The Inverse Spectral Transform for the Dunajski hierarchy and some of its reductions, I: Cauchy problem and longtime behavior of solutions

In this paper we apply the formal Inverse Spectral Transform for integrable dispersionless PDEs arising from the commutation condition of pairs of one-parameter families of vector fields, recently developed by S. V. Manakov and one of the authors, to one distinguished class of equations, the so-called Dunajski hierarchy. We concentrate, for concreteness, i) on the system of PDEs characterizing a general anti-self-dual conformal structure in neutral signature, ii) on its first commuting flow, and iii) on some of their basic and novel reductions. We formally solve their Cauchy problem and we use it to construct the longtime behavior of solutions, showing, in particular, that unlike the case of soliton PDEs, different dispersionless PDEs belonging to the same hierarchy of commuting flows evolve in time in very different ways, exhibiting either a smooth dynamics or a gradient catastrophe at finite time

Magnetic properties of a spin-3 Chromium condensate

We study the ground state properties of a spin-3 Cr condensate subject to an external magnetic field by numerically solving the Gross-Piteavskii equations. We show that the widely adopted single-mode approximation is invalid under a finite magnetic field. In particular, a phase separation like behavior may be induced by the magnetic field. We also point out the possible origin of the phase separation phenomenon.Comment: 6 pages, 5 figure

Physical condition and spin-resolved exchange correlation kernels in an inhomogeneous many electron system

We first exploit the spin symmetry relation $f^{\rm xc}_{s\bar s} (\zeta)=f^{\rm xc}_{\bar s s}(-\zeta)$ for the exact exchange correlation kernel $f^{\rm xc}_{s\bar s}(\zeta)$ in an inhomogeneous many electron system with arbitrary spin polarization $\zeta$. The physical condition required to satisfy the specific symmetry relation $f^{\rm xc}_{s\bar s}(\zeta) = f^{\rm xc}_{\bar s s}(\zeta)$ is derived and examined for simple ferromagnetic-nonmagnetic structure by taking the electrochemical potential into account. The condition is then applied to several composite systems useful in spintronics applications such as the magnetic system with net spin polarization.Comment: 5 pages, 1 figur

Relativistic Precessing Jets and Cosmological Gamma Ray Bursts

We discuss the possibility that gamma-ray bursts may result from cosmological relativistic blob emitting neutron star jets that precess past the line of sight. Beaming reduces the energy requirements, so that the jet emission can last longer than the observed burst duration. One precession mode maintains a short duration time scale, while a second keeps the beam from returning to the line of sight, consistent with the paucity of repeaters. The long life of these objects reduces the number required for production as compared to short lived jets. Blobs can account for the time structure of the bursts. Here we focus largely on kinematic and time scale considerations of beaming, precession, and blobs--issues which are reasonably independent of the acceleration and jet collimation mechanisms. We do suggest that large amplitude electro-magnetic waves could be a source of blob acceleration.Comment: 15 pages, plain TeX, accepted to ApJ

Adsorption of Externally Stretched Two-Dimensional Flexible and Semi-flexible Polymers near an Attractive Wall

We study analytically a model of a two dimensional, partially directed, flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an externally applied force. We find that the wall has a dramatic effect on the polymer. For wall attraction smaller than the non-sequential nearest neighbor attraction, the fraction of monomers at the wall is zero and the model is the same as that of a polymer without a wall. However, for greater than, the fraction of monomers at the wall undergoes a first order transition from unity at low temperature and small force, to zero at higher temperatures and forces. We present phase diagram for this transition. Our results are confirmed by Monte-Carlo simulations.Comment: 15 pages, 6 figure

Aharonov-Bohm Radiation of Fermions

We analyze Aharonov-Bohm radiation of charged fermions from oscillating solenoids and cosmic strings. We find that the angular pattern of the radiation has features that differ significantly from that for bosons. For example, fermionic radiation in the lowest harmonic is approximately isotropically distributed around an oscillating solenoid, whereas for bosons the radiation is dipolar. We also investigate the spin polarization of the emitted fermion-antifermion pair. Fermionic radiation from kinks and cusps on cosmic strings is shown to depend linearly on the ultraviolet cut-off, suggesting strong emission at an energy scale comparable to the string energy scale.Comment: 14 pages, 6 figures. Version 2: Expanded discussion on boundary conditions obeyed by Dirac equation mode functions (in Section V B). Acknowledgements and references added. Version 3: Minor changes made in response to referee's comment

Scheme for preparation of W state via cavity QED

In this paper, we presented a physical scheme to generate the multi-cavity maximally entangled W state via cavity QED. All the operations needed in this scheme are to modulate the interaction time only once.Comment: 8 pages, 1 figur

From Vacuum Fluctuations to Radiation: Accelerated Detectors and Black Holes

The vacuum fluctuations that induce the transitions and the thermalisation of a uniformly accelerated two level atom are studied in detail. Their energy content is revealed through the weak measurement formalism of Aharonov et al. It is shown that each time the detector makes a transition it radiates a Minkowski photon. The same analysis is then applied to the conversion of vacuum fluctuations into real quanta in the context of black hole radiation. Initially these fluctuations are located around the light like geodesic that shall generate the horizon and carry zero total energy. However upon exiting from the star they break up into two pieces one of which gradually acquires positive energy and becomes a Hawking quantum, the other, its ''partner", ends up in the singularity. As time goes by the vacuum fluctuations generating Hawking quanta have exponentially large energy densities. This implies that back reaction effects are large.Comment: definitive version, 39 pages and 5 figures available upon request from S.M., ULB-TH 94/0

Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements

We propose the concept of SLOCC-equivalent basis (SEB) in the multiqubit space. In particular, two special SEBs, the GHZ-type and the W-type basis are introduced. They can make up a more general family of multiqubit states, the GHZ-W-type states, which is a useful kind of entanglement for quantum teleporatation and error correction. We completely characterize the property of this type of states, and mainly classify the GHZ-type states and the W-type states in a regular way, which is related to the enumerative combinatorics. Many concrete examples are given to exhibit how our method is used for the classification of these entangled states.Comment: 16 pages, Revte