7,949 research outputs found
Topological Aspects of the Non-adiabatic Berry Phase
The topology of the non-adiabatic parameter space bundle is discussed for
evolution of exact cyclic state vectors in Berry's original example of split
angular momentum eigenstates. It turns out that the change in topology occurs
at a critical frequency. The first Chern number that classifies these bundles
is proportional to angular momentum. The non-adiabatic principal bundle over
the parameter space is not well-defined at the critical frequency.Comment: 14 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas
78712, to appear in J. Physics
Resonances, Unstable Systems and Irreversibility: Matter Meets Mind
The fundamental time-reversal invariance of dynamical systems can be broken
in various ways. One way is based on the presence of resonances and their
interactions giving rise to unstable dynamical systems, leading to well-defined
time arrows. Associated with these time arrows are semigroups bearing time
orientations. Usually, when time symmetry is broken, two time-oriented
semigroups result, one directed toward the future and one directed toward the
past. If time-reversed states and evolutions are excluded due to resonances,
then the status of these states and their associated backwards-in-time oriented
semigroups is open to question. One possible role for these latter states and
semigroups is as an abstract representation of mental systems as opposed to
material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum
Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior
Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting,
7-22 July 2004, University of Denver. Accepted for publication in the
Internation Journal of Theoretical Physic
Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher Order S-Matrix Poles
In analogy to Gamow vectors that are obtained from first order resonance
poles of the S-matrix, one can also define higher order Gamow vectors which are
derived from higher order poles of the S-matrix. An S-matrix pole of r-th order
at z_R=E_R-i\Gamma/2 leads to r generalized eigenvectors of order k= 0, 1, ...
, r-1, which are also Jordan vectors of degree (k+1) with generalized
eigenvalue (E_R-i\Gamma/2). The Gamow-Jordan vectors are elements of a
generalized complex eigenvector expansion, whose form suggests the definition
of a state operator (density matrix) for the microphysical decaying state of
this higher order pole. This microphysical state is a mixture of non-reducible
components. In spite of the fact that the k-th order Gamow-Jordan vectors has
the polynomial time-dependence which one always associates with higher order
poles, the microphysical state obeys a purely exponential decay law.Comment: 39 pages, 3 PostScript figures; sub2.eps may stall some printers and
should then be printed out separately; ghostview is o.
Entanglement and State Preparation
When a subset of particles in an entangled state is measured, the state of
the subset of unmeasured particles is determined by the outcome of the
measurement. This first measurement may be thought of as a state preparation
for the remaining particles. In this paper, we examine how the duration of the
first measurement effects the state of the unmeasured subsystem. The state of
the unmeasured subsytem will be a pure or mixed state depending on the nature
of the measurement.
In the case of quantum teleportation we show that there is an eigenvalue
equation which must be satisfied for accurate teleportation. This equation
provides a limitation to the states that can be accurately teleported.Comment: 24 pages, 3 figures, submitted to Phys. Rev.
The density matrix in the de Broglie-Bohm approach
If the density matrix is treated as an objective description of individual
systems, it may become possible to attribute the same objective significance to
statistical mechanical properties, such as entropy or temperature, as to
properties such as mass or energy. It is shown that the de Broglie-Bohm
interpretation of quantum theory can be consistently applied to density
matrices as a description of individual systems. The resultant trajectories are
examined for the case of the delayed choice interferometer, for which Bell
appears to suggest that such an interpretation is not possible. Bell's argument
is shown to be based upon a different understanding of the density matrix to
that proposed here.Comment: 15 pages, 4 figure
Irreversible Quantum Mechanics in the Neutral K-System
The neutral Kaon system is used to test the quantum theory of resonance
scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with
complex Hamiltonian is obtained by truncating the complex basis vector
expansion of the exact theory in Rigged Hilbert space. This can be done for K_1
and K_2 as well as for K_S and K_L, depending upon whether one chooses the
(self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP.
As an unexpected curiosity one can show that the exact theory (without
truncation) predicts long-time 2 pion decays of the neutral Kaon system even if
the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include
Chern number spins of Mn acceptor magnets in GaAs
We determine the effective total spin of local moments formed from
acceptor states bound to Mn ions in GaAs by evaluating their magnetic Chern
numbers. We find that when individual Mn atoms are close to the sample surface,
the total spin changes from to , due to quenching of the
acceptor orbital moment. For Mn pairs in bulk, the total depends on the
pair orientation in the GaAs lattice and on the separation between the Mn
atoms. We point out that Berry curvature variation as a function of local
moment orientation can profoundly influence the quantum spin dynamics of these
magnetic entities.Comment: 4 pages, 3 figure
Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC
Previous work on electroweak radiative corrections to high energy scattering
using soft-collinear effective theory (SCET) has been extended to include
external transverse and longitudinal gauge bosons and Higgs bosons. This allows
one to compute radiative corrections to all parton-level hard scattering
amplitudes in the standard model to NLL order, including QCD and electroweak
radiative corrections, mass effects, and Higgs exchange corrections, if the
high-scale matching, which is suppressed by two orders in the log counting, and
contains no large logs, is known. The factorization structure of the effective
theory places strong constraints on the form of gauge theory amplitudes at high
energy for massless and massive gauge theories, which are discussed in detail
in the paper. The radiative corrections can be written as the sum of
process-independent one-particle collinear functions, and a universal soft
function. We give plots for the radiative corrections to q qbar -> W_T W_T, Z_T
Z_T, W_L W_L, and Z_L H, and gg -> W_T W_T to illustrate our results. The
purely electroweak corrections are large, ranging from 12% at 500 GeV to 37% at
2 TeV for transverse W pair production, and increasing rapidly with energy. The
estimated theoretical uncertainty to the partonic (hard) cross-section in most
cases is below one percent, smaller than uncertainties in the parton
distribution functions (PDFs). We discuss the relation between SCET and other
factorization methods, and derive the Magnea-Sterman equations for the Sudakov
form factor using SCET, for massless and massive gauge theories, and for light
and heavy external particles.Comment: 44 pages, 30 figures. Refs added, typos fixed. ZL ZL plots removed
because of a possible subtlet
The Mid-Infrared Emitting Dust Around AB Aur
Using the Keck I telescope, we have obtained 11.7 micron and 18.7 micron
images of the circumstellar dust emission from AB Aur, a Herbig Ae star. We
find that AB Aur is probably resolved at 18.7 micron with an angular diameter
of 1.2" at a surface brightness of 3.5 Jy/arcsec^2. Most of the dust mass
detected at millimeter wavelengths does not contribute to the 18.7 micron
emission, which is plausibly explained if the system possesses a relatively
cold, massive disk. We find that models with an optically thick, geometrically
thin disk, surrounded by an optically thin spherical envelope fit the data
somewhat better than flared disk models.Comment: ApJ in press, 4 color figure
Basis States for Relativistic, Dynamically-Entangled Particles
In several recent papers on entanglement in relativistic quantum systems and
relativistic Bell's inequalities, relativistic Bell-type two-particle states
have been constructed in analogy to non-relativistic states. These
constructions do not have the form suggested by relativistic invariance of the
dynamics. Two relativistic formulations of Bell-type states are shown for
massive particles, one using the standard Wigner spin basis and one using the
helicity basis. The construction hinges on the use of Clebsch-Gordan
coefficients of the Poincar\'e group to reduce the direct product of two
unitary irreducible representations (UIRs) into a direct sum of UIRs.Comment: 19 pages, three tables, revte
- …