An analytic approach to tunnelling magnetoresistance

We present an analytic model for the barrier transmission coefficient that can be used to calculate the tunnelling magnetoresistance (TMR) for metal-insulator-metal systems. It removes the approximations inherent in the Simmons’ and Brinkman models currently used to fit experimental systems that give much lower predictions of the barrier height than would be expected. The model is accurate enough to directly relate to the experiment and hence device optimisation by predicting junction parameters that are in line with bulk properties.     

Semiclassical approach to the three-body muon-transfer collisions

Muon-transfer rates in collisions of hydrogen-like atoms or with light nuclei t, ³He, ⁴He, ⁶Li or ⁷Li, are calculated in a semiclassical approximation to the Faddeev-Hahn equations. The two nuclei involved are treated classically, while the motion of the muon in their Coulomb field is considered from the quantum mechanical point of view. The experimentally observed strong dependence on the charge of the nuclei is reproduced. Received: 1st November 1997 / Revised: 26 March 1998 / Accepted: 18 August 1998     

Semiclassical field theory approach to quantum chaos

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the form of a functional supermatrix non-linear σ-model where the effective action involves the evolution operator of the classical dynamics. Low-lying degrees of freedom of the field theory are shown to reflect the irreversible classical dynamics describing relaxation of phase space distributions. The validity of this approach is investigated over a wide range of energy scales. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach accounts correctly for the short-time limit yielding results which agree with the diagonal approximation of periodic orbit theory.     

Path integral approach to multidimensional quantum tunnelling

Path integral formulation of the coupled channel problem in the case of multidimensional quantum tunneling is presented and two-time influence functionals are introduced. The two-time influence functionals are calculated explicitly for the three simplest cases: Harmonic oscillators linearly or quadratically coupled to the translational motion and a system with finite number of equidistant energy levels linearly coupled to the translational motion. The effects of these couplings on the transmission probability are studied for two limiting cases, adiabatic case and when the internal system has a degenerate energy spectrum. The condition for the transmission probability to show a resonant structure is discussed and exemplified. Finally, the properties of the dissipation factor in the adiabatic limit and its correlation with the friction coefficient in the classically accessible region are studied.     

Semiclassical approach to surface plasmons in spheroidal clusters

The linearized Vlasov equation gives a semiclassical version of the random phase approximation. The solution of this equation is studied for electrons moving in a deformed equilibrium mean field which is approximated by a cavity of a spheroidal shape (both prolate and oblate). Contrary to spherical systems, there is a coupling between excitations of different multipolarity induced by the interaction between constituents. The dipole response presents a typical double-peaked profile with a strong dependence on the deformation. Presented by A. Dellafiore at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Semiclassical stochastic trajectory approach to molecule-solid surface scattering

A semiclassical stochastic trajectory (SST) approach to the sudy of collision induced transitions in gas molecule-solid surface scattering is presented. The time-dependent Schrödinger equation provides the time-evolution of the transition amplitudes for the molecular internal states. Classical mechanics is used to describe the molecule's center of mass motion as well as the surface atoms' motion — the latter through the generalized Langevin equation (GLE) method which allows the treatment of non-rigid surfaces (i.e. surface temperature effects). These quantum and classical equations of motion are coupled through the use of a time-dependent interaction potential in the Schrödinger equation and the use of the expectation value of the interaction potential in the classical equations of motion. Advantages of the SST approach include: (1) flexibility in the choice of quantum versus classical coordinates; (c) strict energy conservation for non-dissipative system; and (3) realistic treatment of surface many-body effects within the GLE. The SST technique is applied to the study of vibrational and rotational inelasticity in a model H₂Pt(111) system. As an initial test, results obtained assuming a rigid, smooth surface with an exponentially repulsive potential are compared to exact quantal and quasi-classical trajectory values to determine the accuracy and utility of the SST approach. A limited practical application is presented for the same H₂Pt(111) system but for a non-rigid surface. These results, calculated at low gas kinetic energies, indicate that surface energy transfer and surface temperature effects should be minimal for this type of system, even though the energy gaps are quite similar for rotational and phonon degrees of freedom.     

