We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m2 ≈ 0.58 such that the system is stable, i.e., the energy is bounded from below, for m in [m_{2}, m_{2}^{-1}]. So far it was not known whether this 2 + 2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N + M system.

In the present work, we extend our previous work with Gwilliam by realizing $\hat {A}(X)$ as the projective volume form associated to the BV operator in our quantization of a one-dimensional sigma model. We also discuss the associated integration/expectation map. We work in the formalism of L ∞ spaces, objects of which are computationally convenient presentations for derived stacks. Both smooth and complex geometry embed into L ∞ spaces and we specialize our results in both of these cases.

We consider a quantum particle interacting with $N$ obstacles, whose positions are independently chosen according to a given probability density, through a two-body potential of the form $N^2 V(Nx)$ (Gross-Pitaevskii potential). We show convergence of the $N$ dependent one-particle Hamiltonian to a limiting Hamiltonian where the quantum particle experiences an effective potential depending only on the scattering length of the unscaled potential and the density of the obstacles. In this sense our Lorentz gas model exhibits a universal behavior for $N$ large. Moreover we explicitely characterize the fluctuations around the limit operator. Our model can be considered as a simplified model for scattering of slow neutrons from condensed matter.

This paper investigates lozenge tilings of non-convex hexagonal regions and more specifically the asymptotic fluctuations of the tilings within and near the strip formed by opposite cuts in the regions, when the size of the regions tend to infinity, together with the cuts. It leads to a new kernel, which is expected to have universality properties.

We compute K-theory for the reduced group C*-algebras of generalized Lamplighter groups.

We study field diffeomorphisms $\Phi(x)= F(\rho(x))=a_0\rho(x)+a_1\rho^2(x)+\ldots=\sum_{j+0}^\infty a_j \rho^{j+1}$, for free and interacting quantum fields $\Phi$. We find that the theory is invariant under such diffeomorphisms if and only if kinematic renormalization schemes are used.

The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary conditions, we find a lower bound to the spectral gap around zero, proportional to $|\Omega|^{-1/2}$, where $\Omega \subset \mathbb{R}^2$ is the bounded region where the Dirac operator acts. This family contains the so-called infinite mass and armchair cases used in the physics literature for the description of graphene quantum dots.

In this note we establish the convergence of the stochastic six-vertex model to the one-dimensional asymmetric simple exclusion process, under a certain limit regime recently predicted by Borodin-Corwin-Gorin. This convergence holds for arbitrary initial data.

In [1, 2, 3] the Corolla Polynomial $ \mathcal C (\Gamma) \in \mathbb C [a_{h_1}, \ldots, a_{h_{\left \vert \Gamma^{[1/2]} \right \vert}}] $ was introduced as a graph polynomial in half-edge variables $ \left \{ a_h \right \} _{h \in \Gamma^{[1/2]}} $ over a 3-regular scalar quantum field theory (QFT) Feynman graph $ \Gamma $. It allows for a covariant quantization of pure Yang-Mills theory without the need for introducing ghost fields, clarifies the relation between quantum gauge theory and scalar QFT with cubic interaction and translates back the problem of renormalizing quantum gauge theory to the problem of renormalizing scalar QFT with cubic interaction (which is super renormalizable in 4 dimensions of spacetime). Furthermore, it is, as we believe, useful for computer calculations. In [4] on which this paper is based the formulation of [1, 2, 3] gets slightly altered in a fashion specialized in the case of the Feynman gauge. It is then formulated as a graph polynomial $ \mathcal C ( \Gamma ) \in \mathbb C [a_{h_{1 \pm}}, \ldots, a_{h_{\left \vert \Gamma^{[1/2]} \right \vert} \vphantom{h}_\pm}, b_{h_1}, \ldots, b_{h_{\left \vert \Gamma^{[1/2]} \right \vert}}] $ in three different types of half-edge variables $ \left \{ a_{h_+} , a_{h_-} , b_h \right \} _{h \in \Gamma^{[1/2]}} $. This formulation is also suitable for the generalization to the case of spontaneously broken gauge theories (in particular all bosons from the Standard Model), as was first worked out in [4] and gets reviewed here.

We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.