49 citations · 91 across the 8 of their papers we have counts for
8 papers
A Local Law for Singular Values from Diophantine Equations
Arka Adhikari, Marius Lemm
We introduce the random matrices $$ X_{j,k}=\exp\left(2πi \sum_{q=1}^d\ ω_{j,q} k^q\right) \quad \text{with } \{ω_{j,q}\}_{\substack{1\leq j\leq N\\ 1\leq q\leq d}} \te…
A central limit theorem for integrals of random waves
Matthew de Courcy-Ireland, Marius Lemm
We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of arbit…
Gaplessness is not generic for translation-invariant spin chains
Marius Lemm
The existence of a spectral gap above the ground state has far-reaching consequences for the low-energy physics of a quantum many-body system. A recent work of Movassagh [R. Movass…
Finite-size criteria for spectral gaps in -dimensional quantum spin systems
Marius Lemm
We generalize the existing finite-size criteria for spectral gaps of frustration-free spin systems to dimensions. We obtain a local gap threshold of , independen…
Condensation of fermion pairs in a domain
Rupert L. Frank, Marius Lemm, Barry Simon
We consider a gas of fermions at zero temperature and low density, interacting via a microscopic two body potential which admits a bound state. The particles are confined to a doma…
Programming complex shapes in thin nematic elastomer and glass sheets
Paul Plucinsky, Marius Lemm, Kaushik Bhattacharya
Nematic elastomers and glasses are solids that display spontaneous distortion under external stimuli. Recent advances in the synthesis of sheets with controlled heterogeneities hav…