Power-law corrections to the Kubo formula vanish in quantum Hall systems

In first order perturbation theory conductivity is given by the Kubo formula, which in a Quantum Hall System equals the first Chern class of a vector bundle. We apply the adiabatic theorem to show that these topological constraints quantize the averaged conductivity to all orders of perturbation theory. Hence the Kubo formula is valid to all orders.     

Zero field isotropic Muonium Kubo — Toyabe relaxation functions

Static zero field Gaussian Kubo — Toyabe relaxation functions for muons in isotropic muonium atoms are presented. That is, as with diamagnetic muons, an average of the spin dynamics of a muon in an isolated isotropic ground state muonium atom is taken over an isotropic Gaussian continuous classical local random magnetic field distribution. This motion approximates the exact quantal spin dynamics generated by the dipole-dipole interactions between the muonium atom and the surrounding nuclear spins associated with the site at which the muonium atom has stopped. Expressions are derived for triplet muonium only since, in general, singlet muonium is not observed. For normal nuclear spins and ground state muonium, the resulting relaxation functions are identical to the standard diamagnetic function (except for a shift in the time scale).     

Kubo formula for frequency dispersion of dielectric permittivity and static conductivity of the Coulomb system

It is proved that the Kubo formula for the conductivity σ(ω) is valid at real frequencies ω. On this basis, an exact relation is derived for the static conductivity σst of the Coulomb system. It is shown that the static conductivity is determined by the time correlation function in the limit t→∞. It is proved that the permittivity ε(ω) satisfies the Kramers-Kronig relations which take into account a singularity associated with static conductivity.     

Heat conductivity in small quantum systems: Kubo formula in Liouville space

We consider chains consisting of several identical subsystems weakly coupled by various types of next neighbor interactions. At both ends the chain is coupled to a respective heat bath with different temperature modeled by a Lindblad formalism. The temperature gradient introduced by this environment is then treated as an external perturbation. We propose a method to evaluate the heat current and the local temperature profile of the resulting stationary state as well as the heat conductivity in such systems. This method is similar to Kubo techniques used e.g. for electrical transport but extended here to the Liouville space.     

An Analog of the Kubo formula for conductivity of spatially inhomogeneous media in spatially inhomogeneous electric fields

The average densities of currents and charges induced by a weak electromagnetic field in spatially inhomogeneous systems at a finite temperature are calculated. The Kubo formula for the electrical conductivity tensor is generalized to spatially inhomogeneous systems and spatially inhomogeneous fields. The contributions containing electric fields and derivatives of the fields with respect to coordinates are separated. It is shown that semiconductor quantum wells, wires, and dots can be treated as spatially inhomogeneous systems.     

Ryogo Kubo and μSR

The author traces the encounter of μSR physicists with the Kubo–Toyabe theory and the subsequent development of zero‐field μSR by mutual communication between experiment and theory. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-Abelian Kubo Formula and the Multiple Time-Scale Method

The non-Abelian Kubo formula is derived from the kinetic theory. That expression is compared with the one obtained using the eikonal for a Chern–Simons theory. The multiple time-scale method is used to study the non-Abelian Kubo formula, and the damping rate for longitudinal color waves is computed.     

Green's functions and matrix elements in the Furry picture for the electroweak theory with a non-Abelian external field

We obtain explict expressions of all types of Green's functions in the Furry picture of the electroweak theory with a free, non-Abelian external field, by solving the corresponding one-particle equations. We also give the expressions for the matrix elements of simple processes in an external field.Tomsk Pedagogical Institute. University of Sao Paulo, Brazil. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 37–41, May, 1993.     

Dynamical zeta functions for Artin''s billiard and the Venkov-Zograf factorization formula

Dynamical zeta functions are expected to relate the Schrödinger operator's spectrum to the periodic orbits of the corresponding fully chaotic Hamiltonian system. The relationship is exact in the case of surfaces of constant negative curvature. The recently found factorization of the Selberg zeta function for the modular surface is known to correspond to a decomposition of the Schrödinger operator's eigenfunctions into two sets obeying different boundary condition on Artin's billiard. Here we express zeta functions for Artin's billiard in terms of generalized transfer operators, providing thereby a new dynamical proof of the above interpretation of the factorization formula. This dynamical proof is then extended to the Artin-Venkov-Zograf formula for finite coverings of the modular surface.     

Canonical partition functions of Hamiltonian systems and the stationary phase formula

We show that there is a Symplectic Action of a Torus associated to Harmonic flows on the Cotangent Bundle of a semi-simple Lie Algebra. This allows to obtain a completely classical proof of the Gallavotti-Marchioro Formula by the method of the Stationary Phase.     

Super-symmetry and non-Abelian gauges

We show that the conventional Yang-Mills Lagrangian with the Yang-Mills field interacting with Majorana fermions belonging to the adjoint representation of an internal symmetry group like SU(n) is super-gauge invariant.     

Half-cylinders and branch-cut response functions

We consider the polarizability of half cylinders (explicitly, circular cylinders cut in half along a diameter), and the permittivity or permeability of dilute arrays of half cylinders, extending the work of of M. Pitkonen. We show that Pitkonen's results for the polarizability of half cylinders may be greatly simplified using a property of the dilogarithm function, and we comment on the correct choice of branches of the resulting simplified expression for complex cylinder permittivities. We discuss the relationship between response functions for systems having discrete resonances, as compared with those having branch-cut spectra, and highlight some of the advantages the latter may have in applications such as energy harvesting and design of metamaterials.     

Properties of universal functions in the Wigner mass formula for nuclei

The properties of the empirical functions in the Wigner mass formula for nuclei, which is based on SU(4) spin-isospin symmetry, are considered. It is shown that the origin of the odd-even effect in nuclei can be explained on the basis of an explicit analytic form of the second-degree Casimir operator for even-even and odd-odd nuclides and for nuclei of odd mass number. Experimental data in support of the proposed Wigner origin of the odd-even effect are presented.     

Tests of numerical simulation algorithms for the Kubo oscillator

Numerical simulation algorithms for multiplicative noise (white or colored) are tested for accuracy against closed-form expressions for the Kubo oscillator. Direct white noise simulations lead to spurious decay of the modulus of the oscillator amplitude. A straightforward colored noise algorithm greatly reduces this decay and also provides highly accurate results in the white noise limit.