974 research outputs found
Kowalevski's analysis of the swinging Atwood's machine
We study the Kowalevski expansions near singularities of the swinging
Atwood's machine. We show that there is a infinite number of mass ratios
where such expansions exist with the maximal number of arbitrary constants.
These expansions are of the so--called weak Painlev\'e type. However, in view
of these expansions, it is not possible to distinguish between integrable and
non integrable cases.Comment: 30 page
Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators
We consider expanding semiflows on branched surfaces. The family of transfer
operators associated to the semiflow is a one-parameter semigroup of operators.
The transfer operators may also be viewed as an operator-valued function of
time and so, in the appropriate norm, we may consider the vector-valued Laplace
transform of this function. We obtain a spectral result on these operators and
relate this to the spectrum of the generator of this semigroup. Issues of
strong continuity of the semigroup are avoided. The main result is the
improvement to the machinery associated with studying semiflows as
one-parameter semigroups of operators and the study of the smoothness
properties of semiflows defined on branched manifolds, without encoding as a
suspension semiflow
From Kondo Effect to Fermi Liquid
The Kondo effect has been playing an important role in strongly correlated
electon systems. The important point is that the magnetic impurity in metals is
a typical example of the Fermi liquid. In the system the local spin is
conserved in the ground state and continuity with respect to Coulomb repulsion
is satisfied. This nature is satisfied also in the periodic systems as far
as the systems remain as the Fermi liquid. This property of the Fermi liquid is
essential to understand the cuprate high-Tc superconductors (HTSC). On the
basis of the Fermi liquid theory we develop the transport theory such as the
resistivity and the Hall coefficient in strongly correlated electron systems,
such as HTSC, organic metals and heavy Fermion systems. The significant role of
the vertex corrections for total charge- and heat-currents on the transport
phenomena is explained. By taking the effect of the current vertex corrections
into account, various typical non-Fermi-liquid-like transport phenomena in
systems with strong magnetic and/or superconducting flucutations are explained
within the Fermi liquid theory.Comment: 14 pages, an article for the special edition of JPSJ "Kondo Effect --
40 Years after the Discovery
Electrical control of spin dynamics in finite one-dimensional systems
We investigate the possibility of the electrical control of spin transfer in
monoatomic chains incorporating spin-impurities. Our theoretical framework is
the mixed quantum-classical (Ehrenfest) description of the spin dynamics, in
the spirit of the s-d-model, where the itinerant electrons are described by a
tight-binding model while localized spins are treated classically. Our main
focus is on the dynamical exchange interaction between two well-separated
spins. This can be quantified by the transfer of excitations in the form of
transverse spin oscillations. We systematically study the effect of an
electrostatic gate bias V_g on the interconnecting channel and we map out the
long-range dynamical spin transfer as a function of V_g. We identify regions of
V_g giving rise to significant amplification of the spin transmission at low
frequencies and relate this to the electronic structure of the channel.Comment: 9 pages, 11 figure
Integrability of one degree of freedom symplectic maps with polar singularities
In this paper, we treat symplectic difference equations with one degree of
freedom. For such cases, we resolve the relation between that the dynamics on
the two dimensional phase space is reduced to on one dimensional level sets by
a conserved quantity and that the dynamics is integrable, under some
assumptions. The process which we introduce is related to interval exchange
transformations.Comment: 10 pages, 2 figure
Chain Formation by Spin Pentamers in eta-Na9V14O35
The nature of the gapped ground state in the quasi-one-dimensional compound
eta-Na9V14O35 cannot easily be understood, if one takes into account the odd
number of spins on each structural element. Combining the results of specific
heat, susceptibility and electron spin resonance measurements we show that
eta-Na9V14O35 exhibits a novel ground state where multi-spin objects build up a
linear chain. These objects - pentamers - consist of five antiferromagnetically
arranged spins with effective spin 1/2. Their spatial extent results in an
exchange constant along the chain direction comparable to the one in the
high-temperature state.Comment: 6 pages, 5 figure
Current-induced non-adiabatic spin torques and domain wall motion with spin relaxation in a ferromagnetic metallic wire
Within the s-d model description, we derive the current-driven spin torque in
a ferromagnet, taking explicitly into account a spin-relaxing Caldeira-Leggett
bath coupling to the s-electrons. We derive Bloch-Redfield equations of motion
for the s-electron spin dynamics, and formulate a systematic gradient expansion
to obtain non-adiabatic (higher-order) corrections to the well-known adiabatic
(first-order) spin torque. We provide simple analytical expressions for the
second-order spin torque. The theory is applied to current-driven domain wall
motion. Second-order contributions imply a deformation of a transverse
tail-to-tail domain wall. The wall center still moves with a constant velocity
that now depends on the spin-polarized current in a non-trivial manner.Comment: Phys. Rev. B, in press, replaced with published versio
Brueckner-Goldstone perturbation theory for the half-filled Hubbard model in infinite dimensions
We use Brueckner-Goldstone perturbation theory to calculate the ground-state
energy of the half-filled Hubbard model in infinite dimensions up to fourth
order in the Hubbard interaction. We obtain the momentum distribution as a
functional derivative of the ground-state energy with respect to the bare
dispersion relation. The resulting expressions agree with those from
Rayleigh-Schroedinger perturbation theory. Our results for the momentum
distribution and the quasi-particle weight agree very well with those obtained
earlier from Feynman-Dyson perturbation theory for the single-particle
self-energy. We give the correct fourth-order coefficient in the ground-state
energy which was not calculated accurately enough from Feynman-Dyson theory due
to the insufficient accuracy of the data for the self-energy, and find a good
agreement with recent estimates from Quantum Monte-Carlo calculations.Comment: 15 pages, 8 fugures, submitted to JSTA
Indirect RKKY interaction in any dimensionality
We present an analytical method which enables one to find the exact spatial
dependence of the indirect RKKY interaction between the localized moments via
the conduction electrons for the arbitrary dimensionality . The
corresponding momentum dependence of the Lindhard function is exactly found for
any as well. Demonstrating the capability of the method we find the RKKY
interaction in a system of metallic layers weakly hybridized to each other.
Along with usual in-plane oscillations the RKKY interaction has the
sign-reversal character in a direction perpendicular to layers, thus favoring
the antiferromagnetic type of layers' stacking.Comment: 3 pages, REVTEX, accepted to Phys.Rev.
Dynamic properties of the spin-1/2 XY chain with three-site interactions
We consider a spin-1/2 XY chain in a transverse (z) field with multi-site
interactions. The additional terms introduced into the Hamiltonian involve
products of spin components related to three adjacent sites. A Jordan-Wigner
transformation leads to a simple bilinear Fermi form for the resulting
Hamiltonian and hence the spin model admits a rigorous analysis. We point out
the close relationships between several variants of the model which were
discussed separately in previous studies. The ground-state phases (ferromagnet
and two kinds of spin liquid) of the model are reflected in the dynamic
structure factors of the spin chains, which are the main focus in this study.
First we consider the zz dynamic structure factor reporting for this quantity a
closed-form expression and analyzing the properties of the two-fermion
(particle-hole) excitation continuum which governs the dynamics of transverse
spin component fluctuations and of some other local operator fluctuations. Then
we examine the xx dynamic structure factor which is governed by many-fermion
excitations, reporting both analytical and numerical results. We discuss some
easily recognized features of the dynamic structure factors which are
signatures for the presence of the three-site interactions.Comment: 28 pages, 10 fugure
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