20 citations · 72 across the 28 of their papers we have counts for
32 papers
Bernoulli flow for Erdős-Rényi graphs
Joscha Henheik, Antti Knowles
We study the eigenvalues and eigenvectors of the adjacency matrix of the Erdős-Rényi graph in the regime . We establish optimal isotropic de…
Anomalous rate of eigenstate thermalisation at singularities of the density of states
László Erdős, Joscha Henheik, Volodymyr Riabov
We prove the Eigenstate Thermalisation Hypothesis (ETH), also known as Quantum Unique Ergodicity (QUE), for large mean-field random matrices with general correlation st…
On a Rosenzweig-Porter-type model
Giorgio Cipolloni, László Erdős, Joscha Henheik
We consider a very general Rosenzweig-Porter-type model, , where is an arbitrary Hermitian matrix and is a standard Wigner matrix. We precisely trace the locali…
Spectral rigidity of two-dimensional Liouville tori
Joscha Henheik, Vadim Kaloshin, Yunzhe Li +1
It is a folklore conjecture that Liouville metrics are the only Riemannian metrics with integrable geodesic flow on the two-dimensional torus. In this paper, we study Laplace-isosp…
Uniform-in-temperature locality estimates for weakly interacting quantum systems
Arka Adhikari, Joscha Henheik, Marius Lemm +1
The locality of thermal quantum states has emerged as a key input for applications to thermalization, response theory, and efficient simulability. Locality is either captured by th…
Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model
László Erdős, Joscha Henheik, Cornelia Vogel
We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve in…
Law of fractional logarithm for random matrices
Zhigang Bao, Giorgio Cipolloni, László Erdős +2
We prove the Paquette-Zeitouni law of fractional logarithm (LFL) for the extreme eigenvalues [arXiv:1505.05627] in full generality, and thereby verify a conjecture from [arXiv:1505…
Decorrelation transition in the Wigner minor process
Zhigang Bao, Giorgio Cipolloni, László Erdős +2
We consider the Wigner minor process, i.e. the eigenvalues of an Wigner matrix together with the eigenvalues of all its minors, , $n\le N…
Cusp Universality for Correlated Random Matrices
László Erdős, Joscha Henheik, Volodymyr Riabov
For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states…
Multi-band superconductors have enhanced critical temperatures
Joscha Henheik, Edwin Langmann, Asbjørn Bækgaard Lauritsen
We introduce a multi-band BCS free energy functional and prove that for a multi-band superconductor the effect of inter-band coupling can only increase the critical temperature, ir…
Response theory for locally gapped systems
Joscha Henheik, Tom Wessel
We introduce a notion of a \emph{local gap} for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo's formula for localized perturbatio…
Loschmidt Echo for Deformed Wigner Matrices
László Erdős, Joscha Henheik, Oleksii Kolupaiev
We consider two Hamiltonians that are close to each other, , and analyze the time-decay of the corresponding Loschmidt echo $\mathfrak{M}(t) := |\langle ψ_0, \mat…
Eigenvector decorrelation for random matrices
Giorgio Cipolloni, László Erdős, Joscha Henheik +1
We study the sensitivity of the eigenvectors of random matrices, showing that even small perturbations make the eigenvectors almost orthogonal. More precisely, we consider two defo…
How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem
Joscha Henheik, Bipul Poudyal, Roderich Tumulka
Particle creation terms in quantum Hamiltonians are usually ultraviolet divergent and thus mathematically ill defined. A rather novel way of solving this problem is based on imposi…
Out-of-time-ordered correlators for Wigner matrices
Giorgio Cipolloni, László Erdős, Joscha Henheik
We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables and in a mean field chaotic quantum system described by a random Wign…
Universal behavior of the BCS energy gap
Joscha Henheik, Asbjørn Bækgaard Lauritsen
We consider the BCS energy gap (essentially given by , the BCS order parameter) at all temperatures up to the critical one, $T_c…
Prethermalization for Deformed Wigner Matrices
László Erdős, Joscha Henheik, Jana Reker +1
We prove that a class of weakly perturbed Hamiltonians of the form , with being a Wigner matrix, exhibits prethermalization. That is, the time evolution generate…
Eigenstate thermalisation at the edge for Wigner matrices
Giorgio Cipolloni, László Erdős, Joscha Henheik
We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices uniformly in the entire spectrum, in particular near the spectral edges, with a bound on the fluctuation that…
Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems
Shoki Sugimoto, Joscha Henheik, Volodymyr Riabov +1
We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with mean field interaction. This mathemati…
Universality in low-dimensional BCS theory
Joscha Henheik, Asbjørn Bækgaard Lauritsen, Barbara Roos
It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature and the critical temperature is (approximately) given by a universal consta…
Gaussian fluctuations in the Equipartition Principle for Wigner matrices
Giorgio Cipolloni, László Erdős, Joscha Henheik +1
The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartitio…
Optimal Lower Bound on Eigenvector Overlaps for non-Hermitian Random Matrices
Giorgio Cipolloni, László Erdős, Joscha Henheik +1
We consider large non-Hermitian matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noi…
Creation Rate of Dirac Particles at a Point Source
Joscha Henheik, Roderich Tumulka
Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of…
Deformational rigidity of integrable metrics on the torus
Joscha Henheik
It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: We consider…