876 research outputs found
Sine-Gordon Model - Renormalization Group Solutions and Applications
The sine-Gordon model is discussed and analyzed within the framework of the
renormalization group theory. A perturbative renormalization group procedure is
carried out through a decomposition of the sine-Gordon field in slow and fast
modes. An effective slow modes's theory is derived and re-scaled to obtain the
model's flow equations. The resulting Kosterlitz-Thouless phase diagram is
obtained and discussed in detail. The theory's gap is estimated in terms of the
sine-Gordon model paramaters. The mapping between the sine-Gordon model and
models for interacting electrons in one dimension, such as the g-ology model
and Hubbard model, is discussed and the previous renormalization group results,
obtained for the sine-Gordon model, are thus borrowed to describe different
aspects of Luttinger liquid systems, such as the nature of its excitations and
phase transitions. The calculations are carried out in a thorough and
pedagogical manner, aiming the reader with no previous experience with the
sine-Gordon model or the renormalization group approach.Comment: 44 pages, 7 figure
Physical realization of coupled Hilbert-space mirrors for quantum-state engineering
Manipulation of superpositions of discrete quantum states has a mathematical
counterpart in the motion of a unit-length statevector in an N-dimensional
Hilbert space. Any such statevector motion can be regarded as a succession of
two-dimensional rotations. But the desired statevector change can also be
treated as a succession of reflections, the generalization of Householder
transformations. In multidimensional Hilbert space such reflection sequences
offer more efficient procedures for statevector manipulation than do sequences
of rotations. We here show how such reflections can be designed for a system
with two degenerate levels - a generalization of the traditional two-state atom
- that allows the construction of propagators for angular momentum states. We
use the Morris-Shore transformation to express the propagator in terms of
Morris-Shore basis states and Cayley-Klein parameters, which allows us to
connect properties of laser pulses to Hilbert-space motion. Under suitable
conditions on the couplings and the common detuning, the propagators within
each set of degenerate states represent products of generalized Householder
reflections, with orthogonal vectors. We propose physical realizations of this
novel geometrical object with resonant, near-resonant and far-off-resonant
laser pulses. We give several examples of implementations in real atoms or
molecules.Comment: 15 pages, 6 figure
On Hilbert-Schmidt operator formulation of noncommutative quantum mechanics
This work gives value to the importance of Hilbert-Schmidt operators in the
formulation of a noncommutative quantum theory. A system of charged particle in
a constant magnetic field is investigated in this framework
Type Ia Supernova Explosion Models
Because calibrated light curves of Type Ia supernovae have become a major
tool to determine the local expansion rate of the Universe and also its
geometrical structure, considerable attention has been given to models of these
events over the past couple of years. There are good reasons to believe that
perhaps most Type Ia supernovae are the explosions of white dwarfs that have
approached the Chandrasekhar mass, M_ch ~ 1.39 M_sun, and are disrupted by
thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such
accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent
progress in modeling Type Ia supernovae as well as several of the still open
questions are addressed in this review. Although the main emphasis will be on
studies of the explosion mechanism itself and on the related physical
processes, including the physics of turbulent nuclear combustion in degenerate
stars, we also discuss observational constraints.Comment: 38 pages, 4 figures, Annual Review of Astronomy and Astrophysics, in
pres
In vivo imaging of neuromelanin in Parkinson's disease using 18F-AV-1451 PET.
The tau tangle ligand (18)F-AV-1451 ((18)F-T807) binds to neuromelanin in the midbrain, and may therefore be a measure of the pigmented dopaminergic neuronal count in the substantia nigra. Parkinson's disease is characterized by progressive loss of dopaminergic neurons. Extrapolation of post-mortem data predicts that a âŒ30% decline of nigral dopamine neurons is necessary to cause motor symptoms in Parkinson's disease. Putamen dopamine terminal loss at disease onset most likely exceeds that of the nigral cell bodies and has been estimated to be of the order of 50-70%. We investigated the utility of (18)F-AV-1451 positron emission tomography to visualize the concentration of nigral neuromelanin in Parkinson's disease and correlated the findings to dopamine transporter density, measured by (123)I-FP-CIT single photon emission computed tomography. A total of 17 patients with idiopathic Parkinson's disease and 16 age- and sex-matched control subjects had (18)F-AV-1451 positron emission tomography using a Siemens high-resolution research tomograph. Twelve patients with Parkinson's disease also received a standardized (123)I-FP-CIT single photon emission computed tomography scan at our imaging facility. Many of the patients with Parkinson's disease displayed visually apparent decreased (18)F-AV-1451 signal in the midbrain. On quantitation, patients showed a 30% mean decrease in total nigral (18)F-AV-1451 volume of distribution compared with controls (P = 0.004), but there was an overlap of the individual ranges. We saw no significant correlation between symptom dominant side and contralateral nigral volume of distribution. There was no correlation between nigral (18)F-AV-1451 volume of distribution and age or time since diagnosis. In the subset of 12 patients, who also had a (123)I-FP-CIT scan, the mean total striatal dopamine transporter signal was decreased by 45% and the mean total (18)F-AV-1451 substantia nigra volume of distribution was decreased by 33% after median disease duration of 4.7 years (0.5-12.4 years). (18)F-AV-1451 positron emission tomography may be the first radiotracer to reflect the loss of pigmented neurons in the substantia nigra of parkinsonian patients. The magnitude of the nigral signal loss was smaller than the decrease in striatal dopamine transporter signal measured by dopamine transporter single photon emission computed tomography. These findings suggest a more severe loss of striatal nerve terminal function compared with neuronal cell bodies, in accordance with the post-mortem literature
Epistemic and Ontic Quantum Realities
Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position
Flat bands as a route to high-temperature superconductivity in graphite
Superconductivity is traditionally viewed as a low-temperature phenomenon.
