Phonon emission and arrival times of electrons from a single-electron source

In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical-phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy

Field-driven topological glass transition in a model flux line lattice

We show that the flux line lattice in a model layered HTSC becomes unstable above a critical magnetic field with respect to a plastic deformation via penetration of pairs of point-like disclination defects. The instability is characterized by the competition between the elastic and the pinning energies and is essentially assisted by softening of the lattice induced by a dimensional crossover of the fluctuations as field increases. We confirm through a computer simulation that this indeed may lead to a phase transition from crystalline order at low fields to a topologically disordered phase at higher fields. We propose that this mechanism provides a model of the low temperature field--driven disordering transition observed in neutron diffraction experiments on ${\rm Bi_2Sr_2CaCu_2O_8\, }$ single crystals.Comment: 11 pages, 4 figures available upon request via snail mail from [email protected]

Entanglement Entropy of Two Spheres

We study the entanglement entropy S_{AB} of a massless free scalar field on two spheres A and B whose radii are R_1 and R_2, respectively, and the distance between the centers of them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r>>R_1,R_2, where S_A and S_B are the entanglement entropy on the inside region of A and B, respectively. We discuss possible connections of this result with the physics of black holes.Comment: 17 pages, 9 figures; v4, added references, revised argument in section V, a typo in eq.(25) corrected, published versio

Three-dimensional Magnetohydrodynamic Simulations of Buoyant Bubbles in Galaxy Clusters

We report results of 3D MHD simulations of the dynamics of buoyant bubbles in magnetized galaxy cluster media. The simulations are three dimensional extensions of two dimensional calculations reported by Jones & De Young (2005). Initially spherical bubbles and briefly inflated spherical bubbles all with radii a few times smaller than the intracluster medium (ICM) scale height were followed as they rose through several ICM scale heights. Such bubbles quickly evolve into a toroidal form that, in the absence of magnetic influences, is stable against fragmentation in our simulations. This ring formation results from (commonly used) initial conditions that cause ICM material below the bubbles to drive upwards through the bubble, creating a vortex ring; that is, hydrostatic bubbles develop into "smoke rings", if they are initially not very much smaller or very much larger than the ICM scale height. Even modest ICM magnetic fields with beta = P_gas/P_mag ~ 10^3 can influence the dynamics of the bubbles, provided the fields are not tangled on scales comparable to or smaller than the size of the bubbles. Quasi-uniform, horizontal fields with initial beta ~ 10^2 bifurcated our bubbles before they rose more than about a scale height of the ICM, and substantially weaker fields produced clear distortions. On the other hand, tangled magnetic fields with similar, modest strengths are generally less easily amplified by the bubble motions and are thus less influential in bubble evolution. Inclusion of a comparably strong, tangled magnetic field inside the initial bubbles had little effect on our bubble evolution, since those fields were quickly diminished through expansion of the bubble and reconnection of the initial field.Comment: 20 pages, 12 figures. Accepted for publication in The Astrophysical Journa

Equation of State in Numerical Relativistic Hydrodynamics

Relativistic temperature of gas raises the issue of the equation of state (EoS) in relativistic hydrodynamics. We study the EoS for numerical relativistic hydrodynamics, and propose a new EoS that is simple and yet approximates very closely the EoS of the single-component perfect gas in relativistic regime. We also discuss the calculation of primitive variables from conservative ones for the EoS's considered in the paper, and present the eigenstructure of relativistic hydrodynamics for a general EoS, in a way that they can be used to build numerical codes. Tests with a code based on the Total Variation Diminishing (TVD) scheme are presented to highlight the differences induced by different EoS's.Comment: To appear in the ApJS September 2006, v166n1 issue. Pdf with full resolution figures can be downloaded from http://canopus.cnu.ac.kr/ryu/ryuetal.pd

Dynamical Phase Transition in a Driven Disordered Vortex Lattice

Using Langevin dynamics, we have investigated the dynamics of vortices in a disordered two dimensional superconductor subjected to a uniform driving current. The results provide direct numerical evidence for a dynamical phase transition between a plastic flow regime and a moving ``hexatic glass." The simulated current-voltage characteristics are in excellent agreement with recent transport measurements on amorphous ${\rm Mo_{77}Ge_{23}}$ thin film superconductors.Comment: 13 pages, latex, revtex, 4 figures available upon request from [email protected]