Scientific Series

Ever since there's been money, there have been people trying to counterfeit it, and governments trying to stop them. In 1969, the physicist Stephen Wiesner raised the remarkable possibility of money whose authenticity would be guaranteed by the laws of quantum mechanics. However, the question of whether one can have secure quantum money that anyone (not only the bank) can verify has remained open for forty years. In this talk, I'll tell you about progress on the question over the last two years. (1) I'll show that no publicly-verifiable quantum money scheme can have security based on quantum physics alone: like in most cryptography, one also needs a computational hardness assumption. (2) I'll show that one can have quantum money that remains hard to counterfeit, even if a counterfeiter gains access to a "black box" for verifying the money. (3) I'll describe a candidate quantum money scheme I proposed last spring, and how that scheme was recently broken by Lutomirski et al. I'll also discuss a new class of schemes that might evade the existing attacks -- schemes with the bizarre property that not even the bank can prepare the same bill twice. The talk is designed to be accessible to those without a quantum information background. Reference for (1)-(2): S. Aaronson, "Quantum copy-protection and quantum money," in Proceedings of CCC'2009, http://www.scottaaronson.com/papers/noclone-ccc.pdf. Reference for (3): A. Lutomirski, S. Aaronson, E. Farhi, D. Gosset, A. Hassidim, J. Kelner, and P. Shor. Breaking and making quantum money: toward a new quantum cryptographic protocol, Proceedings of Innovations in Computer Science (ICS), 2010. http://arxiv.org/abs/0912.3825.

The radio-metric tracking data received from the Pioneer 10 and 11 spacecraft from the distances between 20--70 astronomical units from the Sun has consistently indicated the presence of a small, anomalous, blue-shifted Doppler frequency drift that limited the accuracy of the orbit reconstruction for these vehicles. This drift was interpreted as a sunward acceleration of aP = (8.74 1.33)  1010 m/s2 for each particular spacecraft. This signal has become known as the Pioneer anomaly; the nature of this anomaly is currently being investigated. Recently new Pioneer 10 and 11 radio-metric Doppler and flight telemetry data became available. The newly available Doppler data set is much larger when compared to the data used in previous investigations and is the primary source for new investigation of the anomaly. In addition, the flight telemetry files, original project documentation, and newly developed software tools are now used to reconstruct the engineering history of spacecraft. With the help of this information, a thermal model of the Pioneer vehicles is being developed to study the contribution of thermal recoil force acting on the two spacecraft. The goal of the ongoing efforts is to evaluate the effect of the on-board systems on the spacecrafts' trajectories and possibly identify the nature of this anomaly. The current status of these investigations will be discussed. Besides the Pioneer anomaly, there are other intriguing puzzles in the solar system dynamics still awaiting a proper explanation, notably the, so-called, “fly-by anomaly”, that occurred during Earth gravity assists performed by several interplanetary spacecraft. We will discuss the observed effect, the conditions that led to its observation and will elaborate on the potential causes of this anomaly. This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration.

While the properties of gravity, and its consistency with General Relativity (GR), are well tested on solar system scales, within our system and the decay of binary pulsar orbits, they are, by comparison, poorly tested on cosmic scales. This is of particular interest as we try to understand the origins of cosmic acceleration, and whether they are a signature of deviations from GR. Using the latest measurements of the universe's expansion history, twinned with the evolution of large scale structure, we discuss the current constraints on gravity's behavior on the largest scales observable today.

Standard inflationary theory predicts that primordial fluctuations in the universe were nearly Gaussian random. Therefore, searches for, and limits on, primordial nongaussianity are some of the most fundamental tests of inflation and the early universe in general. I first briefly review the history of its measurements from the cosmic microwave background anisotropies and large-scale structure in the universe. I then present results from recent work where effects of primordial nongaussianity on the distribution of largest virialized objects was studied numerically and analytically. We found that the bias of dark matter halos takes strong scale dependence in nongaussian cosmological models. Therefore, measurements of scale dependence of the bias, using various tracers of large-scale structure, can - and do - constrain primordial nongaussianity more than an order of magnitude better than previously thought.

The graph isomorphism (GI) problem plays a central role in the theory of computational complexity and has importance in physics and chemistry as well. While no general efficient algorithm for solving GI is known, it is unlikely to be NP-complete; in this regard it is similar to the factoring problem, for which Shor has developed an efficient quantum algorithm. In this talk I will discuss our investigations of quantum particles walking on graphs and their implications for possible algorithms for GI. We find that single-particle quantum random walks fail to distinguish some nonequivalent graphs that can be distinguished by random walks with two interacting particles. The implications of these observations for classical and quantum algorithms for GI will be discussed.

It is usually assumed that dark matter direct detection is sensitive to a large fraction of the dark matter (DM) velocity distribution. I will explain an alternative form of dark matter-nucleus scattering which only probes a narrow range of DM velocities due to the existence of a resonance, a DM-nucleus bound state, in the scattering - resonant dark matter (rDM). The scattering cross section becomes highly element dependent, has increased modulation and as a result can explain the DAMA/LIBRA results whilst not being in conflict with other direct detection experiments. I will describe a simple model that realizes the dynamics of rDM, where the DM is the neutral component of a fermionic weak triplet whose charged partners differ in mass by approximately 10 MeV.

The simplest gravity duals for quantum critical theories with 'Lifshitz' scale invariance admit a marginally relevant deformation. We will explore the holographic renormalization of such theories, including this deformation. Additionally we explore how this holographic renormalization illuminates the physics of black holes in the qunatum critical regime.

Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. We review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the equivalence can only be established by passing to Abelian(ised) constraints which is always possible locally in phase space. With the above general considerations, we derive concretely the path integral formulations for GR from the canonical theory. We also show that there in principle exists a spin-foam model consistent with the canonical theory of GR.

The asymptotic formula for the Ponzano-Regge model amplitude is given for non-tardis triangulations of handlebodies in the limit of large boundary spins. The formula produces a sum over all possible immersions of the boundary triangulation in three dimensional Euclidean space weighted by the cosine of the Regge action evaluated on these immersions. Furthermore the asymptotic scaling registers the existence of flexible immersions.

Scalar field models of early universe inflation are effective field theories, typically valid only up to some UV energy scale, and receive corrections through higher dimensional operators due to the UV physics. Corrections to the tree level inflationary potential by these operators can ruin an otherwise suitable model of inflation. In this talk, I will consider higher dimensional kinetic operators, and the corrections that they give to the dynamics of the inflaton field. In particular, I will show how inflationary solutions exist even when the higher dimensional operators are important and not tuned to be negligible. I will then show that these solutions, which include the usual slow roll inflationary solutions, are attractors in phase space. I will end by speculating on the role of the corrections from these higher dimensional operators in alleviating the homogeneous initial conditions problem for inflation.

When a pair of particles is produced close to threshold, they may form a bound state if the potential between them is attractive. Can we use such bound states to obtain information about new colored particles at the LHC? I will discuss the relevant issues using examples from the MSSM and other beyond the standard model scenarios.

In the context of AdS/CFT correspondence the AdS_3/CFT_2 instance of the duality stands apart from other well studied cases, like AdS_5/CFT_4 or AdS_4/CFT_3. One of the reasons is that the CFT side of this duality is not a theory of matrices but rather a two dimensional orbifold based on the group of permutations. In this talk we will discuss some aspects of this theory. In particular a diagrammatic language, akin to Feynman diagrams used for gauge theories, will be developed. Moreover, we will compute a large set of protected quantities in a certain symmetric product orbifold CFT, and show that these are elegantly given in terms of Hurwitz numbers.