Showing papers in "Lecture Notes in Physics in 2011"

On the attraction between two perfectly conducting plates

Abstract: Casimir forces are associated with topological constraints on quantum fields. The most famous such effect was predicted in 1948 by Casimir, who found that there is an attractive force

Introduction to Holographic Superconductors

Abstract: These lectures give an introduction to the theory of holographic superconductors These are superconductors that have a dual gravitational description using gauge/gravity duality After introducing a suitable gravitational theory, we discuss its properties in various regimes: the probe limit, the effects of backreaction, the zero temperature limit, and the addition of magnetic fields Using the gauge/gravity dictionary, these properties reproduce many of the standard features of superconductors Some familiarity with gauge/gravity duality is assumed A list of open problems is included at the end

The CBM Physics Book

Abstract: Part 0: General Introduction.- Part I: Bulk Properties of Strongly Interacting Matter.- Part II: In-Medium Excitations.- Part III Collision Dynamics.- Part IV: Observables and Predictions.- Part V The CBM Experiment.- Glossary.- References.

New Structures for Physics

Abstract: Part I An ABC on Compositionality.- Part II Manifestations of Linearity.- Part III More Example Applications.- Part IV Informatic Geometry.- Part V. Spatio-Temporal Geometry.- Part VI Geometry and Topology in Computation.

Prelude to compressed baryonic matter

Abstract: Why study compressed baryonic matter, or more generally strongly interacting matter at high densities and temperatures? Most obviously, because it’s an important piece of Nature. The whole universe, in the early moments of the big bang, was filled with the stuff. Today, highly compressed baryonic matter occurs in neutron stars and during crucial moments in the development of supernovae. Also, working to understand compressed baryonic matter gives us new perspectives on ordinary baryonic matter, i.e. the matter in atomic nuclei. But perhaps the best answer is a variation on the one George Mallory gave, when asked why he sought to scale Mount Everest: Because, as a prominent feature in the landscape of physics, it’s there. Compressed baryonic matter is a material we can produce in novel, challenging experiments that probe new extremes of temperature and density. On the theoretical side, it is a mathematically well-defined domain with a wealth of novel, challenging problems, as well as wide-ranging connections. Its challenges have already inspired a lot of very clever work, and revealed some wonderful surprises, as documented in this volume.

From gravity to thermal gauge theories : the AdS/CFT correspondence

Abstract: Introduction to the AdS/CFT Correspondence- Perturbations of anti-de Sitter Black Holes- Introduction to the AdS/CFT Correspondence- Improved Holographic QCD- The Dynamics of Quark Gluon Plasma and AdS/CFT- Fluid Dynamics from Gravity- The Gauge-gravity Duality and Heavy Ion-Collisions- AdS/CFT on the Brane- Condensed Matter and AdS/CFT- Introduction to Holographic Superconductors- Flavor Superconductivity and Superfluidity- Holographic Torsion and the Prelude to Kalb-Ramond Superconductivity- Index

Fluctuations, Dissipation and the Dynamical Casimir Effect

Abstract: Vacuum fluctuations provide a fundamental source of dissipation for systems coupled to quantum fields by radiation pressure. In the dynamical Casimir effect, accelerating neutral bodies in free space give rise to the emission of real photons while experiencing a damping force which plays the role of a radiation reaction force. Analog models where non-stationary conditions for the electromagnetic field simulate the presence of moving plates are currently under experimental investigation. A dissipative force might also appear in the case of uniform relative motion between two bodies, thus leading to a new kind of friction mechanism without mechanical contact. In this paper, we review recent advances on the dynamical Casimir and non-contact friction effects, highlighting their common physical origin.

Quantum Chromodynamics and Chiral Symmetry

Abstract: Chiral perturbation theory (ChPT) provides a systematic framework for investigating strong-interaction processes at low energies, as opposed to a perturbative treatment of quantum chromodynamics (QCD) at high momentum transfers in terms of the “running coupling constant.” The basis of ChPT is the global \(\hbox{SU}(3)_L\times \hbox{SU}(3)_R\times{U}(1)_V\) symmetry of the QCD Lagrangian in the limit of massless \(u, d,\) and \(s\) quarks. This symmetry is assumed to be spontaneously broken down to \(\hbox{SU}(3)_V\times{U(1)}_V\) giving rise to eight massless Goldstone bosons. In this chapter we will describe in detail one of the foundations of ChPT, namely the symmetries of QCD and their consequences in terms of QCD Green functions.

