786 research outputs found
Bound state energies and phase shifts of a non-commutative well
Non-commutative quantum mechanics can be viewed as a quantum system
represented in the space of Hilbert-Schmidt operators acting on non-commutative
configuration space. Within this framework an unambiguous definition can be
given for the non-commutative well. Using this approach we compute the bound
state energies, phase shifts and scattering cross sections of the non-
commutative well. As expected the results are very close to the commutative
results when the well is large or the non-commutative parameter is small.
However, the convergence is not uniform and phase shifts at certain energies
exhibit a much stronger then expected dependence on the non-commutative
parameter even at small values.Comment: 12 pages, 8 figure
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
Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
We generalize the formulation of non-commutative quantum mechanics to three
dimensional non-commutative space. Particular attention is paid to the
identification of the quantum Hilbert space in which the physical states of the
system are to be represented, the construction of the representation of the
rotation group on this space, the deformation of the Leibnitz rule accompanying
this representation and the implied necessity of deforming the co-product to
restore the rotation symmetry automorphism. This also implies the breaking of
rotational invariance on the level of the Schroedinger action and equation as
well as the Hamiltonian, even for rotational invariant potentials. For
rotational invariant potentials the symmetry breaking results purely from the
deformation in the sense that the commutator of the Hamiltonian and angular
momentum is proportional to the deformation.Comment: 21 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
Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl
J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian
augmented by a non-Hermitian -symmetric part, is re-examined in the
light of an su(1,1) approach. An alternative derivation, only relying on
properties of su(1,1) generators, is proposed. Being independent of the
realization considered for the latter, it opens the way towards the
construction of generalized non-Hermitian (not necessarily -symmetric)
oscillator Hamiltonians related by similarity to Hermitian ones. Some examples
of them are reviewed.Comment: 11 pages, no figure; changes in title and in paragraphs 3 and 5;
final published versio
Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
In a previous paper (arXiv:math-ph/0604055) we introduced a very simple
PT-symmetric non-Hermitian Hamiltonian with real spectrum and derived a closed
formula for the metric operator relating the problem to a Hermitian one. In
this note we propose an alternative formula for the metric operator, which we
believe is more elegant and whose construction -- based on a backward use of
the spectral theorem for self-adjoint operators -- provides new insights into
the nature of the model.Comment: LaTeX, 6 page
Bosonization in d=2 from finite chiral determinants with a Gauss decomposition
We show how to bosonize two-dimensional non-abelian models using finite
chiral determinants calculated from a Gauss decomposition. The calculation is
quite straightforward and hardly more involved than for the abelian case. In
particular, the counterterm , which is normally motivated from gauge
invariance and then added by hand, appears naturally in this approach.Comment: 4 pages, Revte
Moyal products -- a new perspective on quasi-hermitian quantum mechanics
The rationale for introducing non-hermitian Hamiltonians and other
observables is reviewed and open issues identified. We present a new approach
based on Moyal products to compute the metric for quasi-hermitian systems. This
approach is not only an efficient method of computation, but also suggests a
new perspective on quasi-hermitian quantum mechanics which invites further
exploration. In particular, we present some first results which link the Berry
connection and curvature to non-perturbative properties and the metric.Comment: 14 pages. Submitted to J Phys A special issue on The Physics of
Non-Hermitian Operator
Peptide Sequence and Conformation Strongly Influence Tryptophan Fluorescence
AbstractThis article probes the denatured state ensemble of ribonuclease Sa (RNase Sa) using fluorescence. To interpret the results obtained with RNase Sa, it is essential that we gain a better understanding of the fluorescence properties of tryptophan (Trp) in peptides. We describe studies of N-acetyl-L-tryptophanamide (NATA), a tripeptide: AWA, and six pentapeptides: AAWAA, WVSGT, GYWHE, HEWTV, EAWQE, and DYWTG. The latter five peptides have the same sequence as those surrounding the Trp residues studied in RNase Sa. The fluorescence emission spectra, the fluorescence lifetimes, and the fluorescence quenching by acrylamide and iodide were measured in concentrated solutions of urea and guanidine hydrochloride. Excited-state electron transfer from the indole ring of Trp to the carbonyl groups of peptide bonds is thought to be the most important mechanism for intramolecular quenching of Trp fluorescence. We find the maximum fluorescence intensities vary from 49,000 for NATA with two carbonyls, to 24,400 for AWA with four carbonyls, to 28,500 for AAWAA with six carbonyls. This suggests that the four carbonyls of AWA are better able to quench Trp fluorescence than the six carbonyls of AAWAA, and this must reflect a difference in the conformations of the peptides. For the pentapeptides, EAWQE has a fluorescence intensity that is more than 50% greater than DYWTG, showing that the amino acid sequence influences the fluorescence intensity either directly through side-chain quenching and/or indirectly through an influence on the conformational ensemble of the peptides. Our results show that peptides are generally better models for the Trp residues in proteins than NATA. Finally, our results emphasize that we have much to learn about Trp fluorescence even in simple compounds
Experimental evidence of non-Amontons behaviour at a multicontact interface
We report on normal stress field measurements at the multicontact interface
between a rough elastomeric film and a smooth glass sphere under normal load,
using an original MEMS-based stress sensing device. These measurements are
compared to Finite Elements Method calculations with boundary conditions
obeying locally Amontons' rigid-plastic-like friction law with a uniform
friction coefficient. In dry contact conditions, significant deviations are
observed which decrease with increasing load. In lubricated conditions, the
measured profile recovers almost perfectly the predicted profile. These results
are interpreted as a consequence of the finite compliance of the multicontact
interface, a mechanism which is not taken into account in Amontons' law
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