Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

Altered ultrasonic vocalization and impaired learning and memory in Angelman syndrome mouse model with a large maternal deletion from Ube3a to Gabrb3.

Angelman syndrome (AS) is a neurobehavioral disorder associated with mental retardation, absence of language development, characteristic electroencephalography (EEG) abnormalities and epilepsy, happy disposition, movement or balance disorders, and autistic behaviors. The molecular defects underlying AS are heterogeneous, including large maternal deletions of chromosome 15q11-q13 (70%), paternal uniparental disomy (UPD) of chromosome 15 (5%), imprinting mutations (rare), and mutations in the E6-AP ubiquitin ligase gene UBE3A (15%). Although patients with UBE3A mutations have a wide spectrum of neurological phenotypes, their features are usually milder than AS patients with deletions of 15q11-q13. Using a chromosomal engineering strategy, we generated mutant mice with a 1.6-Mb chromosomal deletion from Ube3a to Gabrb3, which inactivated the Ube3a and Gabrb3 genes and deleted the Atp10a gene. Homozygous deletion mutant mice died in the perinatal period due to a cleft palate resulting from the null mutation in Gabrb3 gene. Mice with a maternal deletion (m-/p+) were viable and did not have any obvious developmental defects. Expression analysis of the maternal and paternal deletion mice confirmed that the Ube3a gene is maternally expressed in brain, and showed that the Atp10a and Gabrb3 genes are biallelically expressed in all brain sub-regions studied. Maternal (m-/p+), but not paternal (m+/p-), deletion mice had increased spontaneous seizure activity and abnormal EEG. Extensive behavioral analyses revealed significant impairment in motor function, learning and memory tasks, and anxiety-related measures assayed in the light-dark box in maternal deletion but not paternal deletion mice. Ultrasonic vocalization (USV) recording in newborns revealed that maternal deletion pups emitted significantly more USVs than wild-type littermates. The increased USV in maternal deletion mice suggests abnormal signaling behavior between mothers and pups that may reflect abnormal communication behaviors in human AS patients. Thus, mutant mice with a maternal deletion from Ube3a to Gabrb3 provide an AS mouse model that is molecularly more similar to the contiguous gene deletion form of AS in humans than mice with Ube3a mutation alone. These mice will be valuable for future comparative studies to mice with maternal deficiency of Ube3a alone.