Fluctuation-Induced Forces Between Atoms and Surfaces: The Casimir–Polder Interaction

Abstract: Electromagnetic fluctuation-induced forces between atoms and surfaces are generally known as Casimir–Polder interactions. The exact knowledge of these forces is rapidly becoming important in modern experimental set-ups and for technological applications. Recent theoretical and experimental investigations have shown that such an interaction is tunable in strength and sign, opening new perspectives to investigate aspects of quantum field theory and condensed-matter physics. In this chapter we review the theory of fluctuation-induced interactions between atoms and a surface, paying particular attention to the physical characterization of the system. We also survey some recent developments concerning the role of temperature, situations out of thermal equilibrium, and measurements involving ultra-cold atoms.

Numerical Methods for Computing Casimir Interactions

Abstract: We review several different approaches for computing Casimir forces and related fluctuation-induced interactions between bodies of arbitrary shapes and materials. The relationships between this problem and well known computational techniques from classical electromagnetism are emphasized. We also review the basic principles of standard computational methods, categorizing them according to three criteria—choice of problem, basis, and solution technique—that can be used to classify proposals for the Casimir problem as well. In this way, mature classical methods can be exploited to model Casimir physics, with a few important modifications.

Observables and predictions

Abstract: 1 Introduction 2 Exploring the QCD phase diagram 3 Review of experimental observations 4 Hadron production 5 Transverse mass spectra 6 Collective flow 7 Dileptons 8 Open and hidden charm 9 Fluctuations and correlations 10 Dibaryons, hypernuclei and strange nuclear systems at FAIR 11 Summary

The Dynamics of Quark-Gluon Plasma and AdS/CFT

Abstract: In these pedagogical lectures, we present the techniques of the AdS/CFT correspondence which can be applied to the study of real time dynamics of a strongly coupled plasma system. These methods are based on solving gravitational Einstein’s equations on the string/gravity side of the AdS/CFT correspondence. We illustrate these techniques with applications to the boost-invariant expansion of a plasma system. We emphasize the common underlying AdS/CFT description both in the large proper time regime where hydrodynamic dynamics dominates, and in the small proper time regime where the dynamics is far from equilibrium. These AdS/CFT methods provide a fascinating arena interrelating General Relativity phenomenae with strongly coupled gauge theory physics.

Massive Stars and their Supernovae

Abstract: Our understanding of stellar evolution and the final explosive endpoints such as supernovae or hypernovae or gamma-ray bursts relies on the combination of (a) (magneto-)hydrodynamics, (b) energy generation due to nuclear reactions accomanying composition changes, (c) radiation transport, (d) thermodynamic properties (such as the equation of state of stellar matter).

Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity

Abstract: From the beginning of the subject, calculations of quantum vacuum energies or Casimir energies have been plagued with two types of divergences: The total energy, which may be thought of as some sort of regularization of the zero-point energy, \(\sum\frac{1}{ 2}\hbar\omega,\) seems manifestly divergent. And local energy densities, obtained from the vacuum expectation value of the energy-momentum tensor, \(\langle T_{00}\rangle ,\) typically diverge near boundaries. These two types of divergences have little to do with each other. The energy of interaction between distinct rigid bodies of whatever type is finite, corresponding to observable forces and torques between the bodies, which can be unambiguously calculated. The divergent local energy densities near surfaces do not change when the relative position of the rigid bodies is altered. The self-energy of a body is less well-defined, and suffers divergences which may or may not be removable. Some examples where a unique total self-stress may be evaluated include the perfectly conducting spherical shell first considered by Boyer, a perfectly conducting cylindrical shell, and dilute dielectric balls and cylinders. In these cases the finite part is unique, yet there are divergent contributions which may be subsumed in some sort of renormalization of physical parameters. The finiteness of self-energies is separate from the issue of the physical observability of the effect. The divergences that occur in the local energy-momentum tensor near surfaces are distinct from the divergences in the total energy, which are often associated with energy located exactly on the surfaces. However, the local energy-momentum tensor couples to gravity, so what is the significance of infinite quantities here? For the classic situation of parallel plates there are indications that the divergences in the local energy density are consistent with divergences in Einstein’s equations; correspondingly, it has been shown that divergences in the total Casimir energy serve to precisely renormalize the masses of the plates, in accordance with the equivalence principle. This should be a general property, but has not yet been established, for example, for the Boyer sphere. It is known that such local divergences can have no effect on macroscopic causality.

