Detecting chiral pairing and topological superfluidity using circular dichroism

Realising and probing topological superfluids is a key goal for fundamental science, with exciting technological promises. Here, we show that chiral $p_x+ip_y$ pairing in a two-dimensional topological superfluid can be detected through circular dichroism, namely, as a difference in the excitation rates induced by a clockwise and counter-clockwise circular drive. For weak pairing, this difference is to a very good approximation determined by the Chern number of the superfluid, whereas there is a non-topological contribution scaling as the superfluid gap squared that becomes signifiant for stronger pairing. This gives rise to a competition between the experimentally driven goal to maximise the critical temperature of the superfluid, and observing a signal given by the underlying topology. Using a combination of strong coupling Eliashberg and Berezinskii-Kosterlitz-Thouless theory, we analyse this tension for an atomic Bose-Fermi gas, which represents a promising platform for realising a chiral superfluid. We identify a wide range of system parameters where both the critical temperature is high and the topological contribution to the dichroic signal is dominant.Comment: 6 pages, 3 figure

Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results

One-dimensional multi-component Fermi or Bose systems with strong zero-range interactions can be described in terms of local exchange coefficients and mapping the problem into a spin model is thus possible. For arbitrary external confining potentials the local exchanges are given by highly non-trivial geometric factors that depend solely on the geometry of the confinement through the single-particle eigenstates of the external potential. To obtain accurate effective Hamiltonians to describe such systems one needs to be able to compute these geometric factors with high precision which is difficult due to the computational complexity of the high-dimensional integrals involved. An approach using the local density approximation would therefore be a most welcome approximation due to its simplicity. Here we assess the accuracy of the local density approximation by going beyond the simple harmonic oscillator that has been the focus of previous studies and consider some double-wells of current experimental interest. We find that the local density approximation works quite well as long as the potentials resemble harmonic wells but break down for larger barriers. In order to explore the consequences of applying the local density approximation in a concrete setup we consider quantum state transfer in the effective spin models that one obtains. Here we find that even minute deviations in the local exchange coefficients between the exact and the local density approximation can induce large deviations in the fidelity of state transfer for four, five, and six particles.Comment: 12 pages, 7 figures, 1 table, final versio

Automatic Verification of Erlang-Style Concurrency

This paper presents an approach to verify safety properties of Erlang-style, higher-order concurrent programs automatically. Inspired by Core Erlang, we introduce Lambda-Actor, a prototypical functional language with pattern-matching algebraic data types, augmented with process creation and asynchronous message-passing primitives. We formalise an abstract model of Lambda-Actor programs called Actor Communicating System (ACS) which has a natural interpretation as a vector addition system, for which some verification problems are decidable. We give a parametric abstract interpretation framework for Lambda-Actor and use it to build a polytime computable, flow-based, abstract semantics of Lambda-Actor programs, which we then use to bootstrap the ACS construction, thus deriving a more accurate abstract model of the input program. We have constructed Soter, a tool implementation of the verification method, thereby obtaining the first fully-automatic, infinite-state model checker for a core fragment of Erlang. We find that in practice our abstraction technique is accurate enough to verify an interesting range of safety properties. Though the ACS coverability problem is Expspace-complete, Soter can analyse these verification problems surprisingly efficiently.Comment: 12 pages plus appendix, 4 figures, 1 table. The tool is available at http://mjolnir.cs.ox.ac.uk/soter

Liveness-Driven Random Program Generation

Randomly generated programs are popular for testing compilers and program analysis tools, with hundreds of bugs in real-world C compilers found by random testing. However, existing random program generators may generate large amounts of dead code (computations whose result is never used). This leaves relatively little code to exercise a target compiler's more complex optimizations. To address this shortcoming, we introduce liveness-driven random program generation. In this approach the random program is constructed bottom-up, guided by a simultaneous structural data-flow analysis to ensure that the generator never generates dead code. The algorithm is implemented as a plugin for the Frama-C framework. We evaluate it in comparison to Csmith, the standard random C program generator. Our tool generates programs that compile to more machine code with a more complex instruction mix.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Variability-aware Datalog

Variability-aware computing is the efficient application of programs to different sets of inputs that exhibit some variability. One example is program analyses applied to Software Product Lines (SPLs). In this paper we present the design and development of a variability-aware version of the Souffl\'{e} Datalog engine. The engine can take facts annotated with Presence Conditions (PCs) as input, and compute the PCs of its inferred facts, eliminating facts that do not exist in any valid configuration. We evaluate our variability-aware Souffl\'{e} implementation on several fact sets annotated with PCs to measure the associated overhead in terms of processing time and database size.Comment: PADL'20 pape

An Experimental Evaluation of Deliberate Unsoundness in a Static Program Analyzer

Abstract. Many practical static analyzers are not completely sound by design. Their designers trade soundness in order to increase automa-tion, improve performance, and reduce the number of false positives or the annotation overhead. However, the impact of such design decisions on the effectiveness of an analyzer is not well understood. In this pa-per, we report on the first systematic effort to document and evaluate the sources of unsoundness in a static analyzer. We present a code in-strumentation that reflects the sources of deliberate unsoundness in the.NET static analyzer Clousot. We have instrumented code from several open source projects to evaluate how often concrete executions violate Clousot’s unsound assumptions. In our experiments, this was the case in 8–29 % of all analyzed methods. Our approach and findings can guide users of static analyzers in using them fruitfully, and designers in finding good trade-offs.

Peptide-oligonucleotide conjugates as nanoscale building blocks for assembly of an artificial three-helix protein mimic

Peptide-based structures can be designed to yield artificial proteins with specific folding patterns and functions. Template-based assembly of peptide units is one design option, but the use of two orthogonal self-assembly principles, oligonucleotide triple helix and a coiled coil protein domain formation have never been realized for de novo protein design. Here, we show the applicability of peptide–oligonucleotide conjugates for self-assembly of higher-ordered protein-like structures. The resulting nano-assemblies were characterized by ultraviolet-melting, gel electrophoresis, circular dichroism (CD) spectroscopy, small-angle X-ray scattering and transmission electron microscopy. These studies revealed the formation of the desired triple helix and coiled coil domains at low concentrations, while a dimer of trimers was dominating at high concentration. CD spectroscopy showed an extraordinarily high degree of α-helicity for the peptide moieties in the assemblies. The results validate the use of orthogonal self-assembly principles as a paradigm for de novo protein design