Official Postgraduate Programs - UCM-Universidad …webs.ucm.es/centros/cont/descargas/documento3263.pdf · · 2009-03-13Official Postgraduate Programs ... - Quantum Information

Master in Fundamental Physics

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Short English version


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Required courses

Quantum Mechanics (6 c) Statistical Physics (6 c) Nuclear and Particle Physics (6 c) Solid State Physics (6 c) Classical Electrodynamics (6 c)

Research Work (30 ECTS)

Optional courses

First year (30 ECTS) Second year (30 ECTS)

Thematic blocks Courses (6 ECTS) Thematic blocks Courses (6 ECTS)

Structure of Matter

- Nuclear Structure - Atomic Processes - Atomic and Molecular Physics

Structure of Matter

- Astroparticle Physics - Physics of the Early Universe

High Energy Physics - Elementary Particles High Energy Physics

- Gauge Theories of the Fundamental Interactions - Statistical Methods and Data Treatment

Quantum Physics - Quantum Field Theory - Advanced Quantum Mechanics

Quantum Physics - Quantum Information and Computation - Fields and Strings

Statistical Physics - Nonequilibrium Systems - Phase Transitions

Condensed Matter Physics

- Advanced Solid State Physics - Kinetics and Equilibrium in Solids - Magnetism in Matter

Condensed Matter Physics

- Physics of Atomic Condensates - Optic and Electronic Semiconductor Properties

Mathematical Methods in Physics

- Functional Analysis - Advanced Differential Geometry - Group Theory

Mathematical Methods in Physics

- Differential Equations and Integrable Systems - Algebraic and Geometrical Methods in Physics

Optics I - Laser Physics - Statistical Optics - Molecular Processes

Optics II

- Laser Beams - Quantum Optics - Laser Systems Dynamics - Nonlinear Optics

General Relativity and Cosmology

- Theoretical Mechanics - Gravitation and Cosmology - General Relativity


- Cosmology and Relativistic Astrophysics - Advance General Relativity and Black Holes

Complex Systems - Collective Phenomena - Computational Physics Complex Systems - Statistical Field Theory

and Applications


BBrriieeff ddeessccrriippttiioonn ooff tthhee LLeeccttuurreess Code: 001 Subject: Quantum Mechanics

Module ECTS credits Type

Basic Module 6 Compulsory subject Lecture hours Practice hours Personal work

40 20 90 Contents

Foundations of Quantum Mechanics (observables, states, measurements, time evolution). Symmetries: space-time symmetries (translations, rotations), discrete symmetries (P, C, T, identical particles). Simple quantum systems (with a finite number of states, 1D systems, 3D systems with rotational symmetry, charged particles in EM fields). Approximation methods (stationary perturbation theory, variation method, semiclassical approximation, transition probabilities, collision theory).

Bibliography

C. Cohen-Tannoudji, B. Diu, F. Laloe: Mécanique Quantique, Hermann, París (1973); English edition: Quantum Mechanics, Wiley Interscience (1977). A. Galindo, P. Pascual: Mecánica Cuántica, 2 vol., Eudema Universidad, Madrid (1989); English edition: Quantum Mechanics, 2 vol., Springer-Verlag (1989 y 1990). L. Schiff: Quantum Mechanics, McGraw-Hill, New York, 3d edition (1968). F. Schwabl: Quantum Mechanics, Springer-Verlag (2002); Advanced Quantum Mechanics, Springer-Verlag (1999). L.E. Ballentine, Quantum Mechanics, a Modern Development, World Scientific Pub. (1998). Prentice Hall (1990).


Code: 002 Subject: Nuclear and Particle Physics



30 15 105 Contents

Nuclear physics: General nuclear properties. Study of the deuteron.

Nucleon-Nucleon scattering. Nuclear forces and symmetries. The Fermi

gas model. Shell model. Collective model. Alfa, Beta and Gamma decay

processes. Fission. Nuclear reactions. Nuclear fusion. Applications of

nuclear physics: from medicine to stellar nucleosynthesis. Particle physics: General properties of elementary particles.

Electromagnetic, strong and weak interactions. Conservation laws and

quantum numbers. Particle structure and quark model, families;

hadrons, quarks and leptons. Theoretical models of elementary particle

interactions. (Note that there are three class groups. Section A is taught in

english and its knowledge is required) Bibliography

K. S. Krane “Introductory Nuclear Physics”, John Wiley and sons, 1987, F. Halzen and A. D. Martin, “Quarks and Leptons”, John Wiley and sons, 1984.


Code: 003 Subject: Solid State Physics



40 20 105 Contenido

Cristal structures. Diffraction. Lattice oscillations: phonons. Electron states: electron gas and band structure. Electronic transport. Dielectrics. Magnetic properties. Superconductivity. Crystal defects.

