ECTS - University of Pisa
| Modules | Area | Type | Hours | Teacher(s) | |
| FISICA DEI SISTEMI A MOLTICORPI | FIS/03 | LEZIONI | 54 |
|
1. Sviluppare conoscenza concettuale, procedurale e fattuale nella fisica di sistemi con molte particelle (quantistiche) interagenti, dove agendo su temperatura, dimensionalità, e forza di interazione è possibile stabilire condizioni di forti correlazioni in proprietà di carica/densità e spin.
Per questo, si prevede di:
(a) discutere qualitativamente mediante la fisica di base le idee emergenti da fatti sperimentali ed esempi di vita quotidiana, approfondendo all'occorrenza metodi sperimentali e possibili applicazioni;
(b) formalizzare i concetti (conoscenza concettuale); e
(c) sviluppare e classificare la conoscenza di metodi teorici e di simulazione per le predizioni quantitative (conoscenza procedurale e fattuale), incluso Teoria della Risposta Lineare e funzioni di correlazione, Fluido- e Idrodinamica quantistiche, Teoria del Funzionale di Densità (Dipendente dal Tempo), metodi Quantum Monte Carlo, Density Matrix Renormalization Group.
1. Develop conceptual, procedural, and factual knowledge in the physics of many interacting quantum particles, where after acting via temperature, dimensionality, interaction strength, extreme quantum behavior and correlation effects can be realized in charge/density and spin properties.
The course is aimed to:
(a) qualitatively discuss via basic physics of emergent ideas from experimental and everyday-life facts, while - whenever possible - deepening on the use of experimental methods;
(b) formalize the concepts (conceptual knowledge) and
(c) develop and classify the knowledge of theoretical methods (with an eye also to simulational methods) needed to perform quantitative predictions (procedural and factual knowledge), including Theory of linear response and correlation functions, Quantum fluido- and hydro-dynamics, (Time-Dependent) Density Functional Theory, Green's functions and perturbative expansions, Bosonization techniques for 1D systems.
La verifica è formulata mediante prova orale. In particolare, la prova parte dall'esame di un problema di fisica dei molti corpi non discusso nel corso, che si richiede allo/a studente di individuare in autonomia o con l'accompagnamento del/la docente. Nel corso della prova, sarà possibile approfondire aspetti dei casi di studio discussi. La verifica viene effettuata secondo le seguenti Aree di competenza:
(a) aver compreso idee e concetti e saperli comunicare utilizzando conoscenze di fisica di base;
(b) saper formalizzare i concetti e saperli trattare attraverso l'uso di uno o più tra i metodi sviluppati nel corso e relative procedure;
(c) saper connettere la comprensione concettuale e la formalizzazione del problema con la fenomenologia e i fatti sperimentali disponibili, e avere un'idea delle applicazioni;
(d) autonomia, consapevolezza della mappa concettuale e di quanto appreso, efficacia ed efficienza nella comunicazione scientifica.
Nel corso della prova orale, utilizzando i seguenti criteri di valutazione della conoscenza procedurale e fattuale. In particolare, le capacità sono valutate in misura del 60% per la conoscenza concettuale del valore del punteggio massimo per ogni Area (a)-(c). I punteggi massimi per ogni Area sono così composti:
– fino a 18 punti per l'Area (a)
– fino a 6 punti per l'Area (b)
– fino a 4 punti per l'Area (c)
– fino a 5 punti per le competenze trasversali (d)
Assessment is performed via oral exam. The exam stems from a problem in many-body physics not discussed during the course, that the student may choose (in autonomy or accompanied by the teacher). Assessment is performed according to the following competences Areas:
(a) understanding ideas and concepts, and competence in communicating them after using basic-physics knowledge;
(b) competence in formalizing the concepts and treating them via one or more among the methods developed during the course with related procedures;
(c) competence in relating the conceptual comprehension and the problem formalization with the phenomenological and experimental available facts, and having hints about possible applications;
(d) autonomy, awareness of conceptual maps, learning process and contents, effectiveness in scientific communication.
The following composition is used
– up 18 points for Area (a)
– up 6 points for Area (b)
– up 4 points for Area (c)
– up 5 points for cross and life-skills (d)
2. Organizzare e mettere in relazione questa conoscenza disciplinare in una stessa mappa concettuale con termodinamica, meccanica statistica e transizioni di fase, meccanica quantistica, teorie di campo, e struttura della materia nelle sue diverse realizzazioni, facendo emergere come le proprietà macroscopiche siano governate da leggi di conservazione e rotture di simmetria accompagnate da elasticità, modi dinamici a bassa frequenza e difetti.
