379 research outputs found
Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles
It is well known that the category of super Lie groups (SLG) is equivalent to
the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we
define the category of unitary representations (UR's) of a super Lie group. We
give an extension of the classical inducing construction and Mackey
imprimitivity theorem to this setting. We use our results to classify the
irreducible unitary representations of semidirect products of super translation
groups by classical Lie groups, in particular of the super Poincar\'e groups in
arbitrary dimension. Finally we compare our results with those in the physical
literature on the structure and classification of super multiplets.Comment: 55 pages LaTeX, some corrections added after comments by Prof. Pierre
Delign
Constructing Extremal Compatible Quantum Observables by Means of Two Mutually Unbiased Bases
We describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as uniformly noisy versions of two mutually unbiased bases (MUB) with possibly different noise intensities affecting each basis. We show that not all pairs of MUB can be used in this construction, and we provide a criterion for determining those MUB that actually do yield extremal compatible observables. We apply our criterion to all pairs of Fourier conjugate MUB, and we prove that in this case extremality is achieved if and only if the quantum system Hilbert space is odd-dimensional. Remarkably, this fact is no longer true for general non-Fourier conjugate MUB, as we show in an example. Therefore, the presence or the absence of extremality is a concrete geometric manifestation of MUB inequivalence, that already materializes by comparing sets of no more than two bases at a time
Competition between symmetry breaking and onset of collapse in weakly coupled atomic condensates
We analyze the symmetry breaking of matter-wave solitons in a pair of
cigar-shaped traps coupled by tunneling of atoms. The model is based on a
system of linearly coupled nonpolynomial Schr\"odinger equations (NPSEs).
Unlike the well-known spontaneous-symmetry-breaking (SSB) bifurcation in
coupled cubic equations, in the present model the SSB competes with the onset
of collapse in this system. Stability regions of symmetric and asymmetric
solitons, as well as the collapse region, are identified in the parameter space
of the system.Comment: Physical Review A, in pres
Variational Monte Carlo for spin-orbit interacting systems
Recently, a diffusion Monte Carlo algorithm was applied to the study of spin
dependent interactions in condensed matter. Following some of the ideas
presented therein, and applied to a Hamiltonian containing a Rashba-like
interaction, a general variational Monte Carlo approach is here introduced that
treats in an efficient and very accurate way the spin degrees of freedom in
atoms when spin orbit effects are included in the Hamiltonian describing the
electronic structure. We illustrate the algorithm on the evaluation of the
spin-orbit splittings of isolated carbon and lead atoms. In the case of the
carbon atom, we investigate the differences between the inclusion of spin-orbit
in its realistic and effective spherically symmetrized forms. The method
exhibits a very good accuracy in describing the small energy splittings,
opening the way for a systematic quantum Monte Carlo studies of spin-orbit
effects in atomic systems.Comment: 7 pages, 0 figure
Counselors as Advocates: Effects of a Pilot Project Designed to Develop Advocacy Knowledge and Confidence in Trainees
While there has been increased attention to advocacy within counseling and counseling psychology, it has been noted that trainees generally feel unprepared to engage in advocacy and do not participant e in this type of work to a large extent, even with increased age or professional experience). The qualitative study summarizes the findings of a project within a graduate multicultural counseling course designed to increase trainee knowledge and confidence related to advocacy. This project required students (N = 19) to complete individual advocacy projects in the community, with opportunities for self-reflection and evaluation of their progress throughout the semester. Student reflection responses about the effects of this project were analyzed using methods from Grounded Theory by a collaborative research team. This process resulted in a core category of responses that included expanded definitions of advocacy, increased self-confidence regarding advocacy work, obstacles encountered, and reactions to the course assignment. Implications and future directions are discussed
Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials
We study the spontaneous symmetry breaking (SSB) of a superfluid Bose-Fermi
(BF) mixture in a double-well potential (DWP). The mixture is described by the
Gross-Pitaevskii equation (GPE) for the bosons, coupled to an equation for the
order parameter of the Fermi superfluid, which is derived from the respective
density functional in the unitarity limit (a similar model applies to the BCS
regime too). Straightforward SSB in the degenerate Fermi gas loaded into a DWP
is impossible, as it requires an attractive self-interaction, while the
intrinsic nonlinearity in the Fermi gas is repulsive. Nonetheless, we
demonstrate that the symmetry breaking is possible in the mixture with
attraction between fermions and bosons, like 40K and 87Rb. Numerical results
are represented by dependencies of asymmetry parameters for both components on
particle numbers of the mixture, N_F and N_B, and by phase diagrams in the
(N_F,N_B) plane, which displays regions of symmetric and asymmetric ground
states. The dynamical picture of the SSB, induced by a gradual transformation
of the single-well potential into the DWP, is reported too. An analytical
approximation is proposed for the case when GPE for the boson wave function may
be treated by means of the Thomas-Fermi (TF) approximation. Under a special
linear relation between N_F and N_B, the TF approximation allows us to reduce
the model to a single equation for the fermionic function, which includes
competing repulsive and attractive nonlinear terms. The latter one directly
displays the mechanism of the generation of the effective attraction in the
Fermi superfluid, mediated by the bosonic component of the mixture.Comment: 10 pages, 6 figures, to be published in Phys. Rev. A (2010)
Quantum Incompatibility Witnesses
We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task with partial intermediate information. This is done by showing that only incompatible measurements allow for an efficient use of premeasurement information in order to improve the probability of guessing the correct state. Thus, the gap between the guessing probabilities with pre- and postmeasurement information is a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme. As an application, we characterize the joint measurability region of two noisy mutually unbiased bases
Informationally complete joint measurements on finite quantum systems
We show that there are informationally complete joint measurements of two conjugated observables on a finite quantum system, meaning that they enable the identification of all quantum states from their measurement outcome statistics. We further demonstrate that it is possible to implement a joint observable as a sequential measurement. If we require minimal noise in the joint measurement, then the joint observable is unique. If d is odd, then this observable is informationally complete. But if d is even, then the joint observable is not informationally complete, and one has to allow more noise in order to obtain informational completeness
A complete characterization of phase space measurements
We characterize all the phase space measurements for a non-relativistic
particle.Comment: 11 pages, latex, no figures, iopart styl
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