12 citations · 22 across the 9 of their papers we have counts for
14 papers
Slow propagation velocities in Schrödinger operators with large periodic potential
Houssam Abdul-Rahman, Mohammed Darras, Christoph Fischbacher +1
Schrödinger operators with periodic potential have generally been shown to exhibit ballistic transport. In this work, we investigate if the propagation velocity, while positive, ca…
Entanglement Entropy Bounds for Droplet States of the XXZ Model on the Strip
Christoph Fischbacher, Lee Fisher
The scaling behavior of the entanglement entropy of droplet states in Heisenberg spin-1/2 XXZ model defined on a strip of width under the presence of a non-negative background…
Complete Non-Selfadjointness for Schrödinger Operators on the Semi-Axis
Christoph Fischbacher, Serguei Naboko, Ian Wood
In this note we investigate complete non-selfadjointness for all maximally dissipative extensions of a Schrödinger operator on a half-line with dissipative bounded potential and di…
Extensions of dissipative operators with closable imaginary part
Christoph Fischbacher
Given a dissipative operator on a complex Hilbert space such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is closable, we give a necessary and…
Entanglement Entropy Bounds in the Higher Spin XXZ Chain
Christoph Fischbacher, Oluwadara Ogunkoya
We consider the Heisenberg XXZ spin- chain () with anisotropy parameter . Assuming that , and introducing threshold energies $E_{K}:=K\left(1-\frac{2J…
Lower Bound to the Entanglement Entropy of the XXZ Spin Ring
Christoph Fischbacher, Ruth Schulte
We study the free XXZ quantum spin model defined on a ring of size and show that the bipartite entanglement entropy of eigenstates belonging to the first energy band above the…
Entanglement bounds in the XXZ quantum spin chain
Houssam Abdul-Rahman, Christoph Fischbacher, Günter Stolz
We consider the XXZ spin chain, characterized by an anisotropy parameter , and normalized such that the ground state energy is and the ground state given by the all spins…
A Schrödinger Operator Approach to Higher Spin XXZ Systems on General Graphs
Christoph Fischbacher
We consider the spin- XXZ-Hamiltonian on general graphs and show its equivalence to a direct sum of discrete many-particle Schrödinger type operators on what we ca…
The Closed Extensions of a Closed Operator
Christoph Fischbacher
Given a densely defined and closed operator acting on a complex Hilbert space , we establish a one-to-one correspondence between its closed extensions and subspace…
Droplet states in quantum XXZ spin systems on general graphs
Christoph Fischbacher, Günter Stolz
We study XXZ spin systems on general graphs. In particular, we describe the formation of droplet states near the bottom of the spectrum in the Ising phase of the model, where the Z…
A Birman-Krein-Vishik-Grubb theory for sectorial operators
Christoph Fischbacher
We consider densely defined sectorial operators that can be written in the form with , where both and…
The Non-Proper Dissipative Extensions of a Dual Pair
Christoph Fischbacher
We consider dissipative operators of the form , where both and are assumed to be symmetric but neither of them needs to be (essentially) selfadjoint. Afte…
The Proper Dissipative Extensions of a Dual Pair
Christoph Fischbacher, Sergey Naboko, Ian Wood
Let and be dissipative operators on a Hilbert space and let form a dual pair, i.e. , resp.\ $\wide…
The infinite XXZ quantum spin chain revisited: Structure of low lying spectral bands and gaps
Christoph Fischbacher, Günter Stolz
We study the structure of the spectrum of the infinite XXZ quantum spin chain, an anisotropic version of the Heisenberg model. The XXZ chain Hamiltonian preserves the number of dow…