Two Black Hole Holography, Lensing and Intensity

We numerically verify the analysis of the "expanding horizon" theory of Susskind in relation to the 't Hooft holographic conjecture. By using a numerical simulation to work out the image formed by two black holes upon a screen very far away, it is seen that it is impossible for a horizon to hide behind another. We also compute the intensity distribution of such an arrangement.Comment: 10 page

Computing the spectrum of black hole radiation in the presence of high frequency dispersion: an analytical approach

We present a method for computing the spectrum of black hole radiation of a scalar field satisfying a wave equation with high frequency dispersion. The method involves a combination of Laplace transform and WKB techniques for finding approximate solutions to ordinary differential equations. The modified wave equation is obtained by adding a higher order derivative term suppressed by powers of a fundamental momentum scale $k_0$ to the ordinary wave equation. Depending on the sign of this new term, high frequency modes propagate either superluminally or subluminally. We show that the resulting spectrum of created particles is thermal at the Hawking temperature, and further that the out-state is a thermal state at the Hawking temperature, to leading order in $k_0$, for either modification.Comment: 26 pages, plain latex, 6 figures included using psfi

Fermionic microstates within Painlev\'e-Gullstrand black hole

We consider the quantum vacuum of fermionic field in the presence of a black-hole background as a possible candidate for the stabilized black hole. The stable vacuum state (as well as thermal equilibrium states with arbitrary temperature) can exist if we use the Painlev\'e-Gullstrand description of the black hole, and the superluminal dispersion of the particle spectrum at high energy, which is introduced in the free-falling frame. Such choice is inspired by the analogy between the quantum vacuum and the ground state of quantum liquid, in which the event horizon for the low-energy fermionic quasiparticles also can arise. The quantum vacuum is characterized by the Fermi surface, which appears behind the event horizon. We do not consider the back reaction, and thus there is no guarantee that the stable black hole exists. But if it does exist, the Fermi surface behind the horizon would be the necessary attribute of its vacuum state. We also consider exact discrete spectrum of fermions inside the horizon which allows us to discuss the problem of fermion zero modes.Comment: LaTeX, 20 pages, 2 figure

Diffusion constant of supercharge density in N=4 SYM at finite chemical potential

We compute holographically the diffusion constant of supercharges in N=4 SYM at finite chemical potential for the R-charge, by solving the equations of motion for the transverse mode of the gravitino in the STU black hole in 5 dimensions. We consider the case of one charge and three charges, and we present analytical solutions for small values of the charges and numerical solutions for arbitrary values. We compare our results with other known results in 4 dimensions.Comment: 20 pages, 4 figures; v2: typos correcte

Fermion zero modes in Painlev\'e-Gullstrand black hole

Painleve-Gullstrand metric of the black hole allows to discuss the fermion zero modes inside the hole. The statistical mechanics of the fermionic microstates can be responsible for the black hole thermodynamics. Fermion zero modes also lead to quantization of the horizon area.Comment: LaTeX, 13 pages, no figures, version submitted to JETP Leter

Large-scale non-locality in "doubly special relativity" with an energy-dependent speed of light

There are two major alternatives for violating the (usual) Lorentz invariance at large (Planckian) energies or momenta - either not all inertial frames (in the Planck regime) are equivalent (e.g., there is an effectively preferred frame) or the transformations from one frame to another are (non-linearly) deformed (``doubly special relativity''). We demonstrate that the natural (and reasonable) assumption of an energy-dependent speed of light in the latter method goes along with violations of locality/separability (and even translational invariance) on macroscopic scales. PACS: 03.30.+p, 11.30.Cp, 04.60.-m, 04.50.+h.Comment: 5 pages RevTeX, several modification

Holographic three-point functions of giant gravitons

Working within the AdS/CFT correspondence we calculate the three-point function of two giant gravitons and one pointlike graviton using methods of semiclassical string theory and considering both the case where the giant gravitons wrap an S^3 in S^5 and the case where the giant gravitons wrap an S^3 in AdS_5. We likewise calculate the correlation function in N=4 SYM using two Schur polynomials and a single trace chiral primary. We find that the gauge and string theory results have structural similarities but do not match perfectly, and interpret this in terms of the Schur polynomials' inability to interpolate between dual giant and pointlike gravitons.Comment: 21 page

Quantum geometry and gravitational entropy

Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S^5 universes. In this sector we devise a "coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.Comment: 29 pages, 2 figures; references adde

Lattice deformation at the sub-micron scale: X-ray nanobeam measurements of elastic strain in electron shuttling devices

The lattice strain induced by metallic electrodes can impair the functionality of advanced quantum devices operating with electron or hole spins. Here we investigate the deformation induced by CMOS-manufactured titanium nitride electrodes on the lattice of a buried, 10 nm-thick Si/SiGe Quantum Well by means of nanobeam Scanning X-ray Diffraction Microscopy. We were able to measure TiN electrode-induced local modulations of the strain tensor components in the range of $2 - 8 \times 10^{-4}$ with ~60 nm lateral resolution. We have evaluated that these strain fluctuations are reflected into local modulations of the potential of the conduction band minimum larger than 2 meV, which is close to the orbital energy of an electrostatic quantum dot. We observe that the sign of the strain modulations at a given depth of the quantum well layer depends on the lateral dimensions of the electrodes. Since our work explores the impact of device geometry on the strain-induced energy landscape, it enables further optimization of the design of scaled CMOS-processed quantum devices.Comment: 16 pages, 6 figure