218 research outputs found
Accuracy of effective mass equation for a single and double cylindrical quantum dot
In this contribution we study the accuracy of various forms of electron
effective mass equation in reproducing spectral and spin-related features of
quantum dot systems. We compare the results of the standard 8 band k.p model to
those obtained from effective mass equations obtained by perturbative
elimination procedures in various approximations for a cylindrical quantum dot
or a system of two such dots. We calculate the splitting of electronic shells,
the electron g-factor and spin-orbit induced spin mixing and show that for a
cylindrical dot the g-factor is reproduced very exactly, while for the two
other quantities the effective mass equation is much less accurate
Structure of nonlinear gauge transformations
Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations
(NGT) defined in terms of a wave function do not form a group. To get
a group property one has to consider transformations that act differently on
different branches of the complex argument function and the knowledge of the
value of is not sufficient for a well defined NGT. NGT that are well
defined in terms of form a semigroup parametrized by a real number
and a nonzero which is either an integer or . An extension of NGT to projectors and general density matrices
leads to NGT with complex . Both linearity of evolution and Hermiticity
of density matrices are gauge dependent properties.Comment: Final version, to be published in Phys.Rev.A (Rapid Communication),
April 199
Geometric Quantum Mechanics
The manifold of pure quantum states is a complex projective space endowed
with the unitary-invariant geometry of Fubini and Study. According to the
principles of geometric quantum mechanics, the detailed physical
characteristics of a given quantum system can be represented by specific
geometrical features that are selected and preferentially identified in this
complex manifold. Here we construct a number of examples of such geometrical
features as they arise in the state spaces for spin-1/2, spin-1, and spin-3/2
systems, and for pairs of spin-1/2 systems. A study is undertaken on the
geometry of entangled states, and a natural measure is assigned to the degree
of entanglement of a given state for a general multi-particle system. The
properties of this measure are analysed for the entangled states of a pair of
spin-1/2 particles. With the specification of a quantum Hamiltonian, the
resulting Schrodinger trajectory induces a Killing field, which is quasiergodic
on a toroidal subspace of the energy surface. When the dynamical trajectory is
lifted orthogonally to Hilbert space, it induces a geometric phase shift on the
wave function. The uncertainty of an observable in a given state is the length
of the gradient vector of the level surface of the expectation of the
observable in that state, a fact that allows us to calculate higher order
corrections to the Heisenberg relations. A general mixed state is determined by
a probability density function on the state space, for which the associated
first moment is the density matrix. The advantage of a general state is in its
applicability in various attempts to go beyond the standard quantum theory.Comment: 27 pages. Extended with additional materia
On classical models of spin
The reason for recalling this old paper is the ongoing discussion on the
attempts of circumventing certain assumptions leading to the Bell theorem
(Hess-Philipp, Accardi). If I correctly understand the intentions of these
Authors, the idea is to make use of the following logical loophole inherent in
the proof of the Bell theorem: Probabilities of counterfactual events A and A'
do not have to coincide with actually measured probabilities if measurements of
A and A' disturb each other, or for any other fundamental reason cannot be
performed simulaneously. It is generally believed that in the context of
classical probability theory (i.e. realistic hidden variables) probabilities of
counterfactual events can be identified with those of actually measured events.
