Zobrazeno 1 - 10
of 121
pro vyhledávání: '"Gnutzmann, Sven"'
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
In this work we present a three step procedure for generating a closed form expression of the Green's function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the approach
Externí odkaz:
http://arxiv.org/abs/2309.11251
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:
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
Publikováno v:
Symmetry 2019, 11(2), 185
We consider stationary waves on nonlinear quantum star graphs, i.e. solutions to the stationary (cubic) nonlinear Schr\"odinger equation on a metric star graph with Kirchhoff matching conditions at the centre. We prove the existence of solutions that
Externí odkaz:
http://arxiv.org/abs/1901.04275
Publikováno v:
J. Phys. A: Math. Theor. 51 464001 (2018)
We present the results of systematic numerical computations relating to the extreme value statistics of the characteristic polynomials of random unitary matrices drawn from the Circular Unitary Ensemble (CUE) of Random Matrix Theory. In particular, w
Externí odkaz:
http://arxiv.org/abs/1806.00286
Autor:
Band, Ram, Gnutzmann, Sven
Studying the spectral theory of Schroedinger operator on metric graphs (also known as quantum graphs) is advantageous on its own as well as to demonstrate key concepts of general spectral theory. There are some excellent references for this study suc
Externí odkaz:
http://arxiv.org/abs/1711.07435
Publikováno v:
Phys. Rev. E 96, 062207 (2017)
We consider two coupled quantum tops with angular momentum vectors $\mathbf{L}$ and $\mathbf{M}$. The coupling Hamiltonian defines the Feinberg-Peres model which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry
Externí odkaz:
http://arxiv.org/abs/1709.03584
Autor:
Gnutzmann, Sven, Waltner, Daniel
We consider exact and asymptotic solutions of the stationary cubic nonlinear Schr\"odinger equation (NLSE) on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism devel
Externí odkaz:
http://arxiv.org/abs/1609.07348
Autor:
Gnutzmann, Sven, Waltner, Daniel
Publikováno v:
Phys. Rev. E 93, 032204 (2016)
In this paper we present a general framework for solving the stationary nonlinear Schr\"odinger equation (NLSE) on a network of one-dimensional wires modelled by a metric graph with suitable matching conditions at the vertices. A formal solution is g
Externí odkaz:
http://arxiv.org/abs/1510.00351