Dynamical description of the buildup process in resonant tunneling: Evidence of exponential and non-exponential contributions

The buildup process of the probability density inside the quantum well of a double-barrier resonant structure is studied by considering the analytic solution of the time dependent Schr\"{o}dinger equation with the initial condition of a cutoff plane wave. For one level systems at resonance condition we show that the buildup of the probability density obeys a simple charging up law, $| \Psi (\tau) / \phi | =1-e^{-\tau /\tau_0},$ where $\phi$ is the stationary wave function and the transient time constant $\tau_0$ is exactly two lifetimes. We illustrate that the above formula holds both for symmetrical and asymmetrical potential profiles with typical parameters, and even for incidence at different resonance energies. Theoretical evidence of a crossover to non-exponential buildup is also discussed.Comment: 4 pages, 2 figure

Book reviews

Teaching/Communication/Extension/Profession,

Free-Boundary Dynamics in Elasto-plastic Amorphous Solids: The Circular Hole Problem

We develop an athermal shear-transformation-zone (STZ) theory of plastic deformation in spatially inhomogeneous, amorphous solids. Our ultimate goal is to describe the dynamics of the boundaries of voids or cracks in such systems when they are subjected to remote, time-dependent tractions. The theory is illustrated here for the case of a circular hole in an infinite two-dimensional plate, a highly symmetric situation that allows us to solve much of the problem analytically. In spite of its special symmetry, this example contains many general features of systems in which stress is concentrated near free boundaries and deforms them irreversibly. We depart from conventional treatments of such problems in two ways. First, the STZ analysis allows us to keep track of spatially heterogeneous, internal state variables such as the effective disorder temperature, which determines plastic response to subsequent loading. Second, we subject the system to stress pulses of finite duration, and therefore are able to observe elasto-plastic response during both loading and unloading. We compute the final deformations and residual stresses produced by these stress pulses. Looking toward more general applications of these results, we examine the possibility of constructing a boundary-layer theory that might be useful in less symmetric situations.Comment: 30 pages (preprint format), 9 figure

Pedestrians moving in dark: Balancing measures and playing games on lattices

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-D\"{o}ring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures

Holographic Technidilaton and LHC searches

We analyze in detail the phenomenology of a model of dynamical electroweak symmetry breaking inspired by walking technicolor, by using the techniques of the bottom-up approach to holography. The model admits a light composite scalar state, the dilaton, in the spectrum. We focus on regions of parameter space for which the mass of such dilaton is 125 GeV, and for which the bounds on the precision electroweak parameter S are satisfied. This requires that the next-to-lightest composite state is the techni-rho meson, with a mass larger than 2.3 TeV. We compute the couplings controlling the decay rates of the dilaton to two photons and to two (real or virtual) Z and W bosons. For generic choices of the parameters, we find a suppression of the decay into heavy gauge bosons, in respect to the analog decay of the standard-model Higgs. We find a dramatic effect on the decay into photons, which can be both strongly suppressed or strongly enhanced, the latter case corresponding to the large-N regime of the dual theory. There is a correlation between this decay rate of the dilaton into photons and the mass splitting between the techni-rho meson and its axial-vector partner: if the decay is enhanced in respect to the standard-model case, then the heavy spin-1 resonances are nearly degenerate in mass, otherwise their separation in mass is comparable to the mass scale itself.Comment: Very minor typos corrected. References adde