Topology of quantum vacuum

Abstract: Topology in momentum space is the main characteristics of the ground states of a system at zero temperature, the quantum vacua. The gaplessness of fermions in bulk, on the surface or inside the vortex core is protected by topology. Irrespective of the deformation of the parameters of the microscopic theory, the energy spectrum of these fermions remains strictly gapless. This solves the main hierarchy problem in particle physics. The quantum vacuum of Standard Model is one of the representatives of topological matter alongside with topological superfluids and superconductors, topological insulators and semi-metals, etc. There is a number of of topological invariants in momentum space of different dimensions. They determine universality classes of the topological matter and the type of the effective theory which emerges at low energy, give rise to emergent symmetries, including the effective Lorentz invariance, and emergent gauge and gravitational fields. The topological invariants in extended momentum and coordinate space determine the bulk-surface and bulk-vortex correspondence, connecting the topology in bulk with the real space. The momentum space topology gives some lessons for quantum gravity. In effective gravity emerging at low energy, the collective variables are the tetrad field and spin connections, while the metric is the composite object of tetrad field. This suggests that the Einstein-Cartan-Sciama-Kibble theory with torsion field is more relevant. There are also several scenarios of Lorentz invariance violation governed by topology, including splitting of Fermi point and development of the Dirac points with quadratic and cubic spectrum. The latter leads to the natural emergence of the Horava-Lifshitz gravity.

Binary Systems and Their Nuclear Explosions

Abstract: The nuclear energy supply of a typical star like the Sun would be ~ 1052 erg if all the hydrogen could be incinerated into iron peak elements. Since the gravitational binding energy is ~ 1049 erg, it is evident that the nuclear energy content is more than enough to blow up the Sun. However, stars are stable thanks to the fact that their matter obeys the equation of state of a classical ideal gas that acts as a thermostat: if some energy is released as a consequence of a thermal fluctuation, the gas expands, the temperature drops and the instability is quenched. The first researchers to discuss the scenario under which stars could explosively release their nuclear energy were Hoyle and Fowler (1960). They showed that this could occur under conditions of dynamic compression, as a consequence of collapse, or under electron degeneracy. They also pointed out in their seminal paper that hydrogen could only be responsible for mild explosions, like novae, as a consequence of the necessity to convert two protons into two neutrons, and that only the thermonuclear fusion of carbon could be energetic enough to feed a strong explosion. They did not consider helium because by this epoch the He-burning mechanism was not yet known.

In-medium excitations

Abstract: 1 Introduction 2 Electromagnetic probes and light vector mesons 3 Hadronic resonance spectroscopy 4 Strangeness 5 Open charm probes 6 Charmonium 7 Excitations of color-superconducting matter 8 Summary and relations to observables

Bulk properties of strongly interacting matter

Abstract: 1 Introduction 2 QCD and its thermodynamics 3 Equation of state and phase boundaries of strongly interacting matter 4 Model descriptions of strongly interacting matter near deconfinement 5 Summary

Progress in Experimental Measurements of the Surface–Surface Casimir Force: Electrostatic Calibrations and Limitations to Accuracy

Abstract: Several new experiments have extended studies of the Casimir force into new and interesting regimes. This recent work will be briefly reviewed. With this recent progress, new issues with background electrostatic effects have been uncovered. The myriad of problems associated with both patch potentials and electrostatic calibrations are discussed and the remaining open questions are brought forward.

