurity interaction with a screening radius longer than the cyclotron radius gives rise to a cyclotron-resonance linewidth for a nondegenerate semiconductor in the quantum limit, which increases and approaches a constant value with increasing magnetic field. This is in contradiction to earlier theoretical work of Kawamura...
Article
A new extension of Hartree-Fock (HF) theory to nonzero temperature T, namely, the thermal single-determinant approximation (TSDA)—based on the variational principle of statistical mechanics—is applied to a model of a crystal of widely separated atoms. It is shown that, in this TSDA, one type of solution to the equations of stationarity of the free...
Article
An application of a diagrammatic technique, given by us recently, is made for the calculation of the coefficients of a transport equation for dynamically independent electrons in random impurities. The coefficients of the transport equation are given for arbitrary wavelength and frequency of the electric field (transverse or longitudinal) and stron...
Article
The transport properties of an interacting fermion gas in the presence of randomly distributed scattering centers and a weak longitudinal force field are studied on the basis of a transport equation for the bare-particle distribution function. This equation, valid for arbitrary wavelength, frequency, and temperature, is derived by a generalization...
Article
The problem of the linear response of a collection of dynamically independent electrons interacting with a random set of scattering centers to an arbitrary electromagnetic field is considered on the basis of quantum kinetic equations. First a projection technique is used to derive a general kinetic equation for that part of the density matrix that...
Chapter
This chapter discusses the magnetic levels and obtains the density of states for simple and complex bands, including the effect of level broadening. This will be applied to the de Haas–van Alphen effect, and results are given for the steady magnetic susceptibility, which is actually a quantum effect because classically the steady susceptibility van...
Article
A quantum-statistical-mechanical theory of spin resonance and relaxation is presented, which avoids the assumptions of earlier theories, is capable of extension to other than the lowest Born approximation for the strength of the relaxation mechanism, and is applicable over a broader range of physical situations. From the Liouville equation for the...
Article
A method is presented which yields a kinetic equation for the time ; development of the one-electron density matrix for dynamically independent ; electrons in phonon and other arbitrary static fields of force under the ; influence of a weak but otherwise general external dynamical disturbance. The ; exclusion principle, the finiteness of the phonon...
Article
A theory of interband tunneling due to a constant electric field is presented which is free of certain objections to previous theories. It is shown that the expression for the Zener current has new terms oscillatory in the electric field, which reflect the Stark quantization of the longitudinal motion of the electron. It is pointed out that for suf...
Article
A quantum-mechanical derivation of the Boltzmann transport equation for inelastic collisions is given along the lines Kohn and Luttinger have developed for elastic collisions. It is shown that for Fermi-Dirac particles the scattering in the collision term of the transport equation is restricted to unoccupied states only, in contradistinction to the...
Article
A quantum-mechanical theory of transport of charge for an electron gas in a magnetic field is presented that takes account of the quantization of the electron orbits. A transport equation for the necessary elements of the density matrix is developed for arbitrary values of the magnetic field. The scattering is taken to be elastic and is treated...
Article
It is pointed out that previous quantum-mechanical theories of transport in high magnetic fields are deficient in that they neglect the effect of the electric field on scattering. It is demonstrated here that in the case of large Hall angles, i.e. ω0τ > 1, the transverse current can be obtained by a direct expansion in powers of the scattering pote...
Article
In magnetic fields so large that all conduction electrons are in the lowest oscillator state, the time between collisions is a strong function of the magnetic field and the scattering mechanism. The galvanomagnetic effects, through their magnetic field dependences in this region provide. therefore, a sensitive tool for the study of the various scat...
Article
An extension of previous work on the effect of quantization of electron orbits in a magnetic field on the lattice relaxation time to include scattering among different oscillator states has been made. It is found that the relaxation time is inversely proportional to the density of states in the presence of the magnetic field. The current for a long...
Article
A study is made of the effect of the quantization of the electron orbits in a magnetic field on the galvanomagnetic properties of an isotropic semiconductor or semimetal in the phonon-scattering range. The conductivity tensor is calculated using the quantum-mechanical density operator. A generalized Boltzmann equation is derived, in which the scatt...

Citations

... Panel (d) plots the T dependences of the 4 SdH extrema shown in (c). Fits to the Lifshitz Kosevich expression [27] (solid curves) yield mcyc = 0.23m0 m * of the bands in B = 0. -1 0 -5 0 5 1 0 0 4 8 1 2 16 -1 0 -5 0 5 1 0 0 5 1 0 0 5 0 1 0 0 1 5 0 20 0 -1 0 -5 0 5 1 0 -1 0 -5 0 5 1 0 0 ...
... Therefore, the observed MIT should closely correlate with the changes in the electron states from classical to the quantum limit. Among dozens of theoretical proposals emphasizing differ- ent aspects [1][2][3][4][5][25][26][27][28], the A-H theory [1] considered var- ious scattering mechanisms including acoustical and optical phonons, point defect, and ionized impurity, being convenient for comparing with the experimental observations. There- fore, next, our results are evaluated based on the A-H theory. ...
... The weights in such interpretation are the occupation numbers of each of those states. The description of such a system resembles the methods of describing electronic structure in finite temperature: the thermal Hartree-Fock [17], thermal single-determinant approximation [18], and finitetemperature DFT [19][20][21] that make use of the variational principle for the Helmholtz free energy known in statistical mechanics. ...
... with j denoting the current operator and H the Hamiltonian. In early work such as [20] some objections were voiced against the MFM, on the grounds that it does not reproduce some standard results for the conductivity. However, according to more recent work such as [21], the MFM is described as a "tool of choice" for the calculation of the conductivity. ...
... The other proposal proceeds by expressing the response function in terms of a self-energy. It is based on the projection technique introduced by Mori [4] and Zwanzig [11] and the memory function formalism [12][13][14]. In the following, we will call it standard formulation of the optical conductivity (SFOC). ...
... Let us also remark that the effective dynamical map commutes with free evolution which is analogous to the dynamical maps for reduced dynamics in the weak coupling limit. [8,9] Usually time-local master equations beyond the weak coupling limit derived by time-convolutionless perturbation theory [11,12] with the Argyres-Kelley projection superoperator [10] and they lack such a commutativity property. But our averaging projector preserves this commutativity property in all the orders of time-convolution perturbation theory. ...
... it follows, that [Ĥ e ,ρ e ] = 0. If, additionally, [Ĥ e ,N] = 0, which is usually the case in non-relativistic quantum mechanics, we may simultaneously diagonalize each of the operators appearing in (6). Parenthetically, the maximization procedure is most conveniently carried out in the basis, in whichρ e is diagonal, i.e.ρ e = D i p i |i i|. ...
... when the conduction electrons are scattered by phonons of the spectrum ω q . In [30] the Boltzmann equation and the above expression were derived from basic principles of the statistical mechanics. Besides the energy conservation laws expressed by the arguments of the δ functions, the phonon spectrum enters the distribution function N q = [exp( ω q /k B T ) − 1] −1 . ...
... is the time-dependent bandgap. Following (Argyres, 1962;Kane, 1959), we have simplified our notation by introducing the modified band energies ...