Zobrazeno 1 - 10
of 245
pro vyhledávání: '"Smilansky, Uzy"'
Autor:
Gnutzmann, Sven, Smilansky, Uzy
Given an arbitrary \(V \times V\) Hermitian matrix, considered as a finite discrete quantum Hamiltonian, we use methods from graph and ergodic theories to construct a \textit{quantum Poincar\'e map} at energy \(E\) and a corresponding stochastic \tex
Externí odkaz:
http://arxiv.org/abs/2401.12898
Autor:
Smilansky, Uzy, Sofer, Gilad
The purpose of the present paper is to discuss the time dependent Schr\"odinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the corresponding time evolution is unitary. We show that the
Externí odkaz:
http://arxiv.org/abs/2210.14652
The Kronig-Penney model in a quadratic channel with $\delta $ interactions. II : Scattering approach
Autor:
Smilansky, Uzy
The main purpose of the present paper is to introduce a scattering approach to the study of the Kronig-Penney model in a quadratic channel with $\delta$ interactions, which was discussed in full generality in the first paper of the present series. In
Externí odkaz:
http://arxiv.org/abs/2201.08325
Autor:
Gnutzmann, Sven, Smilansky, Uzy
We generalize the scattering approach to quantum graphs to quantum graphs with with piecewise constant potentials and multiple excitation modes. The free single-mode case is well-known and leads to the trace formulas of Roth, Kottos and Smilansky. By
Externí odkaz:
http://arxiv.org/abs/2201.06963
Autor:
Maciążek, Tomasz, Smilansky, Uzy
Publikováno v:
Annales Henri Poincar\'e (2021)
The spectrum of a real and symmetric $N\times N$ matrix determines the matrix up to unitary equivalence. More spectral data is needed together with some sign indicators to remove the unitary ambiguities. In the first part of this work we specify the
Externí odkaz:
http://arxiv.org/abs/2106.01819
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le t \le N$,
Externí odkaz:
http://arxiv.org/abs/2008.09211
Autor:
Gnutzmann, Sven, Smilansky, Uzy
Two trace formulas for the spectra of arbitrary Hermitian matrices are derived by transforming the given Hermitian matrix $H$ to a unitary analogue. In the first type the unitary matrix is $e^{i(\lambda\II - H)}$ where $\lambda$ is the spectral param
Externí odkaz:
http://arxiv.org/abs/1907.07527
Autor:
Joyner, Christopher H., Smilansky, Uzy
We investigate the linear statistics of random matrices with purely imaginary Bernoulli entries of the form $H_{pq} = \overline{H}_{qp} = \pm i$, that are either independently distributed or exhibit global correlations imposed by the condition $\sum_
Externí odkaz:
http://arxiv.org/abs/1711.02072
Publikováno v:
Acta Physica Polonica A (2017), vol. 132, 1699-1703
Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schr\"odinger operator is interlaced with that of the orig
Externí odkaz:
http://arxiv.org/abs/1710.07958
Autor:
Smilansky, Uzy, Schanz, Holger
Publikováno v:
J. Phys. A 51 (2017) 075302
We apply the framework developed in the preceding paper in this series (Smilansky 2017 J. Phys. A: Math. Theor. 50, 215301) to compute the time-delay distribution in the scattering of ultra short radio frequency pulses on complex networks of transmis
Externí odkaz:
http://arxiv.org/abs/1709.08845