Zobrazeno 1 - 10
of 616
pro vyhledávání: '"Erdős, László"'
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 deformed Wigner matrices $W+D_1$, $W+D_2$ and show that their bulk eigenve
Externí odkaz:
http://arxiv.org/abs/2410.10718
We consider two Hamiltonians that are close to each other, $H_1 \approx H_2 $, and analyze the time-decay of the corresponding Loschmidt echo $\mathfrak{M}(t) := |\langle \psi_0, \mathrm{e}^{\mathrm{i} t H_2} \mathrm{e}^{-\mathrm{i} t H_1} \psi_0 \ra
Externí odkaz:
http://arxiv.org/abs/2410.08108
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 typically exhibits only square root edge or cubic root cusp singulari
Externí odkaz:
http://arxiv.org/abs/2410.06813
For general large non-Hermitian random matrices $X$ and deterministic normal deformations $A$, we prove that the local eigenvalue statistics of $A+X$ close to the critical edge points of its spectrum are universal. This concludes the proof of the thi
Externí odkaz:
http://arxiv.org/abs/2409.17030
For general non-Hermitian random matrices $X$ and deterministic deformation matrices $A$, we prove that the local eigenvalue statistics of $A+X$ close to the typical edge points of its spectrum are universal. Furthermore, we show that under natural a
Externí odkaz:
http://arxiv.org/abs/2404.17512
Autor:
Riabov, Volodymyr, Erdős, László
We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for observables of arbitrary rank. As the main technical ingredient, we prove ran
Externí odkaz:
http://arxiv.org/abs/2403.10359
We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables $A$ and $B$ in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regime
Externí odkaz:
http://arxiv.org/abs/2402.17609
We prove that the spectral radius of a large random matrix $X$ with independent, identically distributed complex entries follows the Gumbel law irrespective of the distribution of the matrix elements. This solves a long-standing conjecture of Bordena
Externí odkaz:
http://arxiv.org/abs/2312.08325
We prove that a class of weakly perturbed Hamiltonians of the form $H_\lambda = H_0 + \lambda W$, with $W$ being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by $H_\lambda$ relaxes to its ultimate thermal state v
Externí odkaz:
http://arxiv.org/abs/2310.06677
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 is optimal for any observable. This complements earlier works of Cipol
Externí odkaz:
http://arxiv.org/abs/2309.05488