Unified approach to quantum fluctuations in tunnelling including dissipation

Summary A simple procedure for evaluating quantum fluctuations at zero temperature has been applied to derive the decay rate for a metastable state in strongly anharmonic potentials (quartic and cubic). We also derive the tunnelling splitting and the energy shift in symmetrical and nearly symmetrical double-well potentials. Dissipation is then considered for the decay of a metastable state, both in the limit of weak and strong damping.

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Riassunto Un metodo semplificato per la valutazione delle fluttuazioni quantistiche, a temperatura zero, è stato impiegato per ottenere la velocità di decadimento di uno stato metastabile in potenziali fortemente anarmonici (quartico e cubico). Si ricavano pure la separazione per tunnelling e lo spostamento di energia nel caso di potenziale a doppio pozzo, simmetrico e quasi simmetrico. Si considerano poi effetti dissipati per il decadimento di uno stato metastabile, sia nel limite di debole che di forte smorzamento.

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Резюме Простая процедура оценки квантовых флуктуаций при нулевой температуре применяется для вывода скорости распада метастабильного состояния в сильно ангармонических потенциалах (четвертого и кубичкского порядков). Мы также выводим расщепление за счет туннелирования и сдвиг энергии в потенциалах симметричной и почти симметричной двойной ямы. Затем рассматривается влияние диссипации при распаде метастабильного состояния в пределе слабого и сильного затухания.

     

Semiclassical approach to orbital magnetism of interacting diffusive quantum systems

We study interaction effects on the orbital magnetism of diffusive mesoscopic quantum systems. By combining many-body perturbation theory with semiclassical techniques, we show that the interaction contribution to the ensemble-averaged quantum thermodynamic potential can be reduced to an essentially classical operator. We compute the magnetic response of disordered rings and dots for diffusive classical dynamics. Our semiclassical approach reproduces the results of previous diagrammatic quantum calculations.     

Semiclassical approach to resonance-optics polarization effects in coherent and squeezed fields

Equations are derived for the atomic density matrix and relaxation operator for a broadband squeezed field in an arbitrary polarization state and resonance atomic energy levels with an arbitrary degree of degeneracy. It is shown that suppression of the relaxation of the quadrature component of the atomic polarization depends strongly on the type of resonance transition and the polarization state of the squeezed and coherent perturbing fields. When the resonance levels are strongly degenerate, the relaxation of the quadrature component of the atomic polarization under conditions of maximum suppression is nonexponential in character. The mathematical apparatus developed here makes it possible to calculate polarization-related aspects of the multifrequency optical behavior of atomic and molecular systems resonantly excited both by coherent light and by broadband squeezed fields. Zh. éksp. Teor. Fiz. 111, 25–43 (January 1997)     

Semiclassical approach for multiparticle production in scalar theories

We propose a semiclassical approach to calculate multiparticle cross sections in scalar theories, which have been strongly argued to have the exponential form exp(λ⁻¹ F(λn, ϵ)) in the regime λ → 0, λn, ϵ = fixed, where λ is the scalar coupling, n is the number of produced particles, and ϵ is the kinetic energy per final particle. The formalism is based on singular solutions to the field equation, which satisfy certain boundary and extremizing conditions. At low multiplicities and small kinetic energies per final particle we reproduce in the framework of this formalism the main perturbative results. We also obtain a lower bound on the tree-level cross section in the ultra-relativistic regime.     

Thermodynamics of dense high-temperature plasmas: Semiclassical approach

The pseudopotential model of particle interaction of a semiclassical fully ionized plasma, taking into account both quantum effects at short distances and screening field effects at large distances is developed. Radial distribution functions are investigated and it is shown that a short-range order formation can occur in the system under discussion. Correlation energy of dense high-temperature plasma, existing in astrophysical objects is studied and comparison with other methods is performed.     

Efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy

Using a superoperator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is represented by a matrix continued fraction whose coefficients can be obtained from the nonsymmetric block-Lanczos method. The resulting algorithm, which is particularly convenient when large basis sets are used, allows for the calculation of the full spectrum of a system with a computational workload only a few times larger than needed for static polarizabilities within time-independent density-functional perturbation theory. The method is demonstrated with calculation of the spectrum of benzene, and prospects for its application to the large-scale calculation of optical spectra are discussed.