In the paper I give an explicit counterexample to this belief. The "first
variation" on the Aerts model shows that counterfactual and actual problems
formulated for the same classical system may be unrelated. In the model the
first probability does not violate any classical inequality whereas the second
does. Pecularity of the Bell inequality is that on the basis of an in principle
unobservable probability one derives probabilities of jointly measurable random
variables, the fact additionally obscuring the logical meaning of the
construction. The existence of the loophole does not change the fact that I was
not able to construct a local model violating the inequality with all the other
loopholes eliminated.Comment: published as Found. Phys. Lett. 3 (1992) 24
Nonlocal looking equations can make nonlinear quantum dynamics local
A general method for extending a non-dissipative nonlinear Schr\"odinger and
Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles
is described. It is shown at a general level that the dynamics so obtained is
completely separable, which is the strongest condition one can impose on
dynamics of composite systems. It requires that for all initial states
(entangled or not) a subsystem not only cannot be influenced by any action
undertaken by an observer in a separated system (strong separability), but
additionally that the self-consistency condition is fulfilled. It is shown that a correct
extension to particles involves integro-differential equations which, in
spite of their nonlocal appearance, make the theory fully local. As a
consequence a much larger class of nonlinearities satisfying the complete
separability condition is allowed than has been assumed so far. In particular
all nonlinearities of the form are acceptable. This shows that
the locality condition does not single out logarithmic or 1-homeogeneous
nonlinearities.Comment: revtex, final version, accepted in Phys.Rev.A (June 1998
Nonlinear Quantum Mechanics and Locality
It is shown that, in order to avoid unacceptable nonlocal effects, the free
parameters of the general Doebner-Goldin equation have to be chosen such that
this nonlinear Schr\"odinger equation becomes Galilean covariant.Comment: 10 pages, no figures, also available on
http://www.pt.tu-clausthal.de/preprints/asi-tpa/012-97.htm
Geometric Phases and Mielnik's Evolution Loops
The cyclic evolutions and associated geometric phases induced by
time-independent Hamiltonians are studied for the case when the evolution
operator becomes the identity (those processes are called {\it evolution
loops}). We make a detailed treatment of systems having equally-spaced energy
levels. Special emphasis is made on the potentials which have the same spectrum
as the harmonic oscillator potential (the generalized oscillator potentials)
and on their recently found coherent states.Comment: 11 pages, harvmac, 2 figures available upon request; CINVESTAV-FIS
GFMR 11/9
Magnetic operations: a little fuzzy physics?
We examine the behaviour of charged particles in homogeneous, constant and/or
oscillating magnetic fields in the non-relativistic approximation. A special
role of the geometric center of the particle trajectory is elucidated. In
quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an
element of non-commutative geometry which enters into the traditional control
problems. We show that its application extends beyond the usually considered
time independent magnetic fields of the quantum Hall effect. Some simple cases
of magnetic control by oscillating fields lead to the stability maps differing
from the traditional Strutt diagram.Comment: 28 pages, 8 figure
Complete positivity of nonlinear evolution: A case study
Simple Hartree-type equations lead to dynamics of a subsystem that is not
completely positive in the sense accepted in mathematical literature. In the
linear case this would imply that negative probabilities have to appear for
some system that contains the subsystem in question. In the nonlinear case this
does not happen because the mathematical definition is physically unfitting as
shown on a concrete example.Comment: extended version, 3 appendices added (on mixed states, projection
postulate, nonlocality), to be published in Phys. Rev.
Identification of polymorphisms and balancing selection in the male infertility candidate gene, ornithine decarboxylase antizyme 3
Abstract Background The antizyme family is a group of small proteins that play a role in cell growth and division by regulating the biosynthesis of polyamines (putrescine, spermidine, spermine). Antizymes regulate polyamine levels primarily through binding ornithine decarboxylase (ODC), an enzyme key to polyamine production, and targeting ODC for destruction by the 26S proteosome. Ornithine decarboxylase antizyme 3 (OAZ3) is a testis-specific antizyme paralog and the only antizyme expressed in the mid to late stages of spermatogenesis. Methods To see if mutations in the OAZ3 gene are responsible for some cases of male infertility, we sequenced and evaluated the genomic DNA of 192 infertile men, 48 men of known paternity, and 34 African aborigines from the Mbuti tribe in the Democratic Republic of the Congo. The coding sequence of OAZ3 was further screened for polymorphisms by SSCP analysis in the infertile group and an additional 250 general population controls. Identified polymorphisms in the OAZ3 gene were further subjected to a haplotype analysis using PHASE 2.02 and Arlequin 2.0 software programs. Results A total of 23 polymorphisms were identified in the promoter, exons or intronic regions of OAZ3. The majority of these fell within a region of less than two kilobases. Two of the polymorphisms, -239 A/G in the promoter and 4280 C/T, a missense polymorphism in exon 5, may show evidence of association with male infertility. Haplotype analysis identified 15 different haplotypes, which can be separated into two divergent clusters. Conclusion Mutations in the OAZ3 gene are not a common cause of male infertility. However, the presence of the two divergent haplotypes at high frequencies in all three of our subsamples (infertile, control, African) suggests that they have been maintained in the genome by balancing selection, which was supported by a test of Tajima's D statistic. Evidence for natural selection in this region implies that these haplotypes may be associated with a trait other than infertility. This trait may be related to another function of OAZ3 or a region in tight linkage disequilibrium to the gene.</p
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