Dynamics of an Acoustic Polaron in One-Dimensional Electron-Lattice System

The dynamical behavior of an acoustic polaron in typical non-degenerate conjugated polymer, polydiacetylene, is numerically studied by using Su-Schrieffer-Heeger's model for the one dimensional electron-lattice system. It is confirmed that the velocity of a polaron accelerated by a constant electric field shows a saturation to a velocity close to the sound velocity of the system, and that the width of a moving polaron decreases as a monotonic function of the velocity tending to zero at the saturation velocity. The effective mass of a polaron is estimated to be about one hundred times as heavy as the bare electron mass. Furthermore the linear mode analysis in the presence of a polaron is carried out, leading to the conclusion that there is only one localized mode, i.e. the translational mode. This is confirmed also from the phase shift of extended modes. There is no localized mode corresponding to the amplitude mode in the case of the soliton in polyacetylene. Nevertheless the width of a moving polaron shows small oscillations in time. This is found to be related to the lowest odd symmetry extended mode and to be due to the finite size effect.Comment: 12 pages, latex, 9 figures (postscript figures abailble on request to [email protected]) to be published in J. Phys. Soc. Jpn. vol.65 (1996) No.

The anomalous behavior of coefficient of normal restitution in the oblique impact

The coefficient of normal restitution in an oblique impact is theoretically studied. Using a two-dimensional lattice models for an elastic disk and an elastic wall, we demonstrate that the coefficient of normal restitution can exceed one and has a peak against the incident angle in our simulation. Finally, we explain these phenomena based upon the phenomenological theory of elasticity.Comment: 4 pages, 4 figures, to be appeared in PR

Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity

Saari's homographic conjecture in N-body problem under the Newton gravity is the following; configurational measure \mu=\sqrt{I}U, which is the product of square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and the potential function U=\sum m_i m_j/r_{ij}, is constant if and only if the motion is homographic. Where m_k represents mass of body k and r_{ij} represents distance between bodies i and j. We prove this conjecture for planar equal-mass three-body problem. In this work, we use three sets of shape variables. In the first step, we use \zeta=3q_3/(2(q_2-q_1)) where q_k \in \mathbb{C} represents position of body k. Using r_1=r_{23}/r_{12} and r_2=r_{31}/r_{12} in intermediate step, we finally use \mu itself and \rho=I^{3/2}/(r_{12}r_{23}r_{31}). The shape variables \mu and \rho make our proof simple

Photogeneration Dynamics of a Soliton Pair in Polyacetylene

Dynamical process of the formation of a soliton pair from a photogenerated electron-hole pair in polyacetylene is studied numerically by adopting the SSH Hamiltonian. A weak local disorder is introduced in order to trigger the formation. Starting from an initial configuration with an electron at the bottom of the conduction band and a hole at the top of the valence band, separated by the Peierls gap, the time dependent Schr${\rm \ddot{o}}$ndinger equation for the electron wave functions and the equation of motion for the lattice displacements are solved numerically. After several uniform oscillations of the lattice system at the early stage, a large distortion corresponding to a pair of a soliton and an anti-soliton develops from a point which is determined by the location and type of the disorder. In some cases, two solitons run in opposite directions, leaving breather like oscillations behind, and in other cases they form a bound state emitting acoustic lattice vibrational modes.Comment: 16 pages 7 figure

Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Electronic theory for the normal state spin dynamics in Sr2_2RuO4_4: anisotropy due to spin-orbit coupling

Using a three-band Hubbard Hamiltonian we calculate within the random-phase-approximation the spin susceptibility, $\chi({\bf q},\omega)$, and NMR spin-lattice relaxation rate, 1/T$_1$, in the normal state of the triplet superconductor Sr$_2$RuO$_4$ and obtain quantitative agreement with experimental data. Most importantly, we find that due to spin-orbit coupling the out-of-plane component of the spin susceptibility $\chi^{zz}$ becomes at low temperatures two times larger than the in-plane one. As a consequence strong incommensurate antiferromagnetic fluctuations of the quasi-one-dimensional $xz$- and $yz$-bands point into the $z$-direction. Our results provide further evidence for the importance of spin fluctuations for triplet superconductivity in Sr$_2$RuO$_4$.Comment: revised versio

A crib-shaped triplet pairing gap function for an orthogonal pair of quasi-one dimensional Fermi surfaces in Sr2_2RuO4_4

The competition between spin-triplet and singlet pairings is studied theoretically for the tight-binding $\alpha$-$\beta$ bands in Sr$_2$RuO$_4$, which arise from two sets of quasi-one dimensional Fermi surfaces. Using multiband FLEX approximation, where we incorporate an anisotropy in the spin fluctuations as suggested from experiments, we show that (i) the triplet can dominate over the singlet (which turns out to be extended s), and (ii) the triplet gap function optimized in the Eliashberg equation has an unusual, very non-sinusoidal form, whose time-reversal-broken combination exhibits a crib-shaped amplitude with dips.Comment: 5 pages, RevTeX, to appear in Phys.Rev.B (Rapid Communications

Anisotropy in the Antiferromagnetic Spin Fluctuations of Sr2RuO4

It has been proposed that Sr_2RuO_4 exhibits spin triplet superconductivity mediated by ferromagnetic fluctuations. So far neutron scattering experiments have failed to detect any clear evidence of ferromagnetic spin fluctuations but, instead, this type of experiments has been successful in confirming the existence of incommensurate spin fluctuations near q=(1/3 1/3 0). For this reason there have been many efforts to associate the contributions of such incommensurate fluctuations to the mechanism of its superconductivity. Our unpolarized inelastic neutron scattering measurements revealed that these incommensurate spin fluctuations possess c-axis anisotropy with an anisotropic factor \chi''_{c}/\chi''_{a,b} of \sim 2.8. This result is consistent with some theoretical ideas that the incommensurate spin fluctuations with a c-axis anisotropy can be a origin of p-wave superconductivity of this material.Comment: 5 pages, 3 figures; accepted for publication in PR

Spin-triplet superconductivity due to antiferromagnetic spin-fluctuation in Sr_2RuO_4

A mechanism leading to the spin-triplet superconductivity is proposed based on the antiferromagnetic spin fluctuation. The effects of anisotropy in spin fluctuation on the Cooper pairing and on the direction of d vector are examined in the one-band Hubbard model with RPA approximation. The gap equations for the anisotropic case are derived and applied to Sr_2RuO_4. It is found that a nesting property of the Fermi surface together with the anisotropy leads to the triplet superconductivity with the d=z(sin{k_x}\pm isin{k_y}), which is consistent with experiments.Comment: 4 pages, 3 eps figures, revte