Bibliography

C. Kittel, Física del Estado Sólido (3ª ed.). Ed. Reverté, 1998. N.W. Ashcroft and N.D. Mermin, Solid State Physics. Holt-Saunders Int. Ed., 1976. H.Ibach and H. Lüth, Solid-state physics: an introduction to theory and experiment. Springer-Verlag, 1993. J. Piqueras and J.M. Rojo, Problemas de introducción a la física del estado sólido. Alhambra, 1980. F.Domínguez-Adame, Física del Estado Sólido:Teoría y Métodos Numéricos. Paraninfo, Madrid 2001.


Code: 004 Subject: Statistical Physics



40 20 90 Contents

Ensemble theory. Classical and quantum statistics. Ideal systems: classical, photons, phonons, electrons and bosons.

Bibliography

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Code: 005 Subject: Classical Electrodynamics



40 20 90 Contents

1.- Introduction. 2.- Special Relativity and covariance of Maxwell equations. 3.- Lagrangian formulation of Classical Electrodynamics. 4.- Symmetries and conserved quantities. 5.- Electromagnetic waves. 5.- Electromagnetic radiation. 6.- Multipole expansion.

Bibliography

L.D. Landau y E.M. Lifshitz, Teoría clásica de campos, Reverté, 1986. J.D. Jackson, Classical Electrodynamics, 3rd ed., Wiley & Sons, 1999. Bo Thidé, Classical Electrodynamics, http://www.plasma.uu.se/CED/Book. A.O. Barut, Electrodynamics and Classical Theory of Fields and Particles, Dover, 1980. V.V. Batyguin, I.N. Toptygin, Problems in Electrodynamics, Academic Press, 1978.


Code: 006 Subject: Advanced Differential Geometry


Mathematical Methods for Physics

6 Optional subject

Lecture hours Practice hours Personal work

30 15 105 Contents

Tensor spaces. Differentiable manifolds. Tensor fields. Differential forms. Tensor bundles. Integration on manifolds. Lie groups. Lie algebras. Invariant differential forms. Connections on the tangent bundle. Covariant derivative. Torsion. Curvature. Bianchi identities. Parallel transport. Holonomy. Geodesics. Riemannian and pseudo-Riemannian geometries. Applications: General Relativity equations. Electromagnetic field. Symplectic geometry. Hamilton equations. Hamilton-Jacobi equation. Poisson geometry. Gauge fields.

Bibliography

R. L. Bishop, S. I. Goldberg, Tensor Analysis on Manifolds, Dover, New York, 1980. B. F. Schutz, Geometrical Methods of Mathematical Physics, Cambridge University Press, Cambridge 1980. R. Abraham, J. E. Marsden, T. Ratiu, Manifolds, Tensor Analysis, and Applications, Springer-Verlag, New York, 1988. Y. Choquet-Bruhat, C. DeWitt-Morett, M. Dillard-Bleick, Analysis, Manifolds and Physics, North-Holland, Amsterdam, 1991.


Code: 007 Subject: Functional Analysis



6 Optional subject


30 15 105 Contents

Lebesgue integration. Normed spaces. Hilbert spaces. Orthonormal bases. Operators in Hilbert spaces. Spectrum. Applications to Quantum Mechanics. Integral equations. Distributions. Fourier transform of distributions. Fundamental solutions: Green functions and propagators.

Bibliography

N. Boccara, Functional Analysis. An Introduction for Physicists. Academic Press, Boston, 1990. L. Abellanas, A. Galindo, Espacios de Hilbert (Geometría, Operadores, Espectros) Eudema, Madrid, 1987. E. Kreyszig, Introductory Functional Analysis with Applications. Wiley, New York, 1978. V.S. Vladimirov, Equations of mathematical physics. Marcel Dekker, New York, 1971. M. Reed, B. Simon, Methods of Modern Mathematical Physics, vols I, II. Academic Press, New York, 1972.


Code: 008 Subject: Group Theory



6 Optional subject


30 15 105 Contents

A brief introduction to finite groups. Lie groups and Lie algebras: Geometry, Maurer-Cartan equation, classification, linear representations. Applications to Physics.

Bibliography

Basic: D.H. Sattinger, O.L. Weaver: Lie Groups and Algebras with Applications, Springer, 1986 Advanced: H. Georgi: Lie Algebras in Particle Physics, Perseus Books, 1999 C. Chevalley: Theory of Lie Groups, Princeton University Press, 1999 Of historical interest: É. Cartan: Oeuvres Complètes, Springer-Éditions du Centre National de la Recherche Scientifique, 1984


Code: 009 Subject: Differential Equations and Integrable

Systems Module ECTS credits Type


6 Optional subject


30 15 105 Contents

Integrable nonlinear partial differential equations in hydrodynamics, random matrix models and quantum gravitation models in two dimensions. Lax formalism, tau functions, dressing methods and soliton theory. Integrable systems in the zero dispersion limit. Hodograph methods. Applications.

