Band structure of a one-dimensional Peierls-Hubbard-model

A mean field theory for a model Hamiltonian including the Fröhlich electron-phonon coupling term as well as the Hubbard electron-electron interaction term is presented.For the non antiferromagnetic case the band structure is derived; the Peierls-gap is found to be reduced but not to be quenched.     

Theory of one-dimensional and quasi-one-dimensional heat conduction

It is shown that the heat conduction process in a one-dimensional flow of a fluid moving with a velocity V in a constant temperature field follows a law that is considerably more complicated than an “ordinary” exponential law. It is demonstrated that in the quasi-one-dimensional case the heat conduction process in an abstract space of dimension 1+ɛ, where ɛ varies from zero to unity, is described by a modified Fourier equation. Its solution for an infinite space is found. Zh. Tekh. Fiz. 67, 8–12 (July 1997)     

Theory of superfluidity and drag force in the one-dimensional Bose gas

The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau’s criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid–insulator transition in these systems.     

Theory of the period-doubling phenomenon of one-dimensional mappings based on the parameter dependence

A theory is presented of the period-doubling phenomenon of one-dimensional mappings of the form x_n+1 = F(x_n, r), which is different from that of Feigenbaum mainly in that it is based on the r dependence of various quantities rather than on their x dependence. Consequently, it enables us to evaluate, for example, the Lyapunov numbers of periodic orbits as a function of r as well as the Feigenbaum ratio. It is shown that the results of our theory are in good agreement with those of numerical simulations.     

Theory of A ϕ-periodic one-dimensional bundle of dielectric waveguides

Mogil' Division, Institute of Physics, Belorussian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 2, pp. 200–204, February, 1992.     

Theory of one-dimensional quantum pump based on a two-barrier structure

A 1D quantum pump based on a structure of two δ-functional harmonically oscillating potentials is considered. Such a structure can pump electrons from one bank to the other. An ac perturbation induces a steady-state current. The effect takes place in spatially asymmetric systems. Such an asymmetry is formed due to a difference in the initial heights of the barriers or in the amplitudes or phases of ac signals. The pump can operate in various modes depending on its parameters. It is shown that the current displays oscillations with a period such that the wavelength of incident or excited electrons is multiple to the separation of the δ-functions. Resonances at quasi-stationary states between the barriers, at zero energy, and with stationary states (in the case of wells) are investigated.     

Theory of wave propagation in one-dimensional random media containing two-scale inhomogeneities

Pacific Oceanographic Institute, Far-Eastern Branch of the Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 3, pp. 274–279, March, 1991.     

Theory of many-body effects on the frequency dependent conductivity of a model one-dimensional disordered solid

I have calculated the frequency dependent conductivity for an idealized model of a one-dimensional disordered solid. The model includes the effects of both electron localization and interactions. I find that the maximum conductivity is unaffected by interactions regardless of their strength and that strong “attractive” electron correlations can lead to a collective mode whose position approaches zero frequency as its width vanishes even in the presence of strong single-particle scattering.     

Optics of circularly polarized light waves in one-dimensional magneto-photonic crystals: Theory

A theory is presented for propagation of electromagnetic waves through one-dimensional magnetic Bragg structures (magneto-photonic crystals). Within the self-consistent Green-function technique the transfer matrices and magneto-optical characteristics are derived in terms of circularly polarized waves propagating in periodical arrays of alternating magnetic and dielectric layers. For finite-thickness magneto-photonic crystals, the Faraday rotation and other magneto-optical responses are demonstrated to change considerably in the spectral range of stop-bands, the magnetic modulation of the in-plane reflection intensity being essentially enhanced.     

Theory of microwave losses of one-dimensional conductors in the skin effect regime: Application of TTF-TCNQ

Solutions for the microwave cavity losses due to a long isotropic or anisotropic conducting crystal oriented parallel to the maximum cavity E field are reported. The results are used to study the temperature dependent microwave conductivity of TTF-TCNQ along the principal conducting b-axis.     

Theory of circle maps and the problem of one-dimensional optical resonator with a periodically moving wall

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.     

On the quantisation of one-dimensional bags

We discuss the quantisation of one-dimensional MIT bags by expanding the fields as a sum of classical modes and truncating the series after the first term. We obtain the lowest states of a bag in a world containing two scalar quark fields. Problems associated with the zero-point oscillations of the field are discussed.     

Eigenvalues of the one-dimensional Smoluchowski equation

The eigenvalues and eigenfunctions of the Smoluchowski equation are investigated for the case of potentials withN deep wells. The small parameter =kT/V, which measures the ratio of the thermal energy to a typical well depth, is used in connection with the method of matched asymptotic expansion to obtained asymptotic approximations to all the eigenvalues and eigenfunctions. It is found that the eigensolutions fall into two classes, namely (i) the top-of-the-well and (ii) the bottom-of-the-well eigensolutions. The eigenvalues for both classes of solutions are integer multiples of the squqres of the frequencies at the top or bottom of the various wells. The eigenfunctions are, in general, localized to the top or bottom of the corresponding well. The very small eigenvalues require special consideration because the asymptotic analysis is incapable of distinguishing them from the zero eigenvalue with multiplicityN. Another approximation reveals that, in addition to the true zero eigenvalue, there areN-1 eigenvalues of order exp(–). The case of other possible multiple eigenvalues is also examined.     

On the one-dimensional Coulomb problem

We analyse the one-dimensional Coulomb problem (1DCP) pointing out some mistaken beliefs on it. We show that no eigenstates of even or odd parity can represent states of the system. The 1DCP exhibits a sort of spontaneous breaking of parity. We also show that a superselection rule operates in the system. Such rule explains some of its peculiarities. We build the superpotential associated to the 1DCP.