9,956 research outputs found
Letter from E. F. Horn to Perry M. Colson
Letter from E. F. Horn to Perry M. Colson. The handwritten note is dated 2 May 1907
General criterion for the entanglement of two indistinguishable particles
We relate the notion of entanglement for quantum systems composed of two
identical constituents to the impossibility of attributing a complete set of
properties to both particles. This implies definite constraints on the
mathematical form of the state vector associated with the whole system. We then
analyze separately the cases of fermion and boson systems, and we show how the
consideration of both the Slater-Schmidt number of the fermionic and bosonic
analog of the Schmidt decomposition of the global state vector and the von
Neumann entropy of the one-particle reduced density operators can supply us
with a consistent criterion for detecting entanglement. In particular, the
consideration of the von Neumann entropy is particularly useful in deciding
whether the correlations of the considered states are simply due to the
indistinguishability of the particles involved or are a genuine manifestation
of the entanglement. The treatment leads to a full clarification of the subtle
aspects of entanglement of two identical constituents which have been a source
of embarrassment and of serious misunderstandings in the recent literature.Comment: 18 pages, Latex; revised version: Section 3.2 rewritten, new Theorems
added, reference [1] corrected. To appear on Phys.Rev.A 70, (2004
Singular value decomposition and matrix reorderings in quantum information theory
We review Schmidt and Kraus decompositions in the form of singular value
decomposition using operations of reshaping, vectorization and reshuffling. We
use the introduced notation to analyse the correspondence between quantum
states and operations with the help of Jamiolkowski isomorphism. The presented
matrix reorderings allow us to obtain simple formulae for the composition of
quantum channels and partial operations used in quantum information theory. To
provide examples of the discussed operations we utilize a package for the
Mathematica computing system implementing basic functions used in the
calculations related to quantum information theory.Comment: 11 pages, no figures, see
http://zksi.iitis.pl/wiki/projects:mathematica-qi for related softwar
H_2 and CO Emission from Disks around T Tauri and Herbig Ae Pre-Main-Sequence Stars and from Debris Disks around Young Stars: Warm and Cold Circumstellar Gas
We present ISO Short-Wavelength Spectrometer observations of H_2 pure-rotational line emission from the disks around low- and intermediate-mass pre-main-sequence stars as well as from young stars thought to be surrounded by debris disks. The pre-main-sequence sources have been selected to be isolated from molecular clouds and to have circumstellar disks revealed by millimeter interferometry. We detect "warm" (T ≈100-200 K) H_2 gas around many sources, including tentatively the debris-disk objects. The mass of this warm gas ranges from ~ 10^(-4) M_☉ up to 8 x 10^(-3) and can constitute a nonnegligible fraction of the total disk mass. Complementary single-dish ^(12)CO 3-2/^(13)CO 3-2, and ^(12)CO 6-5 observations have been obtained as well. These transitions probe cooler gas at T ≈ 20-80 K. Most objects show a double-peaked CO emission profile characteristic of a disk in Keplerian rotation, consistent with interferometer data on the lower J lines. The ratios of the ^(12)CO 3-2/^(13)CO 3-2 integrated fluxes indicate that ^(12)CO 3-2 is optically thick but that ^(13)CO 3-2 is optically thin or at most moderately thick. The ^(13)CO 3-2 lines have been used to estimate the cold gas mass. If a H_2/CO conversion factor of 1 x 10^(-4) is adopted, the derived cold gas masses are factors of 10-200 lower than those deduced from 1.3 millimeter dust emission assuming a gas/dust ratio of 100, in accordance with previous studies. These findings confirm that CO is not a good tracer of the total gas content in disks since it can be photodissociated in the outer layers and frozen onto grains in the cold dense part of disks, but that it is a robust tracer of the disk velocity field. In contrast, H_2 can shield itself from photodissociation even in low-mass "optically thin" debris disks and can therefore survive longer. The warm gas is typically 1%-10% of the total mass deduced from millimeter continuum emission, but it can increase up to 100% or more for the debris-disk objects. Thus, residual molecular gas may persist into the debris-disk phase. No significant evolution in the H_2 CO, or dust masses is found for stars with ages in the range of 10^6-10^7 yr, although a decrease is found for the older debris-disk star β Pictoris. The large amount of warm gas derived from H_2 raises the question of the heating mechanism(s). Radiation from the central star as well as the general interstellar radiation field heat an extended surface layer of the disk, but existing models fail to explain the amount of warm gas quantitatively. The existence of a gap in the disk can increase the area of material influenced by radiation. Prospects for future observations with ground- and space-borne observations are discussed
Conditions for CP-Violation in the General Two-Higgs-Doublet Model
The most general Higgs potential of the two-Higgs-doublet model (2HDM)
contains three squared-mass parameters and seven quartic self-coupling
parameters. Among these, one squared-mass parameter and three quartic coupling
parameters are potentially complex. The Higgs potential explicitly violates CP
symmetry if and only if no choice of basis exists in the two-dimensional Higgs
``flavor'' space in which all the Higgs potential parameters are real. We
exhibit four independent potentially complex invariant (basis-independent)
combinations of mass and coupling parameters and show that the reality of all
four invariants provides the necessary and sufficient conditions for an
explicitly CP-conserving 2HDM scalar potential. Additional potentially complex
invariants can be constructed that depend on the Higgs field vacuum expectation
values (vevs). We demonstrate how these can be used together with the
vev-independent invariants to distinguish between explicit and spontaneous
CP-violation in the Higgs sector.Comment: 46 pages, minor typographical errors corrected, accepted for
publication in Phys. Rev.