Bibliography

V.E. Zakharov, S.V. Manakov, S.P. Novikov and L.P. Pitayevsky, Theory of Solitons. The Method of the Inverse Scattering, Plenum Press, (1984) M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, (1991) P. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes (1999) P. Di Francesco, P. Ginsparg and J. Zinn-Justin, 2D Gravity and Random Matrices, hep-th/9306153


Code: 209 Subject: Algebraic and Geometrical Methods in

Physics Module ECTS credits Type


6 Optional subject


30 15 105 Contents

- Coupled oscillators and synchronization. - Reaction-diffusion equations - Turing instability and pattern formation - Introduction to complex networks

Bibliography

See http://jacobi.fis.ucm.es/david/docencia/master/


Code: 011 Subject: Advanced Quantum Mechanics


Quantum Physics 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

General Perturbation Theory. Min-max principle. Semiclassic approach. Quantum transitions. Scattering theory. Relativistic wave equations (KleinGordon, Dirac, Maxwell). Relativistic hydrogen atom.

Bibliography

1. A. Galindo, P. Pascual. Quantum Mechanics II. Springer Verlag, 1990 2. C. Cohen-Tannoudji, B. Diu, F. Laloe. Mécanique Quantique. Tome II. Hermann, 1973 3. L.I. Schiff. Quantum Mechanics. McGraw-Hill, 1968 4. J.R. Taylor. Scattering Theory. John Wiley, 1972


Code: 012 Subject: Quantum Field Theory



30 15 105 Contents

Classical fields. Poincaré group and CPT symmetries. Free quantum bosonic, fermionic, and gauge fields. Free propagators. Wick’s Theorem. Gell-Mann-Low formula. Reduction formulae. Dimensional regularization and renormalization. Renormalization group. QED. Introduction to quantization and renormalization of non Abelians gauge theories.

Bibliography

C. Itzykson and J.B Zuber : Quantum Field Theory. McGraw-Hill International Editions. M.E. Peskin and D.V. Schroeder: Quantum Field Theory. Westview Press. D. Bailin and A. Love: Introduction to Gauge Field Theory. Institute of Physics Publishing. S. Pokorski: Gauge Field Theories. Cambridge University Press


Code: 013 Subject: Fields and Strings Module ECTS credits Type


30 15 105 Contents

Path integration. Renormalization of gauge theories. Anomalies. Non perturbative solutions. Introduction to Supersymmetry. String theory. Bosonic strings. Superstrings. Compact dimensions and embedding. Strings in curved spacetimes. Applications to Cosmology.

Bibliography

S. Pokorski: Gauge Field Theories. Cambridge University Press. S. Weinberg: The Quantum Theory of Fields. Vol. II. Cambridge University Press. P. West: Introduction to Supersymmetry and Supergravity. World Scientific M. B. Green, J. H. Schwarz, E. Witten: Superstring Theory. Cambridge University Press. M. Kaku: Introduction to Superstrings and M-Theory. Springer. J. Polchinski: String theory. Vol. I. Cambridge University Press.


Code: 014 Subject: Quantum Information and Computation


Quantum Physics 6 Optional Course Lecture hours Practice hours Personal work

30 15 105 Contents

Quantum information. Quantum computation. Cryptography and communications. Information storage. Entangled states. Non-locality and indetermination principle. Teleportation. Classical and quantum algorithms: similarities and differences.

Bibliography

Bouwmeester, D., A. Eckert, and A. Zeilinger (Eds.), The physics of quantum information. Springer-Verlag 2000. Galindo, A. and Martin-Delgado, M.A.: Information and Computation: Classical and Quantum Aspects. Rev. Mod. Phys. 74 (2002) 347-423. Nielsen, M.A., I.L. Chuang, Quantum Computation and Quantum information. Cambridge Univ. Press 2000. Physics World, March issue, 1998.


Code: 015 Subject: Collective Phenomena


Complex Systems 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

Critical phenomena. Symmetry breaking. The renormalization group. Universality. Analysis of some models.

Bibliography

D.J. Amit, V. Martín-Mayor, Field theory, the renormalization group and critical phenomena, third edition. World Scientific, Singapore (2005). G. Parisi, Statistical Field Theory. Perseus Books Group (1998). A.D. Sokal in Quantum Fields on the Computer, Editor M. Creutz. World Scientific, Singapore (1992). N. Goldenfeld, Scaling, Universality and Renormalization Group Theory. Addison-Wesley (1992). M. Le Bellac, Quantum and Statistical Field Theory. Clarendon Press, Oxford (1991). J. Cardy, Scaling and Renormalization in Statistical Physics. Cambridge University Press (1996). J.J. Binney, N.L. Dowrick, A.J. Fisher and M.E.J. Newman. The Modern Theory of Critical Phenomena. Clarendon Press, Oxford (1992).


Code: 016 Subject: Computational Physics



15 45 105 Contents

Monte Carlo techniques. Numerical methods for differential equations. Fourier transformation algorithm. Applications. Use of Maple, etc.

