7 papers
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…
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…
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…