Probe method and a Carleman function

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions which is called a {\it needle sequence}. The needle sequence blows up on a special curve which connects a given point inside the domain with a point on the boundary of the domain and is convergent locally outside the curve. The sequence yields a reconstruction formula of unknown discontinuity, such as cavity, inclusion in a given medium from the Dirichlet-to-Neumann map. In this paper, an explicit needle sequence in {\it three dimensions} is given in a closed form. It is an application of a Carleman function introduced by Yarmukhamedov. Furthermore, an explicit needle sequence in the probe method applied to the reduction of inverse obstacle scattering problems with an {\it arbitrary} fixed wave number to inverse boundary value problems for the Helmholtz equation is also given.Comment: 2 figures, final versio

Green's function probe of a static granular piling

We present an experiment which aim is to investigate the mechanical properties of a static granular assembly. The piling is an horizontal 3D granular layer confined in a box, we apply a localized extra force at the surface and the spatial distribution of stresses at the bottom is obtained (the mechanical Green's function). For different types of granular media, we observe a linear pressure response which profile shows one peak centered at the vertical of the point of application. The peak's width increases linearly when increasing the depth. This green function seems to be in -at least- qualitative agreement with predictions of elastic theory.Comment: 9 pages, 3 .eps figures, submitted to PR

Quantum-beat Auger spectroscopy

The concept of nonlinear quantum-beat pump-probe Auger spectroscopy is introduced by discussing a relatively simple four-level model system. We consider a coherent wave packet involving two low-lying states that was prepared by an appropriate pump pulse. This wave packet is subsequently probed by a weak, time-delayed probe pulse with nearly resonant coupling to a core-excited state of the atomic or molecular system. The resonant Auger spectra are then studied as a function of the duration of the probe pulse and the time delay. With a bandwidth of the probe pulse approaching the energy spread of the wave packet, the Auger yields and spectra show quantum beats as a function of pump-probe delay. An analytic theory for the quantum-beat Auger spectroscopy will be presented, which allows for the reconstruction of the wave packet by analyzing the delaydependent Auger spectra. The possibility of extending this method to a more complex manifold of electronic and vibrational energy levels is also discussed.Comment: 13 papees,6 figure

Optimal parameter estimation of a depolarizing channel

We investigate strategies for estimating a depolarizing channel for a finite dimensional system. Our analysis addresses the double optimization problem of selecting the best input probe state and the measurement strategy that minimizes the Bayes cost of a quadratic function. In the qubit case, we derive the Bayes optimal strategy for any finite number of input probe particles when bipartite entanglement can be formed in the probe particles

Can one probe the structure function of the pomeron?

We discuss whether the diffractive structure functions defined by current experiments at HERA are indeed probing the partonic structure function of the pomeron. We observe that the {\it pseudorapidity} cuts commonly employed require that the struck parton in the pomeron be far off mass shell in sizeable regions of parameter space. As a result an interpretation in terms of constituent partons within the pomeron is inadequate. One may nevertheless use a partonic description for the {\it amplitude} for virtual photon-pomeron scattering to compute a diffractive structure function for pseudorapidity gap events. The resulting form may have significant scaling violation.Comment: 11 pages LaTeX, uses epsf, 5 eps figures appended as a uuencoded gzipped tarred fil

Heavy Flavour production as probe of Gluon Sivers Function

Heavy flavour production like $J/\psi$ and $D$- meson production in scattering of electrons/unpolarized protons off polarized proton target offer promising probes to investigate gluon Sivers function. In this talk, I will summarize our recent work on trasverse single spin asymmetry in $J/\psi$ -production and $D$ - meson production in $p p^\uparrow$ scattering using a generalized parton model approach. We compare predictions obtained using different models of gluon Sivers function within this approach and then, taking into account the transverse momentum dependent evolution of the unpolarized parton distribution functions and gluon Sivers function, we study the effect of evolution on asymmetry.Comment: Proceedings of Light Cone 2016, September 5-8, 2016, Universidade de Lisboa, Lisbon, Portuga

Propagating Coherent Acoustic Phonon Wavepackets in InMnAs/GaSb

We observe pronounced oscillations in the differential reflectivity of a ferromagnetic InMnAs/GaSb heterostructure using two-color pump-probe spectroscopy. Although originally thought to be associated with the ferromagnetism, our studies show that the oscillations instead result from changes in the position and frequency-dependent dielectric function due to the generation of coherent acoustic phonons in the ferromagnetic InMnAs layer and their subsequent propagation into the GaSb. Our theory accurately predicts the experimentally measured oscillation period and decay time as a function of probe wavelength.Comment: 4 pages, 4 figure

Scanning Fourier Spectroscopy: A microwave analog study to image transmission paths in quantum dots

We use a microwave cavity to investigate the influence of a movable absorbing center on the wave function of an open quantum dot. Our study shows that the absorber acts as a position-selective probe, which may be used to suppress those wave function states that exhibit an enhancement of their probability density near the region where the impurity is located. For an experimental probe of this wave function selection, we develop a technique that we refer to as scanning Fourier spectroscopy, which allows us to identify, and map out, the structure of the classical trajectories that are important for transmission through the cavity.Comment: 4 pages, 5 figure

Phase and amplitude of Aharonov-Bohm oscillations in nonlinear three-terminal transport through a double quantum dot

We study three-terminal linear and nonlinear transport through an Aharonov-Bohm interferometer containing a double quantum dot using the nonequilibrium Green's function method. Under the condition that one of the three terminals is a voltage probe, we show that the linear conductance is symmetric with respect to the magnetic field (phase symmetry). However, in the nonlinear transport regime, the phase symmetry is broken. Unlike two-terminal transport, the phase symmetry is broken even in noninteracting electron systems. Based on the lowest-order nonlinear conductance coefficient with respect to the source-drain bias voltage, we discuss the direction in which the phase shifts with the magnetic field. When the higher harmonic components of the Aharonov-Bohm oscillations are negligible, the phaseshift is a monotonically increasing function with respect to the source-drain bias voltage. To observe the Aharonov-Bohm oscillations with higher visibility, we need strong coupling between the quantum dots and the voltage probe. However, this leads to dephasing since the voltage probe acts as a B\"{u}ttiker dephasing probe. The interplay between such antithetic concepts provides a peak in the visibility of the Aharonov-Bohm oscillations when the coupling between the quantum dots and the voltage probe changes.Comment: 17 pages, 9 figures, accepted for publication in Physical Review