The Pulsations of the Sun and the Stars

Abstract: Preface.- General Overview.- Advances in Global and Local Helioseismology: an Introductory Review.- Section 1: The Sun as a Star.- The Quiet Solar Photosphere: Dynamics and Magnetism.- Modeling and Prediction of Solar Cycles Using Data Assimilation Methods.- Amplitudes of Solar Gravity Modes.- Unveiling Stellar Cores and Multipole Moments via Their Flattening.- From Heliosismology to Asterosismology: Some Recent Developments.- Section 2: Stellar Pulsations.- Issues Relating to Observables of Rapidly Rotating Stars.- Seismic Diagnostics for Rotating Massive Main Sequence Stars.- Asymptotic Theory of Stellar Oscillations Based on Ray Dynamics.- Angular Momentum Transport by Regular Gravito-Inertial Waves in Stellar Radiation Zones.- Stochastic Excitation of Acoustic Modes in Stars.

Casimir Effect in the Scattering Approach: Correlations Between Material Properties, Temperature and Geometry

Abstract: We present calculations of the quantum and thermal Casimir interaction between real mirrors in electromagnetic fields using the scattering approach. We begin with a pedagogical introduction of this approach in simple cases where the scattering is specular. We then discuss the more general case of stationary arbitrarily shaped mirrors and present in particular applications to two geometries of interest for experiments, that is corrugated plates and the plane-sphere geometry. The results nicely illustrate the rich correlations existing between material properties, temperature and geometry in the Casimir effect.

Stochastic Excitation of Acoustic Modes in Stars

Abstract: For more than ten years, solar-like oscillations have been detected and frequencies measured for a growing number of stars with various characteristics (e.g. different evolutionary stages, effective temperatures, gravities, metal abundances...). Excitation of such oscillations is attributed to turbulent convection and takes place in the uppermost part of the convective envelope. Since the pioneering work of Goldreich and Keeley (APJ, 211:934, 1977; 212:243, 1977) more sophisticated theoretical models of stochastic excitation were developed, which differ from each other both by the way turbulent convection is modeled and by the assumed sources of excitation. We review here these different models and their underlying approximations and assumptions. We emphasize how the computed mode excitation rates crucially depend on the way turbulent convection is described but also on the stratification and the metal abundance of the upper layers of the star. In turn we will show how the seismic measurements collected so far allow us to infer properties of turbulent convection in stars.

Introduction to Anti de Sitter Black Holes

Abstract: These introductory notes concern basic properties of negative constant curvature spacetimes and their black holes. For comparison purposes we will begin by reviewing flat spacetime, the spacetime diagram and two particular patches, Milne and Rindler. We will then discuss anti de Sitter, its symmetries, basic properties and the construction of the spacetime diagram. We then look into the properties of anti de Sitter spacetime giving some global and local parametrisations. We will study the static black holes and then discuss their basic properties and novel topological effects due to the presence of a negative cosmological constant. We show using the classical Euclidean path integral approach their thermodynamic properties in the canonical ensemble with a heat bath of constant temperature. Finally we discuss, rather briefly, stationary and axially symmetric spacetimes and some properties of the rotating black holes.

Modern Experiments on Atom-Surface Casimir Physics

Abstract: In this chapter we review past and current experimental approaches to measuring the long-range interaction between atoms and surfaces, the so-called Casimir-Polder force. These experiments demonstrate the importance of going beyond the perfect conductor approximation and stipulate the relevance of the Dzyaloshinskii-Lifshitz-Pitaevskii theory. We discuss recent generalizations of that theory, that include higher multipole polarizabilities, and present a list of additional effects, that may become important in future Casimir-Polder experiments. Among the latter, we see great potential for spectroscopic techniques, atom interferometry, and the manipulation of ultra-cold quantum matter (e.g. BEC) near surfaces. We address approaches based on quantum reflection and discuss the atomic beam spin-echo experiment as a particular example. Finally, some of the advantages of Casimir-Polder techniques in comparison to Casimir force measurements between macroscopic bodies are presented.

