118 research outputs found
Lyapunov Generation of Entanglement and the Correspondence Principle
We show how a classically vanishing interaction generates entanglement
between two initially nonentangled particles, without affecting their classical
dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate
at the Lyapunov exponent of the classical dynamics as the interaction strength
increases. In the saturation regime, the one-particle Wigner function follows
classical dynamics better and better as one goes deeper and deeper in the
semiclassical limit. This demonstrates that quantum-classical correspondence at
the microscopic level requires neither high temperatures, nor coupling to a
large number of external degrees of freedom
Mesoscopic Spin Hall Effect
We investigate the spin Hall effect in ballistic chaotic quantum dots with
spin-orbit coupling. We show that a longitudinal charge current can generate a
pure transverse spin current. While this transverse spin current is generically
nonzero for a fixed sample, we show that when the spin-orbit coupling time is
large compared to the mean dwell time inside the dot, it fluctuates universally
from sample to sample or upon variation of the chemical potential with a
vanishing average. For a fixed sample configuration, the transverse spin
current has a finite typical value ~e^2 V/h, proportional to the longitudinal
bias V on the sample, and corresponding to about one excess open channel for
one of the two spin species. Our analytical results are in agreement with
numerical results in a diffusive system [W. Ren et al., Phys. Rev. Lett. 97,
066603 (2006)] and are further confirmed by numerical simulation in a chaotic
cavity.Comment: 4 pages, 2 figure
Shot noise in semiclassical chaotic cavities
We construct a trajectory-based semiclassical theory of shot noise in clean
chaotic cavities. In the universal regime of vanishing Ehrenfest time \tE, we
reproduce the random matrix theory result, and show that the Fano factor is
exponentially suppressed as \tE increases. We demonstrate how our theory
preserves the unitarity of the scattering matrix even in the regime of finite
\tE. We discuss the range of validity of our semiclassical approach and point
out subtleties relevant to the recent semiclassical treatment of shot noise in
the universal regime by Braun et al. [cond-mat/0511292].Comment: Final version, to appear in Physical Review Letter
Quantum Andreev Map: A Paradigm of Quantum Chaos in Superconductivity. .
We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for a large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time
Topologically Protected Loop Flows in High Voltage AC Power Grids
Geographical features such as mountain ranges or big lakes and inland seas
often result in large closed loops in high voltage AC power grids. Sizable
circulating power flows have been recorded around such loops, which take up
transmission line capacity and dissipate but do not deliver electric power.
Power flows in high voltage AC transmission grids are dominantly governed by
voltage angle differences between connected buses, much in the same way as
Josephson currents depend on phase differences between tunnel-coupled
superconductors. From this previously overlooked similarity we argue here that
circulating power flows in AC power grids are analogous to supercurrents
flowing in superconducting rings and in rings of Josephson junctions. We
investigate how circulating power flows can be created and how they behave in
the presence of ohmic dissipation. We show how changing operating conditions
may generate them, how significantly more power is ohmically dissipated in
their presence and how they are topologically protected, even in the presence
of dissipation, so that they persist when operating conditions are returned to
their original values. We identify three mechanisms for creating circulating
power flows, (i) by loss of stability of the equilibrium state carrying no
circulating loop flow, (ii) by tripping of a line traversing a large loop in
the network and (iii) by reclosing a loop that tripped or was open earlier.
Because voltage angles are uniquely defined, circulating power flows can take
on only discrete values, much in the same way as circulation around vortices is
quantized in superfluids.Comment: 12 pages 6 figures + Supplementary Material, Accepted for publication
in New Journal of Physic
Ground State Properties of Many-Body Systems in the Two-Body Random Ensemble and Random Matrix Theory
We explore generic ground-state and low-energy statistical properties of
many-body bosonic and fermionic one- and two-body random ensembles (TBRE) in
the dense limit, and contrast them with Random Matrix Theory (RMT). Weak
differences in distribution tails can be attributed to the regularity or
chaoticity of the corresponding Hamiltonians rather than the particle
statistics. We finally show the universality of the distribution of the angular
momentum gap between the lowest energy levels in consecutive J-sectors for the
four models considered.Comment: 12 pages, 5 figure
Universal features of spin transport and breaking of unitary symmetries
When time-reversal symmetry is broken, quantum coherent systems with and without spin rotational symmetry exhibit the same universal behavior in their electric transport properties. We show that spin transport discriminates between these two cases. In systems with large charge conductance, spin transport is essentially insensitive to the breaking of time-reversal symmetry, while in the opposite limit of a single exit transport channel, spin currents vanish identically in the presence of time-reversal symmetry but can be turned on by breaking it with an orbital magnetic field
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