Bibliography

M.L. Abell and J.P. Braselton: Maple V by Example. Academic Press G.L. Articolo: Partial Differential Equations and Boundary Value Problems with Maple V. Academic Press. M . Horbastsch: Quantum Mechanics Using Maple. Springer Verlag S. Lynch: Dynamical Systems with Applications using Maple. Birkhauser J.D. Lambert, Computational Methods in Ordinary Differential Equations, John Wiley & Sons (Nueva York 1973). A.R. Mitchell and D.F. Griffiths, The Finite Difference Method in Partial Differential Equations, John Wiley (Nueva York 1980). K. Binder and D.W. Heerman, Monte Carlo Simulation in Statistical Physics, Springer (Berlin 1997).


Code: 017 Subject: Statistical Field Theory and Applications



30 15 105 Contents

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Bibliography

DD..JJ.. AAmmiitt aanndd VV.. MMaarrttíínn MMaayyoorr,, FFiieelldd TThheeoorryy,, tthhee RReennoorrmmaalliizzaattiioonn GGrroouupp aanndd CCrriittiiccaall PPhheennoommeennaa.. WWoorrlldd--SScciieennttiiffiicc SSiinnggaappoorree,, tthhiirrdd eeddiittiioonn ((22000055)).. GG.. PPaarriissii,, SSttaattiissttiiccaall FFiieelldd TThheeoorryy.. PPeerrsseeuuss BBooookkss GGrroouupp ((11999988)).. PP..EE.. KKllooeeddeenn aanndd EE.. PPllaatteenn,, NNuummeerriiccaall SSoolluuttiioonn ooff SSttoocchhaassttiicc DDiiffffeerreennttiiaall EEqquuaattiioonnss.. SSpprriinnggeerr VVeerrllaagg ((11999922)).. MM.. CCrreeuuttzz,, QQuuaarrkkss,, gglluuoonnss aanndd llaattttiicceess,, CCaammbbrriiddggee UUnniivveerrssiittyy PPrreessss ((11998833)).. HH..JJ.. RRootthhee,, LLaattttiiccee GGaauuggee TThheeoorriieess,, AAnn IInnttrroodduuccttiioonn.. WWoorrlldd--SScciieennttiiffiicc SSiinnggaappoorree,, sseeccoonndd eeddiittiioonn ((11999977))..


Code: 018 Subject: Elementary Particles


High Energy Physics 6 Optional subject Lecture hours Practice hours Personal work

25 20 105 Contents

0. S matrix introduction, Feynman rules. 1. Quantum electrodynamics. 2. Quantum chromodynamics. 3. Electroweak model. 4. Standard model.

Bibliography

T-P. Cheng y L-F. Li: Gauge theories of Elementary particle physics, Oxford University Press (New York 1984). D. Griffiths: Introduction to elementary particle physic, Wiley (New York 1987). H. Halzen y A. D. Martin: Quarks and leptons: an introductory course in modern particle physics, Wiley (New York 1984). D. H. Perkins: Introduction to High energy physics, Addison Wesley (Reading 1982).


Code: 019 Subject: Gauge Theories of the Fundamental

Interactions Module ECTS credits Type

High Energy Physics 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

Introduction to Gauge theories and the Standard Model. Strong interactions (Quantum Chromodynamics, Effective Theories) and Electroweak interactions. Elements of Field Theory relevant for phenomenological studies with the Standard Model.

Bibliography

F.J. Halzen and A.D. Martin, Quarks and Leptons, John Wiley&sons 1984. J.F. Donoghue, E. Golowich and B.R.Holstein, Dynamics of the Standard Model, Cambridge University Press 1994. F.J. Yndurain, The theory of quark and gluon interaction, Springer-Verlag 1999. R.J. Rivers, Path Integral Methods in Quantum Field Theory.


Code: 020 Subject: Statistical Methods and Data Treatment


High Energies Physics 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

1. History and concepts of Probability 2. Axiomatic Probability. 3. Conditional Probability and Bayes´ Theorem. 4. Distribution functions. 5. Mathematical Expectation and Stochastic Characteristics. 6. Statistical models. 7. Ordered samples. 8. Characteristic function. 9. Limit theorems and convergence. 10. Stationary Markov chains. 11. The Monte Carlo method. 12. Statistical inference. 13. Information theory

Bibliography

J. Bernardo y A. Smith: Bayesian theory (John Wiley & Sons, ISBN 0 471 924164). A. Gelman et al.: Bayesian data analysis (Champman and Hall, ISBN 0 412 039915). J.K. Ghosh, M. Delampady and T. Samanta: An Introduction to Bayesian Analysis (Springer; ISBN 0 387 400842). A. Gut: Probability: A Graduate Course (Springer; ISBN 0 387 228330). H. Cramer: Mathematical methods of statistics (Princeton University Press; ISBN 0 691 005472). M. Loeve: Probability theory (D. Van Nostrand Company Inc. 1955). S. Kullback: Information theory and statistics (Dover Pub. Inc.; ISBN 0 486 696847).


