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T. Kriecherbauer

Publications and source records attributed to T. Kriecherbauer.

4 recordsLinked to original sources
arXiv2010

Fluctuations of eigenvalues of matrix models and their applications

We study the expectation of linear eigenvalue statistics of matrix models with any $β>0$, assuming that the potential $V$ is a real analytic function and that the corresponding equilibrium measure has a one-interval support. We obtain the first order (with respect to $n^{-1}$) correction terms for the expectation and apply this result to prove bulk universality for real symmetric and symplectic matrix models with the same $V$.

math-ph↗
arXiv2008

Non-adiabacity and large flucutations in a many particle Landau Zener problem

We consider the behavior of an interacting many particle system under slow external driving -- a many body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly different from that of the single particle limit: for practically all values of the driving rate the particle distributions in Hilbert space are very broad, a phenomenon caused by a strong amplification of quantum fluctuations in the driving process. These fluctuations are 'non-adiabatic' in that even at very slow driving it is exceedingly difficult to push the center of the distribution towards the limit of full ground state occupancy. We obtain these results by a number of complementary theoretical approaches, including diagrammatic perturbation theory, semiclassical analysis, and exact diagonalization.

cond-mat.other↗
arXiv2007

Locating the zeros of partial sums of exp(z) with Riemann-Hilbert methods

In this paper we derive uniform asymptotic expansions for the partial sums of the exponential series. We indicate how this information will be used in a later publication to obtain full and explicitly computable asymptotic expansions with error bounds for all zeros of the Taylor polynomials $p_{n-1}(z) = \sum_{k=0}^{n-1} z^k/ k!$. Our proof is based on a representation of $p_{n-1}(nz)$ in terms of an integral of the form $\int_γ \frac{e^{nϕ(s)}}{s-z}ds$. We demonstrate how to derive uniform expansions for such integrals using a Riemann-Hilbert approach. A comparison with classical steepest descent analysis shows the advantages of the Riemann-Hilbert analysis in particular for points $z$ that are close to the critical points of $ϕ$.

math.CA↗