Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

The advent of ultraintense laser pulses generated by the technique of chirped pulse amplification (CPA) along with the development of high-fluence laser materials has opened up an entirely new field of optics. The electromagnetic field intensities produced by these techniques, in excess of ${10}^{18}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$, lead to relativistic electron motion in the laser field. The CPA method is reviewed and the future growth of laser technique is discussed, including the prospect of generating the ultimate power of a zettawatt. A number of consequences of relativistic-strength optical fields are surveyed. In contrast to the nonrelativistic regime, these laser fields are capable of moving matter more effectively, including motion in the direction of laser propagation. One of the consequences of this is wakefield generation, a relativistic version of optical rectification, in which longitudinal field effects could be as large as the transverse ones. In addition to this, other effects may occur, including relativistic focusing, relativistic transparency, nonlinear modulation and multiple harmonic generation, and strong coupling to matter and other fields (such as high-frequency radiation). A proper utilization of these phenomena and effects leads to the new technology of relativistic engineering, in which light-matter interactions in the relativistic regime drives the development of laser-driven accelerator science. A number of significant applications are reviewed, including the fast ignition of an inertially confined fusion target by short-pulsed laser energy and potential sources of energetic particles (electrons, protons, other ions, positrons, pions, etc.). The coupling of an intense laser field to matter also has implications for the study of the highest energies in astrophysics, such as ultrahigh-energy cosmic rays, with energies in excess of ${10}^{20}\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The laser fields can be so intense as to make the accelerating field large enough for general relativistic effects (via the equivalence principle) to be examined in the laboratory. It will also enable one to access the nonlinear regime of quantum electrodynamics, where the effects of radiative damping are no longer negligible. Furthermore, when the fields are close to the Schwinger value, the vacuum can behave like a nonlinear medium in much the same way as ordinary dielectric matter expanded to laser radiation in the early days of laser research.

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Optics in the relativistic regime

http://absimage.aps.org/image/DAMOP12/MWS_DAMOP12-2012-000066.pdf

Optics in the Relativistic Regime

Dark optical solitons: physics and applications

Instability of Solitons and Collapse of Acoustic Waves in Media with Positive Dispersion

The anisotropy due to a magnetic field is shown to result in significant changes in Langmuir collapse. Using a variational approach, the quasi-classical collapse phenomenon is investigated analytically. A hierarchy of quasi-classical collapses is determined, along with the structure of a field in the proximity of a stationary singularity that is sustained by the continuous absorption of wave energy from a wave packet.

Quasi-classical Langmuir wave collapse in a magnetic field

We present results of numerical simulation of the direct cascade in two-dimensional hydrodynamic turbulence (with spatial resolution up to $16384 \times 16384$). If at the earlier stage (at the time of order of the inverse pumping growth rate $\tau\sim\Gamma_{max}^{-1}$), the turbulence develops according to the same scenario as in the case of a freely decaying turbulence \cite{KNNR-07, KKS}: quasi-singular distributions of di-vorticity are formed, which in $k$-space correspond to jets, leading to a strong turbulence anisotropy, then for times of the order of $10\tau$ turbulence becomes almost isotropic. In particular, at these times any significant anisotropy in the angular fluctuations for the energy spectrum (for a fixed $k$) is not visible, while the probability distribution function of vorticity for large arguments has the exponential tail with the exponent linearly dependent on vorticity, in the agreement with the theoretical prediction \cite{FalkovichLebedev2011}.

Isotropization of two-dimensional hydrodynamic turbulence in the direct cascade

Based on Grad-Shafranov-like equations, a gyrotropic plasma where the pressures in the static regime are only functions of the amplitude of the local magnetic field is shown to be amenable to a variational principle with a free energy density given by the parallel tension. This approach is used to demonstrate that small-amplitude static holes constructed slightly below the mirror instability threshold identify with lump solitons of KPII (Kadomtsev-Petviashvili) equation and turn out to be unstable. It is also shown that regularizing effects such as finite Larmor radius corrections cannot be ignored in the description of large-amplitude mirror structures.

Subcritical mirror structures in an anisotropic plasma

1. It is well known (see Ref. 1, the review in Ref. 2, and the literature cited therein) that the generation of a magnetic field by random motions of a conducting liquid is possible only for gyrotropic turbulence. The existence of such generation frequently explains the origin of large-scale magnetic fields in astrophysical objects. In this connection, the problem of the spectra of gyrotropic turbulence, to which the present research is devoted, is of interest.

E. A. Kuznetsov

Papers

Instability of Solitons and Collapse of Acoustic Waves in Media with Positive Dispersion

Quasi-classical Langmuir wave collapse in a magnetic field

Isotropization of two-dimensional hydrodynamic turbulence in the direct cascade

Subcritical mirror structures in an anisotropic plasma

Gyrotropic turbulence spectra