Code: 021 Subject: Theoretical Mechanics



6 Optional subject


30 15 105 Contents

Hamilton equations. Poisson brackets. Canonical transformations. Conservation laws. Hamilton-Jacobi theory and Action-Angles variables. Integrable and non integrable systems. Chaos. Canonical Perturbation theory. Continuous systems.

Bibliography

F. R. Gantmacher, Mecánica Analítica (URSS, Moscú, 1996). H. Goldstein, C. Poole, J. Safko, Classical Mechanics (3rd ed.) (Addison Wesley, San Francisco, 2002). J. V. José, E. J. Saletan, Classical Dynamics: a contemporary approach (Cambridge University Press, New York, 2002). L. Meirovitch, Methods of Analytical Dynamics, (McGraw-Hill, New York, 1988).


Code: 022 Subject: General Relativity



6 Optional subject


30 15 105 Contents

• Pseudo-Riemannian geometry • Equivalence principle • Einstein's equations • Weyl curvature: Tidal forces • Isometries • Some exact solutions and classical results. • Gravitational radiation.

Bibliografía

S.M. Carroll, Lecture notes on general relativity,http://es.arxiv.org/abs/gr-qc/9712019. R.M.Wald, General relativity, University of Chicago Press, 1984. I. Ciufolini and J.A. Wheeler, Gravitation and inertia, Princeton Univ. Press, 1995. C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, Freeman and Co., 1973. H. Stephani, General relativity. An introduction to the theory of the gravitational field, Cambridge University Press, 1990. J. Stewart, Advanced general relativity, Cambridge University Press, 1993. D. Kramer, H. Stephani, E. Herlt, M. MacCallum and E. Schmutzer, Exact solutions of Einstein’s field equations, Cambridge University Press, 1981. A.P. Lightman, W.H. Press, R.H. Price y S.A. Teukolsky, Problem book in relativity and gravitation, Princeton University Press, 1975.


Code: 023 Subject: Gravitation and Cosmology



6 Optional subject


30 15 105 Contents

Equivalence principles. Einstein theory of gravitation and classical tests. Gravitational collapse. Cosmological principles. Standard cosmological model.

Bibliography

S. Weinberg. Gravitation and Cosmology. J. Wiley. 1972 J. B. Hartle. Gravity. Addison-Wesley. 2003 B. Schutz. A First Course in General Relativity. 1984 C. W. Misner, K. J. Thorne and J. A. Wheeler. Gravitation. Freeman. 1972 E. W. Kolb and M. S. Turner. The Early Universe. Addison-Wesley. 1994 A. Liddle. An Introduction to Modern Cosmology. J. Wiley. 2003 T. Padmanabhan. Theoretical Astrophysics Vol III: Galaxies and Cosmology. Cambridge University Press. 2002


Code: 024 Subject: Cosmology and Relativistic Astrophysics



6 Optional subject


30 15 105 Contents

1. Friedmann-Lemaître cosmological models. 2. Thermal history of the universe. 3. Cosmological perturbation theory. 4. Inflationary models. 5. Structure formation and cosmic background radiation. 6. Gravitational collapse: supernova explosion. 7. Compact stars: white dwarfs and neutron stars. Perturbations in stellar models. 9. Accretion in compact stars and black holes. 10. Gravitational radiation.

Bibliography

M. Demianski, Relativistic Astrophysics, Pergamon Press, 1985 N.K. Glendenning, Compact Stars: Nuclear physics, Particle physics, and General Relativity, Springer-Verlag, 1996. E. Kolb, M. Turner, The Early Universe, Addison-Wesley, 1994. A.R. Liddle, D.H. Lyth, Cosmological Inflation and Large Scale Structure, Cambridge University Press, 2000. V.F. Mukhanov, H. A. Feldman, R. H. Branderberger, Theory of Cosmological Perturbations, Phys. Rep. 215 (1992) 203. T. Padmanabhan, Theoretical Astrophysics vol III: Galaxies and Cosmology, Cambridge University Press, 2002. S.L. Shapiro, S.A. Teukolsky, Black Holes, White Dwarfs and Neutron Stars: The Physics of Compat Objects, John Wiley & Sons, 1983.


Code: 025 Subject: Advance General Relativity and Black Holes



6 Optional subject


30 15 105 Contents

Spinors in general relativity. Algebraically special fields. Asymptotic structure. Stationary axisymmetric systems. Schwarzschild, charged and rotating black holes. Black holes thermodynamics. Hawking radiation. Acoustic black holes.

