Time dependent local potential in a Tomonaga-Luttinger liquid

We study the energy deposition in a one dimensional interacting quantum system with a point like potential modulated in amplitude. The point like potential at position $x=0$ has a constant part and a small oscillation in time with a frequency $\omega$. We use bosonization, renormalization group and linear response theory to calculate the corresponding energy deposition. It exhibits a power law behavior as a function of the frequency that reflects the Tomonaga-Luttinger liquid (TLL) nature of the system. Depending on the interactions in the system, characterized by the TLL parameter $K$ of the system, a crossover between week and strong coupling for the backscattering due to the potential is possible. We compute the frequency scale $\omega_\ast$, at which such crossover exists. We find that the energy deposition due to the backscattering shows different exponent for $K>1$ and $K<1$. We discuss possible experimental consequences, in the context of cold atomic gases, of our theoretical results.Comment: 13 pages, 3 figure

Towards Accountable AI: Hybrid Human-Machine Analyses for Characterizing System Failure

As machine learning systems move from computer-science laboratories into the open world, their accountability becomes a high priority problem. Accountability requires deep understanding of system behavior and its failures. Current evaluation methods such as single-score error metrics and confusion matrices provide aggregate views of system performance that hide important shortcomings. Understanding details about failures is important for identifying pathways for refinement, communicating the reliability of systems in different settings, and for specifying appropriate human oversight and engagement. Characterization of failures and shortcomings is particularly complex for systems composed of multiple machine learned components. For such systems, existing evaluation methods have limited expressiveness in describing and explaining the relationship among input content, the internal states of system components, and final output quality. We present Pandora, a set of hybrid human-machine methods and tools for describing and explaining system failures. Pandora leverages both human and system-generated observations to summarize conditions of system malfunction with respect to the input content and system architecture. We share results of a case study with a machine learning pipeline for image captioning that show how detailed performance views can be beneficial for analysis and debugging

Dynamics of a Mobile Impurity in a Two Leg Bosonic Ladder

We have analyzed the behavior of a mobile quantum impurity in a bath formed by a two-leg bosonic ladder by a combination of field theory (Tomonaga-Luttinger liquid) and numerical (Density Matrix Renormalization Group) techniques. Computing the Green's function of the impurity as a function of time at different momenta, we find a power law decay at zero momentum, which signals the breakdown of any quasi-particle description of the impurity motion. We compute the exponent both for the limits of weak and strong impurity-bath interactions. At small impurity-bath interaction, we find that the impurity experiences the ladder as a single channel one-dimensional bath, but effective coupling is reduced by a factor of $\sqrt 2$, thus the impurity is less mobile in the ladder compared to a one dimensional bath. We compared the numerical results for the exponent at zero momentum with a semi-analytical expression that was initially established for the chain and find excellent agreement without adjustable parameters. We analyze the dependence of the exponent in the transverse hopping in the bath and find surprisingly an increase of the exponent at variance with the naive extrapolation of the single channel regime. We study the momentum dependence of the impurity Green's function and find that, as for the single chain, two different regime of motion exist, one dominated by infrared metatrophy and a more conventional polaronic behavior. We compute the critical momentum between these two regimes and compare with prediction based on the structure factor of the bath. In the polaronic regime we also compute numerically the lifetime of the polaron. Finally we discuss how our results could be measured in cold atomic experiments.Comment: 14 Pages, 13 figure

Stochastic Privacy

Online services such as web search and e-commerce applications typically rely on the collection of data about users, including details of their activities on the web. Such personal data is used to enhance the quality of service via personalization of content and to maximize revenues via better targeting of advertisements and deeper engagement of users on sites. To date, service providers have largely followed the approach of either requiring or requesting consent for opting-in to share their data. Users may be willing to share private information in return for better quality of service or for incentives, or in return for assurances about the nature and extend of the logging of data. We introduce \emph{stochastic privacy}, a new approach to privacy centering on a simple concept: A guarantee is provided to users about the upper-bound on the probability that their personal data will be used. Such a probability, which we refer to as \emph{privacy risk}, can be assessed by users as a preference or communicated as a policy by a service provider. Service providers can work to personalize and to optimize revenues in accordance with preferences about privacy risk. We present procedures, proofs, and an overall system for maximizing the quality of services, while respecting bounds on allowable or communicated privacy risk. We demonstrate the methodology with a case study and evaluation of the procedures applied to web search personalization. We show how we can achieve near-optimal utility of accessing information with provable guarantees on the probability of sharing data