TY - CHAP AB - Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept. AU - Biswas, Ranita AU - Bhowmick, Partha ID - 5803 SN - 0302-9743 T2 - Combinatorial image analysis TI - Construction of persistent Voronoi diagram on 3D digital plane VL - 10256 ER - TY - CONF AB - Tunneling of a particle through a potential barrier remains one of the most remarkable quantum phenomena. Owing to advances in laser technology, electric fields comparable to those electrons experience in atoms are readily generated and open opportunities to dynamically investigate the process of electron tunneling through the potential barrier formed by the superposition of both laser and atomic fields. Attosecond-time and angstrom-space resolution of the strong laser-field technique allow to address fundamental questions related to tunneling, which are still open and debated: Which time is spent under the barrier and what momentum is picked up by the particle in the meantime? In this combined experimental and theoretical study we demonstrate that for strong-field ionization the leading quantum mechanical Wigner treatment for the time resolved description of tunneling is valid. We achieve a high sensitivity on the tunneling barrier and unambiguously isolate its effects by performing a differential study of two systems with almost identical tunneling geometry. Moreover, working with a low frequency laser, we essentially limit the non-adiabaticity of the process as a major source of uncertainty. The agreement between experiment and theory implies two substantial corrections with respect to the widely employed quasiclassical treatment: In addition to a non-vanishing longitudinal momentum along the laser field-direction we provide clear evidence for a non-zero tunneling time delay. This addresses also the fundamental question how the transition occurs from the tunnel barrier to free space classical evolution of the ejected electron. AU - Camus, Nicolas AU - Yakaboylu, Enderalp AU - Fechner, Lutz AU - Klaiber, Michael AU - Laux, Martin AU - Mi, Yonghao AU - Hatsagortsyan, Karen AU - Pfeifer, Thomas AU - Keitel, Cristoph AU - Moshammer, Robert ID - 313 IS - 1 SN - 17426588 TI - Experimental evidence for Wigner's tunneling time VL - 999 ER - TY - JOUR AB - The first hundred attoseconds of the electron dynamics during strong field tunneling ionization are investigated. We quantify theoretically how the electron’s classical trajectories in the continuum emerge from the tunneling process and test the results with those achieved in parallel from attoclock measurements. An especially high sensitivity on the tunneling barrier is accomplished here by comparing the momentum distributions of two atomic species of slightly deviating atomic potentials (argon and krypton) being ionized under absolutely identical conditions with near-infrared laser pulses (1300 nm). The agreement between experiment and theory provides clear evidence for a nonzero tunneling time delay and a nonvanishing longitudinal momentum of the electron at the “tunnel exit.” AU - Camus, Nicolas AU - Yakaboylu, Enderalp AU - Fechner, Lutz AU - Klaiber, Michael AU - Laux, Martin AU - Mi, Yonghao AU - Hatsagortsyan, Karen Z. AU - Pfeifer, Thomas AU - Keitel, Christoph H. AU - Moshammer, Robert ID - 6013 IS - 2 JF - Physical Review Letters SN - 0031-9007 TI - Experimental evidence for quantum tunneling time VL - 119 ER - TY - CONF AB - Position based cryptography (PBC), proposed in the seminal work of Chandran, Goyal, Moriarty, and Ostrovsky (SIAM J. Computing, 2014), aims at constructing cryptographic schemes in which the identity of the user is his geographic position. Chandran et al. construct PBC schemes for secure positioning and position-based key agreement in the bounded-storage model (Maurer, J. Cryptology, 1992). Apart from bounded memory, their security proofs need a strong additional restriction on the power of the adversary: he cannot compute joint functions of his inputs. Removing this assumption is left as an open problem. We show that an answer to this question would resolve a long standing open problem in multiparty communication complexity: finding a function that is hard to compute with low communication complexity in the simultaneous message model, but easy to compute in the fully adaptive model. On a more positive side: we also show some implications in the other direction, i.e.: we prove that lower bounds on the communication complexity of certain multiparty problems imply existence of PBC primitives. Using this result we then show two attractive ways to “bypass” our hardness result: the first uses the random oracle model, the second weakens the locality requirement in the bounded-storage model to online computability. The random oracle construction is arguably one of the simplest proposed so far in this area. Our results indicate that constructing improved provably secure protocols for PBC requires a better understanding of multiparty communication complexity. This is yet another example where negative results in one area (in our case: lower bounds in multiparty communication complexity) can be used to construct secure cryptographic schemes. AU - Brody, Joshua AU - Dziembowski, Stefan AU - Faust, Sebastian AU - Pietrzak, Krzysztof Z ED - Kalai, Yael ED - Reyzin, Leonid ID - 605 SN - 978-331970499-9 TI - Position based cryptography and multiparty communication complexity VL - 10677 ER - TY - CHAP AB - In several settings of physics and chemistry one has to deal with molecules interacting with some kind of an external environment, be it a gas, a solution, or a crystal surface. Understanding molecular processes in the presence of such a many-particle bath is inherently challenging, and usually requires large-scale numerical computations. Here, we present an alternative approach to the problem, based on the notion of the angulon quasiparticle. We show that molecules rotating inside superfluid helium nanodroplets and Bose–Einstein condensates form angulons, and therefore can be described by straightforward solutions of a simple microscopic Hamiltonian. Casting the problem in the language of angulons allows us not only to greatly simplify it, but also to gain insights into the origins of the observed phenomena and to make predictions for future experimental studies. AU - Lemeshko, Mikhail AU - Schmidt, Richard ED - Dulieu, Oliver ED - Osterwalder, Andreas ID - 604 SN - 20413181 T2 - Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zero TI - Molecular impurities interacting with a many-particle environment: From ultracold gases to helium nanodroplets VL - 11 ER -