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TBA

We are interested in the problem of understanding the structure of the Bethe roots for the periodic spin-1/2 Heisenberg XXZ chain. To probe this structure it is fruitful to study what happens as one varies the parameters. We start with the (ferromagnetic) Ising limit ∆ → ∞, in which ​the Bethe roots become explicit, and strings of Bethe roots become directly visible on the lattice, already examined by Gaudin. Despite the simplicity of the limiting model, there are some subtleties in the limit. Next we study what happens with the explicit Ising Bethe roots as ∆ is lowered, where bound states may form or unbind. I will present a ‘critical equation’ that determines when Bethe roots switch between real and complex for the sector with M = 2 magnons, generalising Essler–Korepin–Schoutens (1992, ∆ = 1) and Imoto–Sato–Deguchi (2019, ∆ ≥ 1), and discuss some results for M > 2. If time allows, I will outline how a similar game can be played by turning on long-range interactions, going from Heisenberg XXX, via the Inozemtsev chain, to the Haldane-Shasatry chain.

This is based on joint work J.-S. Caux and R. Koch, to appear, and with R. Klabbers (2022).

We study the long-time, large-distance asymptotic behaviour of dynamical two-point correlation functions of the Lieb–Liniger model in the limit of infinite repulsion (the one-dimensional impenetrable Bose gas). Starting with exact representations of correlation functions in terms of Fredholm determinants of an integrable integral operator, we perform the rigorous asymptotic analysis, using Riemann–Hilbert techniques. The integral operator
depends parametrically on time \(t\), distance \(x\) and on the filling fraction — a function that characterizes the thermal or non-thermal equilibrium conditions. We consider a large class of non-thermal equilibrium conditions, extending previous results established for the thermal equilibrium case. The long-time and large-distance asymptotic behaviour is derived for two classes of filling fractions. These classes are characterized by the number of poles on the real axis (a generalization of Fermi points) that, together with the unique saddle point, contribute to the asymptotic expansion. For each class, we derive the long-time, large-distance symptotic behaviour as a series in \(x\)^\(−1/2\) as \(x\) and \(t\) go to infinity for a fixed ratio \(x/t\). We provide explicit closed-form expressions for the leading and sub-leading terms, logarithmic corrections, and overall constants in terms of special functions and simple integrals. For the impenetrable Bose gas in thermal equilibrium, we verify the derived asymptotic expansions by comparing them with the existing results in the literature and with numerical data.
This talk is based on joint work with Frank Göhmann, Karol K. Kozlowski, and Alexander Weiße.

After describing elastic interactions and the discovery of the odderon by the TOTEM and D0 Collaborations, we will discuss new kinematical regimes where the gluon density in the proton or Pb can be very large which leads to new equations in Quantum Chromodynamics.  We will also present the latest expectations on beyond standard model physics and especially the production of axion-like particles using intact protons after the collision.  We will finish by describing briefly the Low Gain Avalanche Detectors and their applications in medicine for cancer treatment and with NASA to measure cosmic rays.