Classification of multipartite entanglement containing infinitely many kinds of states
We give a further investigation of the range criterion and Low-to-High Rank
Generating Mode (LHRGM) introduced in \cite{Chen}, which can be used for the
classification of states under reversible local filtering
operations. By using of these techniques, we entirely classify the family of
states, which actually contains infinitely many kinds of
states. The classifications of true entanglement of
and systems are briefly listed respectively.Comment: 11 pages, revte
Basis-independent methods for the two-Higgs-doublet model II. The significance of tan(beta)
In the most general two-Higgs-doublet model (2HDM), there is no distinction
between the two complex hypercharge-one SU(2) doublet scalar fields, Phi_a
(a=1,2). Thus, any two orthonormal linear combinations of these two fields can
serve as a basis for the Lagrangian. All physical observables of the model must
therefore be basis-independent. For example, tan(beta)=/ is
basis-dependent and thus cannot be a physical parameter of the model. In this
paper, we provide a basis-independent treatment of the Higgs sector with
particular attention to the neutral Higgs boson mass-eigenstates, which
generically are not eigenstates of CP. We then demonstrate that all physical
Higgs couplings are indeed independent of tan(beta). In specialized versions of
the 2HDM, tan(beta) can be promoted to a physical parameter of the
Higgs-fermion interactions. In the most general 2HDM, the Higgs-fermion
couplings can be expressed in terms of a number of physical "tan(beta)--like"
parameters that are manifestly basis-independent. The minimal supersymmetric
extension of the Standard Model provides a simple framework for exhibiting such
effects.Comment: 56 pages, 5 tables, with Eq. (65) corrected (erratum to appear in
Physical Review D
The - divergence and Mixing times of quantum Markov processes
We introduce quantum versions of the -divergence, provide a detailed
analysis of their properties, and apply them in the investigation of mixing
times of quantum Markov processes. An approach similar to the one presented in
[1-3] for classical Markov chains is taken to bound the trace-distance from the
steady state of a quantum processes. A strict spectral bound to the convergence
rate can be given for time-discrete as well as for time-continuous quantum
Markov processes. Furthermore the contractive behavior of the
-divergence under the action of a completely positive map is
investigated and contrasted to the contraction of the trace norm. In this
context we analyse different versions of quantum detailed balance and, finally,
give a geometric conductance bound to the convergence rate for unital quantum
Markov processes
Abstract involutions of algebraic groups and of Kac-Moody groups
Based on the second author's thesis in this article we provide a uniform
treatment of abstract involutions of algebraic groups and of Kac-Moody groups
using twin buildings, RGD systems, and twisted involutions of Coxeter groups.
Notably we simultaneously generalize the double coset decompositions
established by Springer and by Helminck-Wang for algebraic groups and by
Kac-Wang for certain Kac-Moody groups, we analyze the filtration studied by
Devillers-Muhlherr in the context of arbitrary involutions, and we answer a
structural question on the combinatorics of involutions of twin buildings
raised by Bennett-Gramlich-Hoffman-Shpectorov
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