1,934 research outputs found
Nonlinear response for external field and perturbation in the Vlasov system
A nonlinear response theory is provided by use of the transient linearization
method in the spatially one-dimensional Vlasov systems. The theory inclusively
gives responses to external fields and to perturbations for initial stationary
states, and is applicable even to the critical point of a second order phase
transition. We apply the theory to the Hamiltonian mean-field model, a toy
model of a ferromagnetic body, and investigate the critical exponent associated
with the response to the external field at the critical point in particular.
The obtained critical exponent is nonclassical value 3/2, while the classical
value is 3. However, interestingly, one scaling relation holds with another
nonclassical critical exponent of susceptibility in the isolated Vlasov
systems. Validity of the theory is numerically confirmed by directly simulating
temporal evolutions of the Vlasov equation.Comment: 15 pages, 8 figures, accepted for publication in Phys. Rev. E, Lemma
2 is correcte
Landau like theory for universality of critical exponents in quasistatioary states of isolated mean-field systems
An external force dynamically drives an isolated mean-field Hamiltonian
system to a long-lasting quasistationary state, whose lifetime increases with
population of the system. For second order phase transitions in quasistationary
states, two non-classical critical exponents have been reported individually by
using a linear and a nonlinear response theories in a toy model. We provide a
simple way to compute the critical exponents all at once, which is an analog of
the Landau theory. The present theory extends universality class of the
non-classical exponents to spatially periodic one-dimensional systems, and
shows that the exponents satisfy a classical scaling relation inevitably by
using a key scaling of momentum.Comment: 7 page
Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics
The mean-field theory tells that the classical critical exponent of
susceptibility is the twice of that of magnetization. However, the linear
response theory based on the Vlasov equation, which is naturally introduced by
the mean-field nature, makes the former exponent half of the latter for
families of quasistationary states having second order phase transitions in the
Hamiltonian mean-field model and its variances. We clarify that this strange
exponent is due to existence of Casimir invariants which trap the system in a
quasistationary state for a time scale diverging with the system size. The
theoretical prediction is numerically confirmed by -body simulations for the
equilibrium states and a family of quasistationary states.Comment: 6 pages, 3 figure
Tunneling Effects on Fine-Structure Splitting in Quantum Dot Molecules
We theoretically study the effects of bias-controlled interdot tunneling in
vertically coupled quantum dots on the emission properties of spin excitons in
various bias-controlled tunneling regimes. As a main result, for strongly
coupled dots we predict substantial reduction of optical fine structure
splitting without any drop in the optical oscillator strength. This special
reduction diminishes the distinguibility of polarized decay paths in cascade
emission processes suggesting the use of stacked quantum dot molecules as
entangled photon-pair sources.Comment: 12 pages, 4 figures, submitted to a APS journa
Dynamical pattern formations in two dimensional fluid and Landau pole bifurcation
A phenomenological theory is proposed to analyze the asymptotic dynamics of
perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram
provided by the theory is in qualitative agreement with numerical observations,
which include three phases depending on the aspect ratio of the domain and the
size of the perturbation: a steady shear flow, a stationary dipole, and four
traveling vortices. The theory is based on a precise study of the inviscid
damping of the linearized equation and on an analysis of nonlinear effects. In
particular, we show that the dominant Landau pole controlling the inviscid
damping undergoes a bifurcation, which has important consequences on the
asymptotic fate of the perturbation.Comment: 9 pages, 7 figure
Theory of resonant spin Hall effect
A biref review is presented on resonant spin Hall effect, where a tiny
external electric field induces a saturated spin Hall current in a
2-dimensional electron or hole gas in a perpendicular magnetic field. The
phenomenon is attributted to the energy level crossing associated with the
spin-orbit coupling and the Zeeman splitting. We summarize recent theoretical
development of the effect in various systems and discuss possible experiments
to observe the effect.Comment: 5 pages with 1 figure
Spin Hall Effect of Excitons
Spin Hall effect for excitons in alkali halides and in Cu_2O is investigated
theoretically. In both systems, the spin Hall effect results from the Berry
curvature in k space, which becomes nonzero due to lifting of degeneracies of
the exciton states by exchange coupling. The trajectory of the excitons can be
directly seen as spatial dependence of the circularly polarized light emitted
from the excitons. It enables us to observe the spin Hall effect directly in
the real-space time.Comment: 5 pages, 2 figure
- …