465 research outputs found
Moving system with speeded-up evolution
In the classical (non-quantum) relativity theory the course of the moving
clock is dilated as compared to the course of the clock at rest (the Einstein
dilation). Any unstable system may be regarded as a clock. The time evolution
(e.g., the decay) of a uniformly moving physical system is considered using the
relativistic quantum theory. The example of a moving system is given whose
evolution turns out to be speeded-up instead of being dilated. A discussion of
this paradoxical result is presented.Comment: 10 pages, LaTe
Deuteron-equivalent and phase-equivalent interactions within light nuclei
Background: Phase-equivalent transformations (PETs) are well-known in quantum
scattering and inverse scattering theory. PETs do not affect scattering phase
shifts and bound state energies of two-body system but are conventionally
supposed to modify two-body bound state observables such as the rms radius and
electromagnetic moments. Purpose: In order to preserve all bound state
observables, we propose a new particular case of PETs, a deuteron-equivalent
transformation (DET-PET), which leaves unchanged not only scattering phase
shifts and bound state (deuteron) binding energy but also the bound state wave
function. Methods: The construction of DET-PET is discussed; equations defining
the simplest DET-PETs are derived. We apply these simplest DET-PETs to the
JISP16 interaction and use the transformed interactions in
calculations of H and He binding energies in the No-core Full
Configuration (NCFC) approach based on extrapolations of the No-core Shell
Model (NCSM) basis space results to the infinite basis space. Results: We
demonstrate the DET-PET modification of the scattering wave functions and
study the DET-PET manifestation in the binding energies of H and He
nuclei and their correlation (Tjon line). Conclusions: It is shown that some
DET-PETs generate modifications of the central component while the others
modify the tensor component of the interaction. DET-PETs are able to
modify significantly the scattering wave functions and hence the off-shell
properties of the interaction. DET-PETs give rise to significant changes
in the binding energies of H (in the range of approximately 1.5 MeV) and
He (in the range of more than 9 MeV) and are able to modify the correlation
patterns of binding energies of these nuclei
Generalized compactness in linear spaces and its applications
The class of subsets of locally convex spaces called -compact sets is
considered. This class contains all compact sets as well as several noncompact
sets widely used in applications. It is shown that many results well known for
compact sets can be generalized to -compact sets. Several examples are
considered.
The main result of the paper is a generalization to -compact convex sets
of the Vesterstrom-O'Brien theorem showing equivalence of the particular
properties of a compact convex set (s.t. openness of the mixture map, openness
of the barycenter map and of its restriction to maximal measures, continuity of
a convex hull of any continuous function, continuity of a convex hull of any
concave continuous function). It is shown that the Vesterstrom-O'Brien theorem
does not hold for pointwise -compact convex sets defined by the slight
relaxing of the -compactness condition. Applications of the obtained
results to quantum information theory are considered.Comment: 27 pages, the minor corrections have been mad
On Some Lie Groups in Degenerate Clifford Geometric Algebras
In this paper, we introduce and study five families of Lie groups in
degenerate Clifford geometric algebras. These Lie groups preserve the even and
odd subspaces and some other subspaces under the adjoint representation and the
twisted adjoint representation. The considered Lie groups contain degenerate
spin groups, Lipschitz groups, and Clifford groups as subgroups in the case of
arbitrary dimension and signature. The considered Lie groups can be of interest
for various applications in physics, engineering, and computer science.Comment: 30 page
On generalization of Lipschitz groups and spin groups
This paper presents some new Lie groups preserving fixed subspaces of
geometric algebras (or Clifford algebras) under the twisted adjoint
representation. We consider the cases of subspaces of fixed grades and
subspaces determined by the grade involution and the reversion. Some of the
considered Lie groups can be interpreted as generalizations of Lipschitz groups
and spin groups. The Lipschitz groups and the spin groups are subgroups of
these Lie groups and coincide with them in the cases of small dimensions. We
study the corresponding Lie algebras.Comment: 23 page
Continuity of the von Neumann entropy
A general method for proving continuity of the von Neumann entropy on subsets
of positive trace-class operators is considered. This makes it possible to
re-derive the known conditions for continuity of the entropy in more general
forms and to obtain several new conditions. The method is based on a particular
approximation of the von Neumann entropy by an increasing sequence of concave
continuous unitary invariant functions defined using decompositions into finite
rank operators. The existence of this approximation is a corollary of a general
property of the set of quantum states as a convex topological space called the
strong stability property. This is considered in the first part of the paper.Comment: 42 pages, the minor changes have been made, the new applications of
the continuity condition have been added. To appear in Commun. Math. Phy
On properties of the space of quantum states and their application to construction of entanglement monotones
We consider two properties of the set of quantum states as a convex
topological space and some their implications concerning the notions of a
convex hull and of a convex roof of a function defined on a subset of quantum
states.
By using these results we analyze two infinite-dimensional versions (discrete
and continuous) of the convex roof construction of entanglement monotones,
which is widely used in finite dimensions. It is shown that the discrete
version may be 'false' in the sense that the resulting functions may not
possess the main property of entanglement monotones while the continuous
version can be considered as a 'true' generalized convex roof construction. We
give several examples of entanglement monotones produced by this construction.
In particular, we consider an infinite-dimensional generalization of the notion
of Entanglement of Formation and study its properties.Comment: 34 pages, the minor corrections have been mad
Nucleon-deuteron scattering with the JISP16 potential
The nucleon-nucleon J-matrix Inverse Scattering Potential JISP16 is applied
to elastic nucleon-deuteron (Nd) scattering and the deuteron breakup process at
the lab. nucleon energies up to 135 MeV. The formalism of the Faddeev equations
is used to obtain 3N scattering states. We compare predictions based on the
JISP16 force with data and with results based on various NN interactions: the
CD Bonn, the AV18, the chiral force with the semi-local regularization at the
5th order of the chiral expansion and with low-momentum interactions obtained
from the CD Bonn force as well as with the predictions from the combination of
the AV18 NN interaction and the Urbana IX 3N force. JISP16 provides a
satisfactory description of some observables at low energies but strong
deviations from data as well as from standard and chiral potential predictions
with increasing energy. However, there are also polarization observables at low
energies for which the JISP16 predictions differ from those based on the other
forces by a factor of two. The reason for such a behavior can be traced back to
the P-wave components of the JISP16 force. At higher energies the deviations
can be enhanced by an interference with higher partial waves and by the
properties of the JISP16 deuteron wave function. In addition, we compare the
energy and angular dependence of predictions based on the JISP16 force with the
results of the low-momentum forces obtained with different values of the
momentum cutoff parameter. We found that such low-momentum forces can be
employed to interpret the Nd elastic scattering data only below some specific
energy which depends on the cutoff parameter. Since JISP16 is defined in a
finite oscillator basis, it has properties similar to low momentum interactions
and its application to the description of Nd scattering data is limited to a
low momentum transfer region.Comment: 26 pages, 12 eps figures; Version accepted to Phys. Rev. C: text is
shortened, few figures regarding the nucleon-deuteron elastic scattering
observables are removed but a short discussion of the nucleon induced
deuteron breakup cross section is added. Conclusions remain unchange
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