Bibliography

N.D. Birrell, P.C.W. Davies: Quantum fields in curved space, Cambridge University Press, 1982). S.W. Hawking, G.F.R. Ellis: The large scale structure of space-time, Cambridge University Press, 1973). M. Heusler: Black Hole Uniqueness Theorems (Cambridge University Press, 1996). M. Novello, M. Visser, G. Volovik: Artificial black holes (World Scientific, 2002). H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, E. Herlt: Exact Solutions of Einstein’s Field Equations (Cambridge University Press, 2nd ed., 2002). J. Stewart: Advanced General Relativity (Cambridge University Press, reprinted, 2003). P.K. Townsend: Lecture notes on Black Holes (http://www.damtp.cam.ac.uk/user/gr/members/townsend.html). M.S. Volkov, D.V. Gal’tsov: Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields, Phys. Rep. 319 (1999) 1-83. R.M. Wald: General Relativity (University of Chicago Press, 1984).


Code: 026 Subject: Atomic and Molecular Physics


Matter Structure 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

Many-electron atoms: Atomic structure; central field approximation and its corrections; Computational techniques; Interaction with external static fields; Spectroscopy. Molecules: Born Oppenheimer approximation; Molecular bond theory; Electronic, vibrational and rotational wave functions; Diatomic molecule spectroscopy.

Bibliography

B.H. Bransden, C.J. Joachain: Physics of Atoms and Molecules. Ed Prentice Hall 2001


Code: 027 Subject: Nuclear Structure



30 15 120 Contents

Nuclear decay processes: alpha, beta and gamma decay. Spectroscopy and nuclear structure. Angular momentum. Models. Nuclear reactions. Nuclear fusion and fission. Applications.

Bibliography

K.S. Krane, Introductory Nuclear Physics (Wiley, 1988)


Code: 028 Subject: Atomic Processes



30 15 105 Contents

Different schemes of coupling: jj; jK and intermediate. Configuration mixing. Hyperfine structure: Effect of an external magnetic field. Quadratic and linear Stark effect. Forbidden transitions: Dipolar magnetic and Quadrupolar electric. Transition probabilities. Atomic clocks. Atomic levels excitation by charged particle collisions. Isotopic shifts. Spectra of multicharged ions. Plasmas produced by laser.

Bibliography

I.I. Sobelman: Atomic Spectra and Radiative Transitions. Springer-Verlag. 1991 S. Svanberg: Atomic and Molecular Spectroscopy. Basic Aspects and Practical Applications. Springer. 2001


Code: 029 Subject: Astroparticle Physics



30 15 105 Contents

Introduction to astroparticle physics. Cosmic particle detection methods. Observation from Earth and from outer space. Sources. Acceleration mechanisms. Propagation. Overview of the field.

Bibliography

F. Aharonian. Very High Energy Cosmic Gamma Radiation.World Scientific 2004 M.S. Longair. High Energy Astrophysics Vol 1. Particles, photons and their detection. Cambridge Univ. Press 1994. C. Grupen, G. Cowan, et al: Astroparticle Physics. Springer 2005.


Code: 030 Subject: Physics of the Early Universe



30 15 105 Contents

First principles. The Friedmann models. Thermal history of the Big Bang model. The very early universe. Phase transitions and inflation. The lepton era. The plasma era. Cosmological perturbations. The cosmic microwave background.

Bibliography

P. Coles, F. Lucchin, Cosmology: The Origin and Evolution of Cosmic Structure. John Wiley & Sons, New York, 2003. S. Weinberg, Gravitation and Cosmology. John Wiley & Sons, New York, 1972. A. Linde, Particle Physics and Inflationary Cosmology. Harwood Academic Publishers, London, 1990. K.S. Krane, Introductory Nuclear Physics. John Wiley & Sons, New York, 1988.


Code: 031 Subject: Nonequilibrium Systems


Statistical Physics 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

Transport equations, kinetic equations. Hydrodynamics and normal modes. Transport coefficients. Time correlation functions. Fluctuation-Dissipation theorem. Diffusion processes. Einstein and Langevin theories. Fokker-Planck equation.

Bibliography

R. Balescu, Equilibrium and Non-equilibrium Statistical Mechanics, John Wiley and Sons, 1975. J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes, Springer Verlag, 1987. P. Resibois y M. de Leener, Classical Kinetic Theory of Fluids, John Wiley and Sons, 1977.


Code: 032 Subject: Phase Transitions


Statistical Physics 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

Phases of matter: crystals, quasicrystals, fluids, mixtures, colloidal dispersions, liquid crystals, polymers. Phase stability, phase transitions and critical phenomena.

Bibliography

C. Fernández Tejero y M. Baus, Física estadística del equilibrio. Fases de la materia. Aula Documental de Investigación (2000)


Code: 033 Subject: Advanced Solid State Physics Module ECTS credits Type

Condensed Matter Physics 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

Energy bands. Elementary excitations. Superconductivity. Magnetism. Non crystalline solids. Defects.

Bibliography

C. Kittel: Quantum Theory of Solids, Ed. Wiley J. M. Ziman: Principles of the Theory of Solids, Ed. Cambridge J. R. Hook and H. E. Hall: Solid State Physics, Ed. Wiley


Code: 034 Subject: Magnetism in Matter Module ECTS credits Type


30 15 105 Contents

Microscopic origin of Magnetism. Magnetic resonances. Dia and paramagnetism. Types of spontaneous magnetic order. Exchange theories. Spin waves. Neutron diffraction.