Within the BCS theory this is understood to result from the fact that the
pairing of electrons takes place only close to the usually two-dimensional
Fermi surface residing at a finite chemical potential. Because of this, the
critical temperature is exponentially suppressed compared to the microscopic
energy scales. On the other hand, pairing electrons around a dispersionless
(flat) energy band leads to very strong superconductivity, with a mean-field
critical temperature linearly proportional to the microscopic coupling
constant. The prize to be paid is that flat bands can generally be generated
only on surfaces and interfaces, where high-temperature superconductivity would
show up. The flat-band character and the low dimensionality also mean that
despite the high critical temperature such a superconducting state would be
subject to strong fluctuations. Here we discuss the topological and
non-topological flat bands discussed in different systems, and show that
graphite is a good candidate for showing high-temperature flat-band interface
superconductivity.Comment: Submitted as a chapter to the book on "Basic Physics of
functionalized Graphite", 21 pages, 12 figure
Combustion in thermonuclear supernova explosions
Type Ia supernovae are associated with thermonuclear explosions of white
dwarf stars. Combustion processes convert material in nuclear reactions and
release the energy required to explode the stars. At the same time, they
produce the radioactive species that power radiation and give rise to the
formation of the observables. Therefore, the physical mechanism of the
combustion processes, as reviewed here, is the key to understand these
astrophysical events. Theory establishes two distinct modes of propagation for
combustion fronts: subsonic deflagrations and supersonic detonations. Both are
assumed to play an important role in thermonuclear supernovae. The physical
nature and theoretical models of deflagrations and detonations are discussed
together with numerical implementations. A particular challenge arises due to
the wide range of spatial scales involved in these phenomena. Neither the
combustion waves nor their interaction with fluid flow and instabilities can be
directly resolved in simulations. Substantial modeling effort is required to
consistently capture such effects and the corresponding techniques are
discussed in detail. They form the basis of modern multidimensional
hydrodynamical simulations of thermonuclear supernova explosions. The problem
of deflagration-to-detonation transitions in thermonuclear supernova explosions
is briefly mentioned.Comment: Author version of chapter for 'Handbook of Supernovae,' edited by A.
Alsabti and P. Murdin, Springer. 24 pages, 4 figure
Accretion Disc Theory: From the Standard Model Until Advection
Accretion disc theory was first developed as a theory with the local heat
balance, where the whole energy produced by a viscous heating was emitted to
the sides of the disc. One of the most important new invention of this theory
was a phenomenological treatment of the turbulent viscosity, known as ''alpha''
prescription, when the (r) component of the stress tensor was
approximated by ( P) with a unknown constant . This
prescription played the role in the accretion disc theory as well important as
the mixing-length theory of convection for stellar evolution. Sources of
turbulence in the accretion disc are discussed, including nonlinear
hydrodynamical turbulence, convection and magnetic field role. In parallel to
the optically thick geometrically thin accretion disc models, a new branch of
the optically thin accretion disc models was discovered, with a larger
thickness for the same total luminosity. The choice between these solutions
should be done of the base of a stability analysis. The ideas underlying the
necessity to include advection into the accretion disc theory are presented and
first models with advection are reviewed. The present status of the solution
for a low-luminous optically thin accretion disc model with advection is
discussed and the limits for an advection dominated accretion flows (ADAF)
imposed by the presence of magnetic field are analysed.Comment: Roceeding of the Int. Workshop "Observational Evidence for Black
Holes in the Universe". Calcutta, 11-17 January 1998. Kluwer Acad. Pu
Quantum Point Contacts and Coherent Electron Focusing
I. Introduction
II. Electrons at the Fermi level
III. Conductance quantization of a quantum point contact
IV. Optical analogue of the conductance quantization
V. Classical electron focusing
VI. Electron focusing as a transmission problem
VII. Coherent electron focusing (Experiment, Skipping orbits and magnetic
edge states, Mode-interference and coherent electron focusing)
VIII. Other mode-interference phenomenaComment: #3 of a series of 4 legacy reviews on QPC'
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