Sierra and Townsend (ST) [1] showed that the ``absorption spectrum''model of Connes [2] arises as the lowest-Landau-level (LLL) limit of a charged particle in crossed electric and magnetic fields, and suggested that the higher Landau levels supply the fluctuation part of the Riemann-zero counting function $N(E)$. Within the approximation used by ST we construct the eigenfunctions of an arbitrary Landau level $n$ and derive their asymptotics at the two box boundaries that ST identify. The boundary condition is the same as for $n=0$ up to an $E$-independent phase $(-\ii)^n$, so no $\ln E$ term arises for any fixed $n$. We also note that the $\ln E$ term in the semiclassical Eq.~(29) of ST is the first-order shift of the smooth LLL counting function, $E\to E+\gamma z^2$.
In the late 1990s, Suzuki and Yasuta proposed a compact formula that extracts the decay rate per unit volume of a false vacuum in the $D$-dimensional $O(N)$ $\lambda(\phi^2)^2$ theory with an unbounded potential from conventional perturbative coefficients of the vacuum energy density, i.e., vacuum bubble diagrams. The...
The free energy of any CFT, $ \ln Z(\beta; \omega_i)$, admits two expansions: high temperature ($\beta \rightarrow 0$) and fast rotation ($\omega_i \rightarrow 1$). We demonstrate that in $4d$, locality of the thermal effective action forces $\ln Z$ to take a simple analytic form at all orders in the high temperature e...
Arnav Advant, H. Anand, Nathan Benjamin et al.· 0 citations
We calculate the $\theta$ dependence of the vacuum energy in an infinite family of cousins of QCD, where the vacuum structure can be analyzed exactly. These theories are $\mathcal{N}=1$ EFTs that descend from $\mathcal{N}=2$ $SU(N_c)$ gauge theory with $N_f$ flavors of fundamental hypermultiplets, that are then deforme...
Dhruv Aldas, Hitoshi Murayama, B. Noether et al.· 0 citations
We study the focusing one-dimensional cubic nonlinear Schr\"odinger / Gross--Pitaevskii equation (NLS-GP), where the potential of the underlying linear Schr\"odinger operator, $H_V=-\partial_x^2+V(x)$, is compactly supported. In \cite{turner2026resonance} the authors proved that purely imaginary zeros (transmission res...
Luttinger theorem relates Fermi surface volume to electron density per spin $n$. It holds in an arbitrary Fermi liquid but is widely believed to break when a fermionic self-energy has a pole. We show that this is not necessarily the case. As an example, we consider a fermionic system consisting of two gapped bands, ori...
Let $Z_N$ be the partition function of the Sherrington-Kirkpatrick model at inverse temperature $\beta>1$. Replica theory (Kondor near the critical temperature, Parisi and Rizzo at all temperatures) predicts that the probability that $N^{-1}\log Z_N$ exceeds its typical value by $\delta$ decays like $\exp(-Na\delta^{6/...
Ru-Pei Yan· 0 citations
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