243 research outputs found
Spin and orbital effects in a 2D electron gas in a random magnetic field
Using the method of superbosonization we consider a model of a random
magnetic field (RMF) acting on both orbital motion and spin of electrons in two
dimensions. The method is based on exact integration over one particle degrees
of freedom and reduction of the problem to a functional integral over
supermatrices . We consider a general case when
both the direction of the RMF and the g-factor of the Zeeman splitting are
arbitrary. Integrating out fast variations of we come to a standard
collisional unitary non-linear -model. The collision term consists of
orbital, spin and effective spin-orbital parts. For a particular problem of a
fixed direction of RMF, we show that additional soft excitations identified
with spin modes should appear. Considering % -correlated weak RMF and
putting g=2 we find the transport time . This time is 2 times
smaller than that for spinless particles.Comment: 9 pages, no figure
Anderson transition of three dimensional phonon modes
Anderson transition of the phonon modes is studied numerically. The critical
exponent for the divergence of the localization length is estimated using the
transfer matrix method, and the statistics of the modes is analyzed. The latter
is shown to be in excellent agreement with the energy level statistics of the
disrodered electron system belonging to the orthogonal universality class.Comment: 2 pages and another page for 3 figures, J. Phys. Soc. Japa
Comment on ``Critical Behavior in Disordered Quantum Systems Modified by Broken Time--Reversal Symmetry''
In a recent Letter [Phys. Rev. Lett. 80, 1003 (1998)] Hussein and Pato
employed the maximum entropy principle (MEP) in order to derive interpolating
ensembles between any pair of universality classes in random matrix theory.
They apply their formalism also to the transition from random matrix to Poisson
statistics of spectra that is observed for the case of the Anderson-type
metal-insulator transition. We point out the problems with the latter
procedure.Comment: 1 page in PS, to appear in PRL Sept. 2
Anomalous diffusion at the Anderson transitions
Diffusion of electrons in three dimensional disordered systems is
investigated numerically for all the three universality classes, namely,
orthogonal, unitary and symplectic ensembles. The second moment of the wave
packet at the Anderson transition is shown to behave as . From the temporal autocorrelation function , the
fractal dimension is deduced, which is almost half the value of space
dimension for all the universality classes.Comment: Revtex, 2 figures, to appear in J. Phys. Soc. Jpn.(1997) Fe
One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions
Based on the spectral statistics obtained in numerical simulations on three
dimensional disordered systems within the tight--binding approximation, a new
superuniversal scaling relation is presented that allows us to collapse data
for the orthogonal, unitary and symplectic symmetry () onto a
single scaling curve. This relation provides a strong evidence for
one-parameter scaling existing in these systems which exhibit a second order
phase transition. As a result a possible one-parameter family of spacing
distribution functions, , is given for each symmetry class ,
where is the dimensionless conductance.Comment: 4 pages in PS including 3 figure
Spectral Properties of the Chalker-Coddington Network
We numerically investigate the spectral statistics of pseudo-energies for the
unitary network operator U of the Chalker--Coddington network. The shape of the
level spacing distribution as well the scaling of its moments is compared to
known results for quantum Hall systems. We also discuss the influence of
multifractality on the tail of the spacing distribution.Comment: JPSJ-style, 7 pages, 4 Postscript figures, to be published in J.
Phys. Soc. Jp
Critical statistics in a power-law random banded matrix ensemble
We investigate the statistical properties of the eigenvalues and eigenvectors
in a random matrix ensemble with . It is known that
this model shows a localization-delocalization transition (LDT) as a function
of the parameter . The model is critical at and the eigenstates
are multifractals. Based on numerical simulations we demonstrate that the
spectral statistics at criticality differs from semi-Poisson statistics which
is expected to be a general feature of systems exhibiting a LDT or `weak
chaos'.Comment: 4 pages in PS including 5 figure
Metal-insulator transitions in anisotropic 2d systems
Several phenomena related to the critical behaviour of non-interacting
electrons in a disordered 2d tight-binding system with a magnetic field are
studied. Localization lengths, critical exponents and density of states are
computed using transfer matrix techniques. Scaling functions of isotropic
systems are recovered once the dimension of the system in each direction is
chosen proportional to the localization length. It is also found that the
critical point is independent of the propagation direction, and that the
critical exponents for the localization length for both propagating directions
are equal to that of the isotropic system (approximately 7/3). We also
calculate the critical value of the scaling function for both the isotropic and
the anisotropic system. It is found that the isotropic value equals the
geometric mean of the two anisotropic values. Detailed numerical studies of the
density of states for the isotropic system reveals that for an appreciable
amount of disorder the critical energy is off the band center.Comment: 6 pages RevTeX, 6 figures included, submitted to Physical Review
Generation of 10-m-lengthscale plasma columns by resonant and off-resonant laser pulses
Creating extended, highly homogeneous plasma columns like that required by
plasma wakefield accelerators can be a challenge. We study the propagation of
ultra-short, TW power ionizing laser pulses in a 10-meter-long rubidium vapor
and the plasma columns they create. We perform experiments and numerical
simulations for pulses with 780 nm central wavelength, which is resonant with
the D transition from the ground state of rubidium atoms, as well as for
pulses with 810 nm central wavelength, some distance from resonances. We
measure transmitted energy and transverse width of the pulse and use schlieren
imaging to probe the plasma column in the vapor close to the end of the vapor
source. We find, that resonant pulses are more confined in a transverse
direction by the interaction than off-resonant pulses are and that the plasma
channels they create are more sharply bounded. Off-resonant pulses leave a
wider layer of partially ionized atoms and thus lose more energy per unit
propagation distance. Using experimental data, we estimate the energy required
to generate a 20-meter-long plasma column and conclude that resonant pulses are
much more suitable for creating a long, homogeneous plasma.Comment: 12 pages, 14 figure
Magnetic Field Effect for Two Electrons in a Two Dimensional Random Potential
We study the problem of two particles with Coulomb repulsion in a
two-dimensional disordered potential in the presence of a magnetic field. For
the regime, when without interaction all states are well localized, it is shown
that above a critical excitation energy electron pairs become delocalized by
interaction. The transition between the localized and delocalized regimes goes
in the same way as the metal-insulator transition at the mobility edge in the
three dimensional Anderson model with broken time reversal symmetry.Comment: revtex, 7 pages, 6 figure
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