The Classification of Zp\mathbb{Z}_p-Modules with Partial Decomposition Bases in L∞ωL_{\infty\omega}

Ulm's Theorem presents invariants that classify countable abelian torsion groups up to isomorphism. Barwise and Eklof extended this result to the classification of arbitrary abelian torsion groups up to $L_{\infty \omega}$-equivalence. In this paper, we extend this classification to a class of mixed $\mathbb{Z}_p$-modules which includes all Warfield modules and is closed under $L_{\infty\omega}$-equivalence. The defining property of these modules is the existence of what we call a partial decomposition basis, a generalization of the concept of decomposition basis. We prove a complete classification theorem in $L_{\infty\omega}$ using invariants deduced from the classical Ulm and Warfield invariants

Influence of surface-related strain and electric field on acceptor wave functions in Zincblende semiconductors

The spatial distribution of the local density of states (LDOS) at Mn acceptors near the (110) surface of p-doped InAs is investigated by Scanning Tunneling Microscopy (STM). The shapes of the acceptor contrasts for different dopant depths under the surface are analyzed. Acceptors located within the first ten subsurface layers of the semiconductor show a lower symmetry than expected from theoretical predictions of the bulk acceptor wave function. They exhibit a (001) mirror asymmetry. The degree of asymmetry depends on the acceptor atoms' depths. The measured contrasts for acceptors buried below the 10th subsurface layer closely match the theoretically derived shape. Two effects are able to explain the symmetry reduction: the strain field of the surface relaxation and the tip-induced electric field.Comment: 8 pages, 4 figure

Anomalously large capacitance of an ionic liquid described by the restricted primitive model

We use Monte Carlo simulations to examine the simplest model of an ionic liquid, called the restricted primitive model, at a metal surface. We find that at moderately low temperatures the capacitance of the metal/ionic liquid interface is so large that the effective thickness of the electrostatic double-layer is up to 3 times smaller than the ion radius. To interpret these results we suggest an approach which is based on the interaction between discrete ions and their image charges in the metal surface and which therefore goes beyond the mean-field approximation. When a voltage is applied across the interface, the strong image attraction causes counterions to condense onto the metal surface to form compact ion-image dipoles. These dipoles repel each other to form a correlated liquid. When the surface density of these dipoles is low, the insertion of an additional dipole does not require much energy. This leads to a large capacitance $C$ that decreases monotonically with voltage $V$, producing a "bell-shaped" curve $C(V)$. We also consider what happens when the electrode is made from a semi-metal rather than a perfect metal. In this case, the finite screening radius of the electrode shifts the reflection plane for image charges to the interior of the electrode and we arrive at a "camel-shaped" $C(V)$. These predictions seem to be in qualitative agreement with experiment.Comment: 7 pages, 5 figures; some numerical comparisons added; schematic figure added, additional discussion of effect of electrode material, section added with comparison to semiconductor devices; plotting error fixed in Fig.

The emergence of classical behavior in magnetic adatoms

A wide class of nanomagnets shows striking quantum behavior, known as quantum spin tunneling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behavior emerges in the case of magnetic adatoms, as the strength of their coupling, either to the substrate or to each other, is increased. Both spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization.Comment: 5 pages, 4 figure

Courts in quest for legitimacy; the case of wrongful life

This discussion will consider how different courts deal with difficult cases, and how courts seek to maintain the legitimacy of their judicial authority. How do courts search for legitimacy? From what sources do they draw their legitimacy? As a central example I will use the problem often referred to as the “wrongful life” cases: can a medical care provider be held liable for negligent malpractice that results in the creation or preservation of a life that is not considered worth living? This question touches upon the autonomy of the plaintiff. By comparing three judicial decisions in “wrongful life” cases from courts from the United States, France and the Netherlands I hope to illustrate different possible sources of judicial legitimacy

Limits of Private Law

In 2005 the Dutch Supreme Court decided a wrongful life case.2 This case concerned a woman who consulted her midwife during her pregnancy because there had been two cases of handicaps in her husband’s family, due to chromosomal disorder. The midwife did not think it necessary to investigate the matter any further. This was later considered a professional failure with dramatic effects. When born, baby Kelly turned out to have serious mental and physical handicaps from which she suffered severely. The parents claimed damage – both on their own accord and in Kelly’s name – and their claims were sustained by both the court of appeal and the Supreme Court. The Supreme Court not only considered the strictly legal issues but also considered moral and pragmatic arguments that had been put forward against such so-called ‘wrongful life claims’. Firstly, there is the moral opposition that sustaining these claims violates the principle regarding the dignity of human life, since it acknowledges that not being born is preferable to living in a condition like hers. Secondly, there is the pragmatic argument that sustaining claims like this will tempt doctors to practice ‘defensive medicine’ to avoid serious risk. Both arguments were carefully examined by the court and subsequently rejected. What does the Supreme Court in fact do here? Does it call out or explain the law to us? Or does it exceed its limits by elaborating on principles and policies, taking into account the moral grounds and the possible consequences of the ruling itself? In both directions the question arises: what constitutes the limits of private law