3. Saper individuare la procedura più funzionale alla soluzione di un dato problema
4. Saper applicare le tecniche di calcolo relative alle diverse procedure di soluzione
1. Organizing the present disciplinary knowledge in the same conceptual mapalong with thermodinamics, statistical mechanics, phase transitions, qantum mechanics, quantum field theories, condensed matter in its diverse realizations, making clear the emergence of how macroscopic properties are governed by conservation laws and spontaneous symmetry breakings accompanied by the appearence of elasticity, low-frequency dynamical modes, and defects.
2. Selecting the most convenient procedure for the solution of a given problem
3. Application of calculus techniques related to different solution procedures
La verifica è formulata mediante prova orale. In particolare, la prova parte dall'esame di un problema di fisica dei molti corpi non discusso nel corso, che si richiede allo/a studente di individuare in autonomia o con l'accompagnamento del/la docente. Nel corso della prova, sarà possibile approfondire aspetti dei casi di studio discussi. La verifica viene effettuata secondo le seguenti Aree di competenza:
(a) aver compreso idee e concetti e saperli comunicare utilizzando conoscenze di fisica di base;
(b) saper formalizzare i concetti e saperli trattare attraverso l'uso di uno o più tra i metodi sviluppati nel corso e relative procedure;
(c) saper connettere la comprensione concettuale e la formalizzazione del problema con la fenomenologia e i fatti sperimentali disponibili, e avere un'idea delle applicazioni;
(d) autonomia, consapevolezza della mappa concettuale e di quanto appreso, efficacia ed efficienza nella comunicazione scientifica.
Nel corso della prova orale, utilizzando i seguenti criteri di valutazione della conoscenza procedurale e fattuale. In particolare, le capacità sono valutate in misura del 30% per la conoscenza procedurale e del 10% per quella fattuale, del valore del punteggio massimo per ogni Area (a)-(d). I punteggi massimi per ogni Area sono così composti:
– fino a 18 punti per l'Area (a)
– fino a 6 punti per l'Area (b)
– fino a 4 punti per l'Area (c)
– fino a 5 punti per le competenze trasversali (d)
Assessment is performed via oral exam. The exam stems from a problem in many-body physics not discussed during the course, that the student may choose (in autonomy or accompanied by the teacher). Assessment is performed according to the following competences Areas:
(a) understanding ideas and concepts, and competence in communicating them after using basic-physics knowledge;
(b) competence in formalizing the concepts and treating them via one or more among the methods developed during the course with related procedures;
(c) competence in relating the conceptual comprehension and the problem formalization with the phenomenological and experimental available facts, and having hints about possible applications;
(d) autonomy, awareness of conceptual maps, learning process and contents, effectiveness in scientific communication.
The following composition is used
– up 18 points for Area (a)
– up 6 points for Area (b)
– up 4 points for Area (c)
– up 5 points for cross and life-skills (d)
La verifica del comportamenti viene operata in aula mediante osservazione, utilizzando i dati d'uso del materiale collocato sul portale elearning, e di nuovo mediante osservazione in aula nel corso dell'esame.
During the lecturing time, via interactions with students.
Prerequisito di accesso al corso è la conoscenza di base di dinamica, termodinamica ed elementi di meccanica statistica, elettromagnetismo, struttura della materia e meccanica quantistica acquisiti nel corso di studi triennale.
Utili e molto preferibili sebbene non indispensabili sono conoscenze di fisica dei solidi
Prerequisite is the basic knowledge of classical dynamics, thermodynamics and elements of statistical mechanics, electromagnetism, structure of matter, quantum physics.
Very useful and preferable, though not compulsory, is the knowledge of solid-state physics
Siintende utilizzare due esempi complementari rispetto alle caratteristiche di carica/densità e di spin, tratti da campi di ricerca di frontiera (fluidi elettronici in sistemi a bassa dimensionalità e gas atomici ultrafreddi quantistici) per acquisire le seguenti competenze, ovvero imparare a saper:
(a) discutere qualitativamente le idee emergenti a partire da concetti di fisica di base già acquisiti nel corso di studio triennale e dalla fenomenologia - preferibilmente disponibile dalla vita di tutti i giorni - e fatti sperimentali;
(b) formalizzare i concetti utili;
(c) sviluppare i principali strumenti e metodi teorici e di simulazione per le previsioni quantitative;
(d) discutere la connessione tra funzioni di correlazione e misure (teorema di fluttuazione e dissipazione) e, all'occorrenza, i principi alla base dei principali metodi sperimentali; (d) mettere in luce le possibile applicazioni;
(e) al termine di ogni argomento, costruire in modo interattivo una mappa concettuale che lo rappresenta, evidenziando concetti e relazioni tra questi.
