Theory of "Jitter" Radiation from Small-Scale Random Magnetic Fields and Prompt Emission from Gamma-Ray Burst Shocks

Abridged.-- We demonstrate that the radiation emitted by ultrarelativistic electrons in highly nonuniform, small-scale magnetic fields is different from synchrotron radiation if the electron's transverse deflections in these fields are much smaller than the beaming angle. A quantitative analytical theory of this radiation, which we refer to as jitter radiation, is developed. It is shown that the emergent spectrum is determined by statistical properties of the magnetic field. As an example,we then use the model of a magnetic field in internal shocks of GRBs. The spectral power distribution of radiation produced by the power-law electrons is well described by a sharply broken power-law with indices 1 and -(p-1)/2 and the jitter break frequency is independent of the field strength but depends on the electron density in the ejecta. Since large-scale fields may also be present in the ejecta, we construct a two-component, jitter+synchrotron spectral model of the prompt $\gamma$-ray emission. Quite surprisingly, this model seems to be readily capable of explaining several properties of time-resolved spectra of some GRBs, such as (i) the violation of the constraint on the low-energy spectral index called the synchrotron ``line of death'', (ii) the sharp spectral break at the peak frequency, inconsistent with the broad synchrotron bump, (iii) the evidence for two spectral sub-components, and (iv) possible existence of emission features called ``GRB lines''. We believe these facts strongly support both the existence of small-scale magnetic fields and the proposed radiation mechanism from GRB shocks. As an example, we use the composite model to analyze GRB 910503 which has two spectral peaks.Comment: 12 pages (emulateapj), 11 figures (EPS), ApJ, accepted. For related work, see http://cfa-www.harvard.edu/~mmedved

Spatial separation of large dynamical blue shift and harmonic generation

We study the temporal and spatial dynamics of the large amplitude and frequency modulation that can be induced in an intense, few cycle laser pulse as it propagates through a rapidly ionizing gas. Our calculations include both single atom and macroscopic interactions between the non-linear medium and the laser field. We analyze the harmonic generation by such pulses and show that it is spatially separated from the ionization dynamics which produce a large dynamical blue shift of the laser pulse. This means that small changes in the initial laser focusing conditions can lead to large differences in the laser frequency modulation, even though the generated harmonic spectrum remains essentially unchanged.Comment: 4 pages, 5 figures. Under revisio

Spin-orbit lateral superlattices: energy bands and spin polarization in 2DEG

The Bloch spinors, energy spectrum and spin density in energy bands are studied for the two-dimensional electron gas (2DEG) with Rashba spin-orbit (SO) interaction subject to one-dimensional (1D) periodic electrostatic potential of a lateral superlattice. The space symmetry of the Bloch spinors with spin parity is studied. It is shown that the Bloch spinors at fixed quasimomentum describe the standing spin waves with the wavelength equal to the superlattice period. The spin projections in these states have the components both parallel and transverse to the 2DEG plane. The anticrossing of the energy dispersion curves due to the interplay between the SO and periodic terms is observed, leading to the spin flip. The relation between the spin parity and the interband optical selection rules is discussed, and the effect of magnetization of the SO superlattice in the presence of external electric field is predicted.Comment: 6 pages, 5 figures, reported at the International Conferences "Nanophysics and Nanoelectronics" (Nizhny Novgorod, Russia, March 2006) and "Nanostructures: Physics and Technology" (St Petersburg, Russia, June 2006

Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling

We show that the spin Hall conductivity in insulators is related with a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin Hall effect. As a result, we theoretically predict that bismuth will show the quantum spin Hall effect, both by calculating the helical edge states, and by showing the non-triviality of the Z_2 topological number, and propose possible experiments.Comment: 5 pages, 2 figures, accepted for publication in Phys. Rev. Let

Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase

Phase transitions between the quantum spin Hall and the insulator phases in three dimensions are studied. We find that in inversion-asymmetric systems there appears a gapless phase between the quantum spin Hall and insulator phases in three dimensions, which is in contrast with the two-dimensional case. Existence of this gapless phase stems from a topological nature of gapless points (diabolical points) in three dimensions, but not in two dimensions.Comment: 16 pages, 5 figure

Spin Hall effects in diffusive normal metals

We consider spin and charge flow in normal metals. We employ the Keldysh formalism to find transport equations in the presence of spin-orbit interaction, interaction with magnetic impurities, and non-magnetic impurity scattering. Using the quasiclassical approximation, we derive diffusion equations which include contributions from skew scattering, side-jump scattering and the anomalous spin-orbit induced velocity. We compute the magnitude of various spin Hall effects in experimental relevant geometries and discuss when the different scattering mechanisms are important.Comment: 10 pages, 4 figure

Tuning phase transition between quantum spin Hall and ordinary insulating phases

An effective theory is constructed for analyzing a generic phase transition between the quantum spin Hall and the insulator phases. Occurrence of degeneracies due to closing of the gap at the transition are carefully elucidated. For systems without inversion symmetry the gap-closing occurs at \pm k_0(\neq G/2) while for systems with inversion symmetry, the gap can close only at wave-numbers k=G/2, where G is a reciprocal lattice vector. In both cases, following a unitary transformation which mixes spins, the system is represented by two decoupled effective theories of massive two-component fermions having masses of opposite signs. Existence of gapless helical modes at a domain wall between the two phases directly follows from this formalism. This theory provides an elementary and comprehensive phenomenology of the quantum spin Hall system.Comment: 6 pages, 2 figures, to appear in Phys. Rev.

Trigonometric R Matrices related to `Dilute' Birman--Wenzl--Murakami Algebra

Explicit expressions for three series of $R$ matrices which are related to a ``dilute'' generalisation of the Birman--Wenzl--Murakami are presented. Of those, one series is equivalent to the quantum $R$ matrices of the $D^{(2)}_{n+1}$ generalised Toda systems whereas the remaining two series appear to be new.Comment: 5 page

Decoherence without dissipation?

In a recent article, Ford, Lewis and O'Connell (PRA 64, 032101 (2001)) discuss a thought experiment in which a Brownian particle is subjected to a double-slit measurement. Analyzing the decay of the emerging interference pattern, they derive a decoherence rate that is much faster than previous results and even persists in the limit of vanishing dissipation. This result is based on the definition of a certain attenuation factor, which they analyze for short times. In this note, we point out that this attenuation factor captures the physics of decoherence only for times larger than a certain time t_mix, which is the time it takes until the two emerging wave packets begin to overlap. Therefore, the strategy of Ford et al of extracting the decoherence time from the regime t < t_mix is in our opinion not meaningful. If one analyzes the attenuation factor for t > t_mix, one recovers familiar behaviour for the decoherence time; in particular, no decoherence is seen in the absence of dissipation. The latter conclusion is confirmed with a simple calculation of the off-diagonal elements of the reduced density matrix.Comment: 8 pages, 4 figure

SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors

Following our previous work [S. Murakami, N. Nagaosa, S. C. Zhang, Science 301, 1348 (2003)] on the dissipationless quantum spin current, we present an exact quantum mechanical calculation of this novel effect based on the linear response theory and the Kubo formula. We show that it is possibxle to define an exactly conserved spin current, even in the presence of the spin-orbit coupling in the Luttinger Hamiltonian of p-type semiconductors. The light- and the heavy-hole bands form two Kramers doublets, and an SU(2) non-abelian gauge field acts naturally on each of the doublets. This quantum holonomy gives rise to a monopole structure in momentum space, whose curvature tensor directly leads to the novel dissipationless spin Hall effect, i.e., a transverse spin current is generated by an electric field. The result obtained in the current work gives a quantum correction to the spin current obtained in the previous semiclassical approximation.Comment: 14 pages, 2 figures, added some discussions, to appear in Phys. Rev.