Bibliography

D. Jiles, Magnetism and Magnetic Materials. Champman and Hall A. Hernando, J.M. Rojo, Física de los Materiales Magnéticos. Síntesis


Code: 035 Subject: Kinetics and Equilibrium in Solids



30 15 105 Contents

Crystalline materials: structure and symmetries. Phase transformations. Diffusion in solids. Material reactivity. Surface reactions.

Bibliography

W.D. Callister, Jr.: Introducción a la Ciencia e Ingeniería de los Materiales, Reverté 1997 D.A. Porter and K.E. Easterling: Phase transformations in metals and alloys, Van Nostrand Reinhold 1986 C.N.R. Rao and K.J. Rao: Phase transitions in solids, McGraw-Hill 1978 M.F. Ashby and D.R.H. Jones: Engineering materials 2, Pergamon 1994 H. Lüth: Surfaces and interfaces of solid materials, Springer 1995 A.W. Adamson: Physical Chemistry of surfaces, Wiley 1990 G.A. Somorjai: Introduction to surface chemistry and catalysis, Wiley 1994 G.A. Somorjai: Fundamentos de química de superficies, Alhambra 1975


Code: 036 Subject: Physics of Atomic Condensates


Condensed Matter Structure 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

History. Independent bosonic condensation. Bosonic interactions: Bogoliubov quasiparticles. Gross-Pitaevskii equation. Macroscopic quantum interference: Josephson efect. Magnetic and optical trapping. Laser cooling. 4He superfluidity.

Bibliography

C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002). L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003). A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971). A. J. Leggett, Bose-Einstein condensation in the alkali gases: Some fundamental concepts, Rev. Mod. Phys. 73, 307 (2001).


Code: 037 Subject: Optical and Electronic Semiconductor Properties



30 15 105 Contents

EElleemmeennttaall aanndd ccoommppoouunndd sseemmiiccoonndduuccttoorrss.. EElleeccttrroonniicc pprrooppeerrttiieess ooff sseemmiiccoonndduuccttoorrss.. OOppttiiccaall pprroocceesssseess:: AAbbssoorrppttiioonn aanndd rraaddiiaattiioonn pprroocceessss.. OOppttiiccaall aanndd eelleeccttrriiccaall sseemmiiccoonndduuccttoorr pprrooppeerrttiieess iinn llooww ddiimmeennssiioonnaall ssyysstteemmss..

Bibliography

P. Yu, M. Cardona, Fundamentals of Semiconductors, Springer 1996 K. Seeger, Semiconductor Physics, Springer, 1989 P. Bhattacharya, Semiconductor Optoelectronic Devices, Prentice Hall, 1997


Code: 038 Subject: Laser Physics Module ECTS credits Type

Optics I 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

Electromagnetic radiation and matter interaction theory. Transition probabilities. Homogeneous and inhomogeneous broadening. Empty cavity modes: Paraxial equation solutions and optical resonators. Light amplification, avalanche lasers and resonance regenerative amplifiers. Rate equations. Output optimisation. Optical pumping. Gas pumping in electrical discharges. Semiconductor injection pumping. Simple dynamical processes. Some applications in investigation and in industrial processes.

Bibliography

J. M. Guerra: Física del Láser, Ed. Alqua (libro libre) 2005 (download for free from : http://www.ucm.es/info/laserlab/docencia.html) Mark Fox: Quantum Optics. An Introduction. Oxford University Press. 2006


Code: 039 Subject: Statistical Optics



30 15 105 Contents

Green’s functions. Light propagation and diffraction integral equation. Relevant approaches. Coherence time. Michelson interferometer. Fourier transform spectroscopy. Spatial coherence. Young interferometer. Second order mutual coherence function and statistical properties. Propagation of the mutual coherence function. Van Cittert-Zernike theorem. Fundamentals of Holography. Volume holograms and volume gratings. Photons correlation: Degeneration parameter. Intensity interferometer. Classical description limit of the optical correlation.

Bibliography

Calvo, M.L. (Coord.), Óptica Avanzada (Advanced Optics), Editorial Ariel, Ariel Ciencia, Barcelona, 2002 [in Spanish]. Calvo, M.L., Alieva, T, Rodrigo J.A. et al., Laboratorio virtual de óptica. Guía práctica. (Virtual laboratory of optics. Practical guide). Delta Publicaciones, Madrid, 2005. [with interactive CD, in Spanish]. Mandel, L., Wolf, E., Optical Coherence and Quantum Optics, Cambridge University Press, New York, 1995. Goodman, J.W., Introduction to Fourier Optics, Editorial McGraw Hill, Third Edition, 2006.


