Wolfgang Spitzer

Computerized tomography examination for the detection of positional changes in the temporomandibular joint after ramus osteotomies with screw fixation

Changes in the position of the temporomandibular joint following sagittal splitting osteotomy of the mandibular ramus with screw fixation were examined using computerized tomography. Ten patients were involved in the study. Rotational movement of the condyle-bearing fragment was most commonly seen in the transverse computer tomograms. However, the use of screw fixation seems to cause no major malpositioning of the condyle-bearing fragment.

A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy

We prove a special case of a conjecture in asymptotic analysis by Harold Widom. More precisely, we establish the leading and next-to-leading term of a semi-classical expansion of the trace of the square of certain integral operators on the Hilbert space

ABSOLUTELY CONTINUOUS SPECTRUM FOR A RANDOM POTENTIAL ON A TREE WITH STRONG TRANSVERSE CORRELATIONS AND LARGE WEIGHTED LOOPS

L^2(\R^d)

Ferromagnetic ordering of energy levels

. As already observed by Gioev and Klich, this implies that the bi-partite entanglement entropy of the free Fermi gas in its ground state grows at least as fast as the surface area of the spatially bounded part times a logarithmic enhancement.

A NEW COHERENT STATES APPROACH TO SEMICLASSICS WHICH GIVES SCOTT'S CORRECTION ∗

We consider random Schrodinger operators on tree graphs and prove absolutely continuous spectrum at small disorder for two models. The first model is the usual binary tree with certain strongly correlated random potentials. These potentials are of interest since for complete correlation they exhibit localization at all disorders. In the second model, we change the tree graph by adding all possible edges to the graph inside each sphere, with weights proportional to the number of points in the sphere.

Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions

We study a natural conjecture regarding ferromagnetic ordering of energy levels in the Heisenberg model which complements the Lieb–Mattis Theorem of 1962 for antiferromagnets: for ferromagnetic Heisenberg models the lowest energies in each subspace of fixed total spin are strictly ordered according to the total spin, with the lowest, i.e., the ground state, belonging to the maximal total spin subspace. Our main result is a proof of this conjecture for the spin-1/2 Heisenberg XXX and XXZ ferromagnets in one dimension. Our proof has two main ingredients. The first is an extension of a result of Koma and Nachtergaele which shows that monotonicity as a function of the total spin follows from the monotonicity of the ground state energy in each total spin subspace as a function of the length of the chain. For the second part of the proof we use the Temperley–Lieb algebra to calculate, in a suitable basis, the matrix elements of the Hamiltonian restricted to each subspace of the highest weight vectors with a given total spin. We then show that the positivity properties of these matrix elements imply the necessary monotonicity in the volume. Our method also shows that the first excited state of the XXX ferromagnet on any finite tree has one less than maximal total spin.

Improved Bounds on the Spectral Gap Above Frustration-Free Ground States of Quantum Spin Chains

We introduce a new semiclassical calculus by generalizing the standard coherent states. This is applied to the semiclassical expansion for the sum of negative eigenvalues of Schrödinger operators which leads to a new proof of the Scott correction for non-relativistic molecules.

Improved Gap Estimates for Simulating Quantum Circuits by Adiabatic Evolution

Abstract.We give a precise definition for excitations consisting of a droplet of size n in the XXZ chain with various choices of boundary conditions, including kink boundary conditions and prove that, for each n, the droplet energies converge to a boundary condition independent value in the thermodynamic limit. We rigorously compute an explicit formula for this limiting value using the Bethe Ansatz.

Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature*

Nachtergaele obtained explicit lower bounds for the spectral gap above many frustration free quantum spin chains by using the ‘martingale method’. We present simple improvements to his main bounds which allow one to obtain a sharp lower bound for the spectral gap above the spin-1/2 ferromagnetic XXZ chain. As an illustration of the method, we also calculate a lower bound for the spectral gap of the AKLT model, which is about 1/3 the size of the expected gap.

A Geometric Approach to Absolutely Continuous Spectrum for Discrete Schrödinger Operators

We use elementary variational arguments to prove, and improve on, gap estimates which arise in simulating quantum circuits by adiabatic evolution.