Chiral Perturbation Theory for Baryons

Abstract: So far we have considered the purely mesonic sector of chiral perturbation theory, involving the interaction of Goldstone bosons with each other and with external fields. However, ChPT can be extended to also describe the dynamics of baryons at low energies. Here we will concentrate on matrix elements with a single baryon in the initial and final states. As in the mesonic sector, Green functions are calculated in an effective-Lagrangian approach in combination with a power counting. The symmetries of QCD and the pattern of their breaking again constrain the possible interaction terms appearing in the effective Lagrangian, and we will discuss several approaches to obtain a consistent power counting.

Geometry and material effects in Casimir physics - Scattering theory

Abstract: We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, to nonzero temperatures, and to spatial arrangements in which one object is enclosed in another. Our method combines each object’s classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. This approach, which combines methods of statistical physics and scattering theory, is well suited to analyze many diverse phenomena. We illustrate its power and versatility by a number of examples, which show how the interplay of geometry and material properties helps to understand and control Casimir forces. We also examine whether electrodynamic Casimir forces can lead to stable levitation. Neglecting permeabilities, we prove that any equilibrium position of objects subject to such forces is unstable if the permittivities of all objects are higher or lower than that of the enveloping medium; the former being the generic case for ordinary materials in vacuum.

The Early Solar System

Abstract: This chapter presents a (partial) review of the information we can derive on the early history of the Solar System from radioactive nuclei of very different half-life, which were recognized to have been present alive in pristine solids. In fact, radioactivities open for us a unique window on the evolution of the solar nebula and provide tools for understanding the crucial events that determined and accompanied the formation of the Sun. Discussing these topics will require consideration of (at least) the following issues. (i) The determination of an age for solar system bodies, as it emerged especially from the application of radioactive dating. (ii) A synthetic account of the measurements that proved the presence of radioactive nuclei (especially those of half-life lower than about 100 Million years) in the Early Solar System (hereafter ESS). (iii) An explanation of their existence in terms of galactic nucleosynthesis, and/or of local processes (either exotic or in-situ) preceding and accompanying the formation of the Sun. This will also need some reference to the present scenarios for star formation, as applied to the ESS.

Modeling and Prediction of Solar Cycles Using Data Assimilation Methods

Abstract: Variations of solar activity are a result of a complicate dynamo process in the convection zone We consider this phenomenon in the context of sunspot number variations, which have detailed observational data during the past 23 solar cycles However, despite the known general properties of the solar cycles a reliable forecast of the 11-year sunspot number is still a problem The main reasons are imperfect dynamo models and deficiency of the necessary observational data To solve this problem we propose to use data assimilation methods These methods combine observational data and models for best possible, efficient and accurate estimates of physical properties that cannot be observed directly The methods are capable of providing a forecast of the system future state It is demonstrated that the Ensemble Kalman Filter (EnKF) method can be used to assimilate the sunspot number data into a non-linear \(\alpha{-}\Upomega\) mean-field dynamo model, which takes into account dynamics of turbulent magnetic helicity We apply this method for characterization of the solar dynamo properties and for prediction of the sunspot number

AdS/CFT on the Brane

Abstract: It is widely recognized that the AdS/CFT correspondence is a useful tool to study strongly coupled field theories. On the other hand, Randall-Sundrum (RS) braneworld models have been actively discussed as a novel cosmological framework. Interestingly, the geometrical set up of braneworlds is quite similar to that in the AdS/CFT correspondence. Hence, it is legitimate to seek a precise relation between these two different frameworks. In this lecture, I will explain how the AdS/CFT correspondence is related to the RS braneworld models. There are two different versions of RS braneworlds, namely, the single-brane model and the two-brane model. In the case of the single-brane model, we reveal the relation between the geometrical and the AdS/CFT correspondence approach using the gradient expansion method. It turns out that the high energy and the Weyl term corrections found in the geometrical approach correspond to the CFT matter correction found in the AdS/CFT correspondence approach. In the case of two-brane system, we also show that the AdS/CFT correspondence play an important role in the sense that the low energy effective field theory can be described by the conformally coupled scalar-tensor theory where the radion plays the role of the scalar field. We also discuss dilatonic braneworld models from the point of view of the AdS/CFT correspondence.