New coherent states and a new proof of the Scott correction

We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for molecules. This is the short version of a paper by the authors archived at math-ph/0208044.Comment: A misprint in definition of new coherent states corrected. To appear in Proceedings of the UAB 2002 Int'l Conference on Differential Equations and Mathematics Physic

On the dynamics of interfaces in the ferromagnetic XXZ chain under weak perturbations

We study the time evolution of interfaces of the ferromagnetic XXZ chain in a magnetic field. A scaling limit is introduced where the strength of the magnetic field tends to zero and the microscopic time to infinity while keeping their product constant. The leading term and its first correction are determined and further analyzed in more detail for the case of a uniform magnetic field.Comment: 20 pages, 2 figures, uses conm-p-l.cls. 1 reference adde

The relativistic Scott correction for atoms and molecules

We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy, established in [Sorensen], as well as the correction given here are of semi-classical nature. Our result on atoms and molecules is proved from a general semi-classical estimate for relativistic operators with potentials with Coulomb-like singularities. This semi-classical estimate is obtained using the coherent state calculus introduced in [Solovej-Spitzer]. The paper contains a unified treatment of the relativistic as well as the non-relativistic case.Comment: 59 page

A new coherent states approach to semiclassics which gives Scott's correction

We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for molecules.Comment: A misprint in the definition of new coherent states correcte

Time Evolution of Spin Waves

A rigorous derivation of macroscopic spin-wave equations is demonstrated. We introduce a macroscopic mean-field limit and derive the so-called Landau-Lifshitz equations for spin waves. We first discuss the ferromagnetic Heisenberg model at T=0 and finally extend our analysis to general spin hamiltonians for the same class of ferromagnetic ground states.Comment: 4 pages, to appear in PR

Long-term outcome and prognosis of dissociative disorder with onset in childhood or adolescence

<p>Abstract</p> <p>Background</p> <p>In the majority of cases short-term treatment outcome of juvenile dissociative disorder is rather favourable. In contrast, the long-term course seems to be less positive, but meaningful results are still fragmentary. The aim of this follow-up study is to bridge this gap to some extent describing the long-term outcome of juvenile dissociative disorder in a clinical sample. To our knowledge there is no comparable other long-term follow-up study which is based on a case definition according to actual classification systems using standardized interviews for individual assessment of the patients at the time of follow-up.</p> <p>Methods</p> <p>The total study group was made up of all patients treated for dissociative disorder at our department for child and adolescent psychiatry between 1983 and 1992 (<it>N </it>= 62). Two of these former patients committed suicide during the follow-up period (3%). We got information on the clinical course of 27 former patients (44%). 17 out of these 27 former patients were female (63%). The mean age of onset of dissociative disorder was11.7 years and the mean follow-up time was 12.4 years. Most of the patients were reassessed personally (n = 23) at a mean age of 24.8 years using structured interviews covering dissociative disorders, other Axis I disorders and personality disorders (Heidelberg Dissociation Inventory HDI; Expert System for Diagnosing Mental Disorders, DIA-X; Structured Clinical Interview for DSM-IV, SCID-II). Social adjustment was assessed by a semi-structured interview and by patient self report (Social Adjustment Scale – Self Report, SAS-SR). Psychosocial outcome variables were additionally assessed in 36 healthy controls (67% female, mean age = 22.9 years).</p> <p>Results</p> <p>At the time of follow-up investigation 82.6% of the patients met the criteria for some form of psychiatric disorder, while 26.1% were still suffering from dissociative disorder. A total of 56.5% presented with an Axis I disorder (especially anxiety, dissociative and somatoform disorders). Personality disorders were seen in 47.8% (especially borderline, obsessive-compulsive and negativistic personality disorders). More dissociative symptoms and inpatient treatment in childhood or adolescence were significantly related to a lower level of psychosocial adjustment in adulthood.</p> <p>Conclusion</p> <p>Treatment strategies have to consider that in a significant portion of young patients initial recovery may not be stable over time. Limitations of the study refer to the small sample size and the low rate of former patients taking part in the follow-up investigation.</p