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pro vyhledávání: '"Fischbacher, Christoph"'
The purpose of this paper is to study nonnegative self-adjoint extensions associated with singular Sturm-Liouville expressions with strictly positive minimal operators. We provide a full characterization of all possible nonnegative self-adjoint exten
Externí odkaz:
http://arxiv.org/abs/2410.04647
We use a model operator approach and the spectral theorem for self-adjoint operators in a Hilbert space to derive the basic results of abstract left-definite theory in a straightforward manner. The theory is amply illustrated with a variety of concre
Externí odkaz:
http://arxiv.org/abs/2408.01514
Schr\"odinger operators with periodic potential have generally been shown to exhibit ballistic transport. In this work, we investigate if the propagation velocity, while positive, can be made arbitrarily small by a suitable choice of the periodic pot
Externí odkaz:
http://arxiv.org/abs/2401.11508
We provide an elementary derivation of the Bessel analog of the celebrated Riesz composition formula and use the former to effortlessly derive the latter.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/2311.05095
Autor:
Fischbacher, Christoph, Fisher, Lee
The scaling behavior of the entanglement entropy of droplet states in Heisenberg spin-1/2 XXZ model defined on a strip of width $M$ under the presence of a non-negative background magnetic field is investigated. Without any assumptions on $V$, a loga
Externí odkaz:
http://arxiv.org/abs/2305.00649
In this note we investigate complete non-selfadjointness for all maximally dissipative extensions of a Schr\"odinger operator on a half-line with dissipative bounded potential and dissipative boundary condition. We show that all maximally dissipative
Externí odkaz:
http://arxiv.org/abs/2108.09617
Autor:
Fischbacher, Christoph
Given a dissipative operator $A$ on a complex Hilbert space $\mathcal{H}$ such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is closable, we give a necessary and sufficient condition for an extension of $A$ to still be dissipative.
Externí odkaz:
http://arxiv.org/abs/2012.12920
We consider the Heisenberg XXZ spin-$J$ chain ($J\in\mathbb{N}/2$) with anisotropy parameter $\Delta$. Assuming that $\Delta>2J$, and introducing threshold energies $E_{K}:=K\left(1-\frac{2J}{\Delta}\right)$, we show that the bipartite entanglement e
Externí odkaz:
http://arxiv.org/abs/2011.11977
Autor:
Fischbacher, Christoph, Schulte, Ruth
We study the free XXZ quantum spin model defined on a ring of size $L$ and show that the bipartite entanglement entropy of eigenstates belonging to the first energy band above the vacuum ground state satisfies a logarithmically corrected area law. Al
Externí odkaz:
http://arxiv.org/abs/2007.00735
Publikováno v:
Annales Henri Poincar\'e volume 21, pages 2327-2366 (2020)
We consider the XXZ spin chain, characterized by an anisotropy parameter $\Delta>1$, and normalized such that the ground state energy is $0$ and the ground state given by the all spins up state. The energies $E_K = K(1-1/\Delta)$, $K=1,2,\ldots$, can
Externí odkaz:
http://arxiv.org/abs/1907.11420