The universal Khovanov chain complex of a knot modulo an appropriate equivalence relation is shown to yield a homomorphism on the smooth concordance group, which is strictly stronger than all Rasmussen invariants over fields of different characteristics combined.

Lukas Lewark

Using a recent result of Bowden, Hensel and Webb, we prove the existence of a homeomorphism with positive stable commutator length in the group of homeomorphisms of the Klein bottle which are isotopic to the identity.

Lukas Böke

As new technologies are invented, their commercial viability needs to be carefully examined along with their technical merits and demerits. The posit data format, proposed as a drop-in replacement for IEEE 754 float format, is one such invention that requires extensive theoretical and experimental study to identify products that can benefit from the advantages of posits for specific market segments. In this paper, we present an extensive empirical study of posit-based arithmetic vis-\`a-vis IEEE 754 compliant arithmetic for the optical flow estimation method called Lucas-Kanade (LuKa). First, we use SoftPosit and SoftFloat format emulators to perform an empirical error analysis of the LuKa method. Our study shows that the average error in LuKa with SoftPosit is an order of magnitude lower than LuKa with SoftFloat. We then present the integration of the hardware implementation of a posit adder and multiplier in a RISC-V open-source platform. We make several recommendations, along with the analysis of LuKa in the RISC-V context, for future generation platforms incorporating posit arithmetic units.

Vinay Saxena Ankitha Reddy Jonathan Neudorfer John Gustafson Sangeeth Nambiar Rainer Leupers Farhad Merchant

Superfluids can transport heat via simultaneous opposite flows of their spatially interpenetrating condensate and thermal components. While this internal convection is usually described within Landau's phenomenological two fluid hydrodynamics, we apply quantum kinetic theory to a dilute Bose gas held beween thermal reservoirs at different temperatures, and show that the phenomenon also appears in collisionless kinetic regimes, and should be directly observable in currently feasible experiments on trapped ultracold vapors.

Lukas Gilz James R. Anglin

We analyze an autonomous micro-engine as a closed quantum mechanical system, including the work it performs and the fuel it consumes. Our model system shows by example that it is possible to transfer energy steadily and spontaneously between fast and slow degrees of freedom, in analogy to the way combustion engines convert chemical energy into work. Having shown this possibility, we observe close analogies between the closed-system quantum dynamics of our micro-engine and the First and Second Law of Thermodynamics. From these analogies we deduce a generalized formulation of thermodynamics that remains valid on the micro-scale.

Lukas Gilz Eike P. Thesing James R. Anglin

Nonclassical quantum effects gradually reach domains of physics of large systems previously considered as purely classical. We derive a hierarchy of operational criteria suitable for a reliable detection of nonclassicality of light from an arbitrarily large ensemble of independent single-photon emitters. We show, that such large ensemble can always emit nonclassical light without any phase reference and under realistic experimental conditions including incoherent background noise. The nonclassical light from the large ensemble of the emitters can be witnessed much better than light coming from a single or a few emitters.

Lukáš Lachman Lukáš Slodička Radim Filip

We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant version of excision and prove that it extends to an equivariant topological field theory with values in the $(\infty,1)$-category of cospans of $E_\infty$-algebras.

Lukas Müller Lukas Woike

We prove a decomposition formula for the dimensional reduction of an extended topological field theory that arises as an orbifold of an equivariant topological field theory. Our decomposition formula can be expressed in terms of a categorification of the integral with respect to groupoid cardinality. The application of our result to topological field theories of Dijkgraaf-Witten type proves a recent conjecture of Qiu-Wang.

Lukas Müller Lukas Woike

We prove that for a self-injective ribbon Grothendieck-Verdier category $\mathcal{C}$ in the sense of Boyarchenko-Drinfeld the cyclic action on the Hochschild complex of $\mathcal{C}$ extends to an action of the diffeomorphism group of the solid closed torus $\mathbb{S}^1 \times \mathbb{D}^2$.

Lukas Müller Lukas Woike

Carlo is a Monte Carlo simulation framework written in Julia. It provides MPI-parallel scheduling, organized storage of input, checkpoint, and output files, as well as statistical postprocessing. With a minimalist design, it aims to aid the development of high-quality Monte Carlo codes, especially for demanding applications in condensed matter and statistical physics. This hands-on user guide shows how to implement a simple code with Carlo and provides benchmarks to show its efficacy.

Lukas Weber