Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane

The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their relation to a choice of gauge in the solution of the problem is addressed. The Landau problem is then extended to different contexts, in particular the singular situation of a purely linear potential term being added as an interaction, for which a complete purely algebraic solution is presented. This solution is then exploited to solve this same singular Landau problem in the half-plane, with as motivation the potential relevance of such a geometry for quantum Hall measurements in the presence of an electric field or a gravitational quantum well

Formulation, Interpretation and Application of non-Commutative Quantum Mechanics

In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on Positive Operator Valued Measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non commutativity are identified.Comment: 11 page

The N=1 Supersymmetric Landau Problem and its Supersymmetric Landau Level Projections: the N=1 Supersymmetric Moyal-Voros Superplane

The N=1 supersymmetric invariant Landau problem is constructed and solved. By considering Landau level projections remaining non trivial under N=1 supersymmetry transformations, the algebraic structures of the N=1 supersymmetric covariant non(anti)commutative superplane analogue of the ordinary N=0 noncommutative Moyal-Voros plane are identified

Noncommutative quantum mechanics -- a perspective on structure and spatial extent

We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we find two equivalent pictures: a constrained local description in position containing additional degrees of freedom, and an unconstrained nonlocal description in terms of the position without any other degrees of freedom. Both these descriptions have a corresponding classical theory which shows that the concept of extended, structured objects emerges quite naturally and unavoidably there. It is explicitly demonstrated that the conserved energy and angular momentum contain corrections to those of a point particle. We argue that these notions also extend naturally to the quantum level. The local description is found to be the most convenient as it manifestly displays additional information about structure of quantum states that is more subtly encoded in the nonlocal, unconstrained description. Subsequently we use this picture to discuss the free particle and harmonic oscillator as examples.Comment: 25 pages, no figure

A (p,q)-deformed Landau problem in a spherical harmonic well: spectrum and noncommuting coordinates

A (p,q)-deformation of the Landau problem in a spherically symmetric harmonic potential is considered. The quantum spectrum as well as space noncommutativity are established, whether for the full Landau problem or its quantum Hall projections. The well known noncommutative geometry in each Landau level is recovered in the appropriate limit p,q=1. However, a novel noncommutative algebra for space coordinates is obtained in the (p,q)-deformed case, which could also be of interest to collective phenomena in condensed matter systems.Comment: 9 pages, no figures; updated reference

Voros product and the Pauli principle at low energies

Using the Voros star product, we investigate the status of the two particle correlation function to study the possible extent to which the previously proposed violation of the Pauli principle may impact at low energies. The results show interesting features which are not present in the computations made using the Moyal star product.Comment: 5 pages LateX, minor correction

Supersymmetry breaking in noncommutative quantum mechanics

Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the number of supercharges are conserved. It is argued that this breaking is closely related to the breaking of time reversal symmetry arising from noncommutativity

Dibaryons as axially symmetric skyrmions

Dibaryons configurations are studied in the framework of the bound state soliton model. A generalized axially symmetric ansatz is used to determine the soliton background. We show that once the constraints imposed by the symmetries of the lowest energy torus configuration are satisfied all spurious states are removed from the dibaryon spectrum. In particular, we show that the lowest allowed state in the $S=-2$ channel carries the quantum numbers of the H particle. We find that, within our approximations, this particle is slightly bound in the model. We discuss, however, that vacuum effects neglected in the present calculation are very likely to unbind the H.Comment: 24 pages, LaTeX, TAN-FNT-93-12 (it replaces old version which was truncated

Link between increased gut hormones signaling satiety and reduced food reward following gastric bypass surgery for obesity

CONTEXT: Roux-en-Y gastric bypass (RYGB) surgery is an effective long-term intervention for weight loss maintenance, reducing appetite, and also food reward, via unclear mechanisms. OBJECTIVE: To investigate the role of elevated satiety gut hormones after RYGB, we examined food hedonic-reward responses after their acute post-prandial suppression. DESIGN: These were randomized, placebo-controlled, double-blind, crossover experimental medicine studies. PATIENTS: Two groups, more than 5 months after RYGB for obesity (n = 7-11), compared with nonobese controls (n = 10), or patients after gastric banding (BAND) surgery (n = 9) participated in the studies. INTERVENTION: Studies were performed after acute administration of the somatostatin analog octreotide or saline. In one study, patients after RYGB, and nonobese controls, performed a behavioral progressive ratio task for chocolate sweets. In another study, patients after RYGB, and controls after BAND surgery, performed a functional magnetic resonance imaging food picture evaluation task. MAIN OUTCOME MEASURES: Octreotide increased both appetitive food reward (breakpoint) in the progressive ratio task (n = 9), and food appeal (n = 9) and reward system blood oxygen level-dependent signal (n = 7) in the functional magnetic resonance imaging task, in the RYGB group, but not in the control groups. RESULTS: Octreotide suppressed postprandial plasma peptide YY, glucagon-like peptide-1, and fibroblast growth factor-19 after RYGB. The reduction in plasma peptide YY with octreotide positively correlated with the increase in brain reward system blood oxygen level-dependent signal in RYGB/BAND subjects, with a similar trend for glucagon-like peptide-1. CONCLUSIONS: Enhanced satiety gut hormone responses after RYGB may be a causative mechanism by which anatomical alterations of the gut in obesity surgery modify behavioral and brain reward responses to food

Twist Deformations of the Supersymmetric Quantum Mechanics

The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.Comment: 18 pages; two references adde