Code: 040 Subject: Molecular processes



30 15 105 Contents

Basic approximations. Emission and absorption of radiation in infrared and microwave ranges. Effects due to nuclear spin, conformational changes, size, temperature and symmetry. Classical limit. Raman processes. Radiative transitions between electronic states. Symmetry requirements. Competition with radiationless processes. Electronic excitation transfer. Nuclear magnetic resonance and applications

Bibliography

Atkins and Friedman, Molecular Quantum Mechanics. Oxford Univ. Tercera edición 1997 Levine, Espectroscopía Molecular. Editorial AC, Madrid 1980 Haken and Wolf, Molecular Physics and Elements of Quantum Chemistry. Springer, 1994 Landau y Lifshitz, Mecánica cuántica no relativista. Reverté, Barcelona 1967 Tinkham, Group Theory and Quantum Mechanics. McGraw-Hill, London 1955


Code: 041 Subject: Laser Systems Dynamics


Optics II 6 Optional subject Lecture hours Practice hours Personal work

30 15 105 Contents

Stochastic processes, master equation, second order approach. The Fokker–Planck and Langevin equations. Itoh and Stratonovitch calculus. Electron-photon interaction. Langevin equations in the two levels laser. Quantum noise dynamics in lasers. Semiclasical equations. Rabi frequency. Axial and transverse instabilities. Space time chaos. Adiabatic approach: rate equations. Relaxation oscillations, giant pulses and mode beating or mode locking. Pico and femto pulses. Slow light and superluminal propagation.

Bibliography

H.Haken: Enciclopedia of physics, Vol.XXV/2c, Ligtht and Matter 1c, Springer-Verlag (1970) J.M.Guerra: Fisica del Laser, Ed.Alqua (libro libre) (2005), (Can be found for free in : http://www.ucm.es/info/laserlab/docencia.html) Mark Fox: Quantum Optics. An Introduction. Oxford University Press. (2006) C.W. Gardiner and P. Zoller: Quantum noise, Springer-Verlag (2001) N. Van Kampen: Stocastic Proceses in Physics and Chemistry. North Holland, (2003) S.Barnet: Methods in Quantum Optics, Oxford University Press, (2005)


Code: 042 Subject: Laser Beams



30 15 105 Contents

Stable and unstable laser resonators. Transverse modes in optical resonators. Laser beam propagation. Spatial structure and laser beam polarization. Parameterization standards. Laser safety.

Bibliography

A. E. Siegman, Lasers. University Science Books, Mill Valley (1986). H. Weber (editor), Laser beam quality. Optical and Quantum Electronics 24 (1992). Special issue. P.M. Mejías, H. Weber, R. Martínez-Herrero and A. González-Ureña (editors), Laser Beam Characterization, SEDO, Madrid (1993). P.M. Mejías, R. Martínez-Herrero, G. Piquero and J. M. Movilla, Parametric characterization of the spatial structure of non-uniformly polarized laser beams. Progress in Quantum Electronics 26, 65–130 (2002).


Code: 043 Subject: Quantum Optics



30 15 105 Contents

Electromagnetic field quantification. Coherence and correlations. Non classical light states. Non classical light generation, detection and applications. Approximate methods. Radiation-matter interaction: Jaynes-Cummings models and spontaneous emission. Quantum effects in non linear optics. Optical effects of atomic quantum coherence. Quantum information elements and experimental tests.

Bibliography

M. Fox: Quantum Optics. An Introduction Oxford University Press, 2006 R. Loudon: The Quantum Theory of Light third edition Oxford University Press, 2000 W.H. Louisell: Quantum Statistical Properties of Radiation John Wiley and Sons, 1973 P.W. Milonni: The Quantum Vacuum Academic Press, 1994 H. Paul: Introduction to Quantum Optics Cambridge University Press, 2004 M.O. Scully and M.S. Zubairy: Quantum Optics Cambridge University Press, 1997 D.F. Walls and G.J. Milburn: Quantum Optics Springer Verlag,1995


Code: 044 Subject: Nonlinear Optics



30 15 105 Contents

1. Introduction: Nonlinear polarization. Propagation equations. Short and ultrashort laser pulses

2. Second-order effects: Second Harmonic Generation. Sum and Difference. Frequency Generation. Parametric processes. Applications

3. Third-order effects: Third Harmonic Generation. Kerr effect. Self Phase. Modulation and supercontinuum generation. Optical bistability. Optical solitons. Phase conjugation. Stimulated Raman scattering. Applications

4. Multiphotonic processes Bibliography

R.W. Boyd, Nonlinear Optics, Academic Press, New York, 1992 Y.R. Shen, The Principles of Nonlinear Optics, Wiley, New York, 1984 G.P. Agrawal, Nonlinear Fiber Optics, Academic Press, S. Diego, 1989


Code: 045 Subject: Research Work


30 Compulsory subject Lecture hours Practice hours Personal work

0 150 300 Contents

The subjects of investigation follow the lines of research of the Master lecturers.


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Dpto. de Física Teórica I

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