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 ∼30% 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$\phi$) component of the stress tensor was approximated by ($\alpha$ P) with a unknown constant $\alpha$. 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'