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.     

Semiclassical Yang-Mills theory I: Instantons

The partition functions of quantum Yang-Mills theory have an expansion in powers of the coupling constant; the leading order term in this expansion is called the semiclassical approximation. We study the semiclassical approximation for Yang-Mills theory on a compact Riemannian 4-manifold using geometric techniques, and do explicit calculations for the case when the manifold is the 4-sphere. This involves calculating the Riemannian measure and certain functional determinants on the moduli space of self-dual connections. The main result is that the contribution to the semiclassical partition functions coming from thek=1 connections on the 4-sphere isfinite andcalculable. We also discuss a renormalization procedure in which the radius of the 4-sphere is allowed to tend to infinity.Partially supported by N.S.F. grant DMS-8905211Partially supported by N.S.F. grant DMS-8802885     

Semiclassical theory of nuclear rotation

The semiclassical theory of large amplitude collective motion developed previously by the author is applied to uniform nuclear rotation. In this way a sophisticated foundation of the self-consistent cranking model is given and its quantization is accomplished. The obtained quantization condition already contains the leading order correction to the self-consistent cranking model and also reveals the relation between the total angular momentum and the total signature. In the low frequency limit it yields the I(I + 1) law of a quantum rotor.     

Magnetization and spin-spin energy diffusion in the XY model: a diagrammatic approach

It is shown that the diagrammatic cluster expansion technique for equilibrium averages of spin operators may be straightforwardly extended to the calculation of time-dependent correlation functions of spin operators. We use this technique to calculate exactly the first two non-vanishing moments of the spin-spin and energy-energy correlation functions of the XY model with arbitrary couplings, in the long-wavelength, infinite temperature limit appropriate for spin diffusion. These moments are then used to estimate the magnetization and spin-spin energy diffusion coefficients of the model using a phenomenological theory of Redfield. Qualitative agreement is obtained with recent experiments measuring diffusion of dipolar energy in calcium fluoride.     

Semiclassical theory of chaotic conductors

We calculate the Landauer conductance through chaotic ballistic devices in the semiclassical limit, to all orders in the inverse number of scattering channels without and with a magnetic field. Families of pairs of entrance-to-exit trajectories contribute, similarly to the pairs of periodic orbits making up the small-time expansion of the spectral form factor of chaotic dynamics. As a clue to the exact result we find that close self-encounters slightly hinder the escape of trajectories into leads. Our result explains why the energy-averaged conductance of individual chaotic cavities, with disorder or "clean," agrees with predictions of random-matrix theory.     

Semiclassical real-time tunneling by multiple spawning of classical trajectories

We systematically extend semiclassical real-time propagation methods based on Gaussian wave packets by using the composition property of the time-dependent quantum-mechanical Green function. For the first time, in an application to the problem of barrier tunneling, a semiclassical time-domain calculation of the transmission probability exhibits good agreement with exact quantum mechanical values at energies below the barrier top. Only two insertions of unity are needed for these results in a benchmark model of reactive scattering.     

Scattering theory of Bardeen's formalism for tunneling: new approach to near-field microscopy

We propose a new theoretical approach to near-field microscopy, which allows one to deal with scanning tunneling microscopy and scanning near-field optical microscopy with a unified formalism. Under the approximation of weak tip-sample coupling, we show that Bardeen's perturbation formula, originally derived for electron tunneling, can be derived from a scattering formalism which extends its validity to electromagnetic vector fields. This result should find broad applications in near-field imaging and spectroscopy.     

Calculation of spin-density matrix by diagrammatic perturbation theory

A diagrammatic perturbation-theory method for direct calculation of spin-density matrix of open-shellN-electron systems described by the restricted Hartree-Fock one-particle functions is formulated. The formulae correct up to the second order of perturbation theory (second order in correlation effects) are presented. Their generalization to account for infinite summations of dominant correlation effects is simple, realized by making use of the so-called coupled cluster approach.     

Semiclassical theory of superradiant scattering from a Bose-Einstein condensate

A semiclassical theory of superradiant scattering of light from a Bose-Einstein condensate of a dilute atomic gas is proposed. Choosing atomic states with definite values of the momenta as a basis, we derive a nonlinear Schrödinger equation. Its solutions describe the evolution of the scattered light intensity and of the populations of the coherent atomic states with different recoil momenta.     

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.     

Semiclassical theory of the Coulomb anomaly

An effective action approach for the problem of Coulomb blocking of tunneling is discussed. The method is applied to the strong-coupling problem arising near zero bias, where perturbation theory diverges. We find an instanton for the electrodynamics in imaginary time, and express the anomaly in terms of the exact conductivity of the system σ(ω,q) and the exact interaction. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 200–205 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Semiclassical theory of chaotic quantum transport

We present a refined semiclassical approach to the Landauer conductance and Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for systems with uniformly hyperbolic dynamics that including off-diagonal contributions to double sums over classical paths gives a weak-localization correction in quantitative agreement with results from random matrix theory. We further discuss the magnetic-field dependence. This semiclassical treatment accounts for current conservation.