209,698 research outputs found
Coupled oscillators and Feynman's three papers
According to Richard Feynman, the adventure of our science of physics is a
perpetual attempt to recognize that the different aspects of nature are really
different aspects of the same thing. It is therefore interesting to combine
some, if not all, of Feynman's papers into one. The first of his three papers
is on the ``rest of the universe'' contained in his 1972 book on statistical
mechanics. The second idea is Feynman's parton picture which he presented in
1969 at the Stony Brook conference on high-energy physics. The third idea is
contained in the 1971 paper he published with his students, where they show
that the hadronic spectra on Regge trajectories are manifestations of
harmonic-oscillator degeneracies. In this report, we formulate these three
ideas using the mathematics of two coupled oscillators. It is shown that the
idea of entanglement is contained in his rest of the universe, and can be
extended to a space-time entanglement. It is shown also that his parton model
and the static quark model can be combined into one Lorentz-covariant entity.
Furthermore, Einstein's special relativity, based on the Lorentz group, can
also be formulated within the mathematical framework of two coupled
oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman
Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction
Standing waves in the Lorentz-covariant world
When Einstein formulated his special relativity, he developed his dynamics
for point particles. Of course, many valiant efforts have been made to extend
his relativity to rigid bodies, but this subject is forgotten in history. This
is largely because of the emergence of quantum mechanics with wave-particle
duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have
to deal with Lorentz transformations of waves. We now have some understanding
of plane waves or running waves in the covariant picture, but we do not yet
have a clear picture of standing waves. In this report, we show that there is
one set of standing waves which can be Lorentz-transformed while being
consistent with all physical principle of quantum mechanics and relativity. It
is possible to construct a representation of the Poincar\'e group using
harmonic oscillator wave functions satisfying space-time boundary conditions.
This set of wave functions is capable of explaining the quantum bound state for
both slow and fast hadrons. In particular it can explain the quark model for
hadrons at rest, and Feynman's parton model hadrons moving with a speed close
to that of light.Comment: LaTex 20 pages, presented at the 2004 meeting of the International
Association of Relativistic Dynamincs, to be published in the proceeding
Generalized BFT Formalism of Electroweak Theory in the Unitary Gauge
We systematically embed the SU(2)U(1) Higgs model in the unitary
gauge into a fully gauge-invariant theory by following the generalized BFT
formalism. We also suggest a novel path to get a first-class Lagrangian
directly from the original second-class one using the BFT fields.Comment: 14 pages, Latex, no figure
Structure and correlation effects in semiconducting SrTiO₃
We have investigated the effects of structure change and electron correlation on SrTiO₃ single crystals using angle-resolved photoemission spectroscopy. We show that the cubic to tetragonal phase transition at 105 K is manifested by a charge transfer from in-plane (dyz and dzx) bands to out-of-plane (dxy) band, which is opposite to the theoretical predictions. Along this second-order phase transition, we find a smooth evolution of the quasiparticle strength and effective masses. The in-plane band exhibits a peak-dip-hump lineshape, indicating a high degree of correlation on a relatively large (170 meV) energy scale, which is attributed to the polaron formation
Feynman's Decoherence
Gell-Mann's quarks are coherent particles confined within a hadron at rest,
but Feynman's partons are incoherent particles which constitute a hadron moving
with a velocity close to that of light. It is widely believed that the quark
model and the parton model are two different manifestations of the same
covariant entity. If this is the case, the question arises whether the Lorentz
boost destroys coherence. It is pointed out that this is not the case, and it
is possible to resolve this puzzle without inventing new physics. It is shown
that this decoherence is due to the measurement processes which are less than
complete.Comment: RevTex 15 pages including 6 figs, presented at the 9th Int'l
Conference on Quantum Optics (Raubichi, Belarus, May 2002), to be published
in the proceeding
Distances of qubit density matrices on Bloch sphere
We recall the Einstein velocity addition on the open unit ball \B of
and its algebraic structure, called the Einstein gyrogroup. We
establish an isomorphism between the Einstein gyrogroup on \B and the set of
all qubit density matrices representing mixed states endowed with an
appropriate addition. Our main result establishes a relation between the trace
metric for the qubit density matrices and the rapidity metric on the Einstein
gyrogroup \B.Comment: I thank to my supervisor, Jimmie Lawson. This was accepted in Journal
of Mathematical Physics at September 26, 201
A band structure scenario for the giant spin-orbit splitting observed at the Bi/Si(111) interface
The Bi/Si(111) (sqrt{3} x sqrt{3})R30 trimer phase offers a prime example of
a giant spin-orbit splitting of the electronic states at the interface with a
semiconducting substrate. We have performed a detailed angle-resolved
photoemission (ARPES) study to clarify the complex topology of the hybrid
interface bands. The analysis of the ARPES data, guided by a model
tight-binding calculation, reveals a previously unexplored mechanism at the
origin of the giant spin-orbit splitting, which relies primarily on the
underlying band structure. We anticipate that other similar interfaces
characterized by trimer structures could also exhibit a large effect.Comment: 11 pages, 13 figure
A molecular dynamics computer simulation study of room-temperature ionic liquids. I. Equilibrium solvation structure and free energetics
Solvation in 1-ethyl-3-methylmidazolium chloride and in
1-ethyl-3-methylimidazolium hexafluorophosphate near equilibrium is
investigated via molecular dynamics computer simulations with diatomic and
benzenelike molecules employed as probe solutes. It is found that
electrostriction plays an important role in both solvation structure and free
energetics. The angular and radial distributions of cations and anions become
more structured and their densities near the solute become enhanced as the
solute charge separation grows. Due to the enhancement in structural rigidity
induced by electrostriction, the force constant associated with solvent
configuration fluctuations relevant to charge shift and transfer processes is
also found to increase. The effective polarity and reorganization free energies
of these ionic liquids are analyzed and compared with those of highly polar
acetonitrile. Their screening behavior of electric charges is also
investigated.Comment: 12 page
The language of Einstein spoken by optical instruments
Einstein had to learn the mathematics of Lorentz transformations in order to
complete his covariant formulation of Maxwell's equations. The mathematics of
Lorentz transformations, called the Lorentz group, continues playing its
important role in optical sciences. It is the basic mathematical language for
coherent and squeezed states. It is noted that the six-parameter Lorentz group
can be represented by two-by-two matrices. Since the beam transfer matrices in
ray optics is largely based on two-by-two matrices or matrices, the
Lorentz group is bound to be the basic language for ray optics, including
polarization optics, interferometers, lens optics, multilayer optics, and the
Poincar\'e sphere. Because the group of Lorentz transformations and ray optics
are based on the same two-by-two matrix formalism, ray optics can perform
mathematical operations which correspond to transformations in special
relativity. It is shown, in particular, that one-lens optics provides a
mathematical basis for unifying the internal space-time symmetries of massive
and massless particles in the Lorentz-covariant world.Comment: LaTex 8 pages, presented at the 10th International Conference on
Quantum Optics (Minsk, Belarus, May-June 2004), to be published in the
proceeding
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