(f) al termine di ogni argomento, si sviluppa lo studio di un caso per acquisire pratica d'applicazione della conoscenza procedurale e fattuale
Two case studies are illustrated, complementary with respect to charge/density and spin charecteristics, and extracted from frontier research fields. In particular, quantum fluids in reduced, dimensionality and ultracold quantum gases. Case studies are used to acquire the following competences:
(a) qualitatively discuss via basic physics of emergent ideas from experimental and everyday-life facts, while - whenever possible - deepening on the use of experimental methods;
(b) formalize the concepts (conceptual knowledge);
(c) develop and classify the knowledge of theoretical methods (with an eye also to simulational methods) needed to perform quantitative predictions (procedural and factual knowledge);
(c) relate the conceptual comprehension and the problem formalization with the phenomenological and experimental available facts, and having hints about possible applications;
(d) autonomy, awareness of conceptual maps, learning process and contents, effectiveness in scientific communication.
A. Introduction and conceptual map of the essential ideas...
...qualitatively discussed via examples anticipated from the course itself
B. Structure and scattering
Generalities and essential concepts. Measurements and Correlation functions, Response functions, Quantum Hydrodynamics via a simple model.
C. Theoretical Methods for strongly correlated many-body systems
C.1 Systems with maximal symmetry. Development of theoretical methods, starting from the measurement of correlation functions which have been phenomenologically introduced in B. Discussion of the relationships among the different methods, enlightening goods and bads.
Formal development of the Theory of Linear Response: Definitions and properties- Fluctuation Dissipation Thorem - Sum rules - Applications: calculation of response function within the Random-Phase Approximation (fermions and bosons) - Concept od local field factor and self.-consistent theories beyond mean-field
Quantum Hydrodynamics: Microscopic derivation of the equations starting from conservation laws - Transport coefficients as special limits of response functions and Kubo relations- Static susceptibilities as theoremodynamic derivatives of conserved quantities. Relationship with Linear Response. Relationship with experiments: landau-Placzek ratio and examples.
(Time-Dependent) Density Functional Theory: Definitions - Theorem of Hohenberg and Kohn - Kohn and Sham scheme - Local Density Approximation - Exchange and correlation potentials and relationship with lineas response theory - Current functional and TDDFT, Funzionale di corrente e TDDFT, relationship with Linear Response and microscopic formulation of Navier-Stokes equations as related to quantum hydrodynamics.
Correlation functions and Green's functions (zero and finite temperature): Definitions and properties - Boundary conditions - Equations of motion as a technique to derive consistent approximations - Non-equilibrium Green's functions - A dictionary with response functions - Generating functionals - Wick's theorem - Finite temperature and the contour-integral method - Perturbative techniques and Feynman diagrams - Examples including phonon and fermion systems to low-order - Landau Theory of Fermi Liquids
Introduction to Path Integrals [If time allows it]
Relationship between the theoretical methods learned and experimental methods, with examples from different spectroscopies (matter, spin, and optical probes) and transport measurements
C.2 Systems with broken symmetry
Concept of order parameter
Landau and Landau-Ginzburg theory for uniform (Ising model) and non-uniform order parameter – Complex order parameter and neutral/charged superfluid - Critical exponents
Dynamical effects: Anderson-Higgs mechanism and Goldstone modes - Analogy between superconductivity and electroweak theory
Introduction to the concepts of scaling, critical and universality – Physical meaning of the Renormalization Gropuo Theory-Map of order parameters by broken symmetry -
Conditions of validity for mean-field theories and thermal and quantum (as e.g. due to correlations and reduced dimensionality) fluctuations
C.3 Effects of reduced dimensionality: the 1D case
Specialty of 1D systems: always strongly correlated and collectivization of excitations
Bosonization techniques
Luttinger Liquids: structure and theremodynamic properties
D. Applications of the methods via two case studies:
D.1 Case stuudy: superfluidity and Bose-Einstein Condensation of neutral and charged Fermi and Bose systems. Applying: Theory of linear response to the microscopic calculation of the superfluid density/moment of inertia and the relationship between superfluid and condensate fraction - DFT and TD extension - Hydrodynamics and microscopic two-fluid equations - Green's functions treatment (peculiarities: Ward identities and conseving vs. gapless approximations).
D.2 Case study: Typical phase diagrams in 1D systems with Charge/density and Spin-Density Waves. 1D systems and bosonization techniques.
In addition, the following parts can be discussed after specific agreement and planning:
E. Principles for Simulational methods for strongly correlated systems
[Via ad hoc seminars within collaborations with other courses and teachers]
E.1 Quantum Monte Carlo (QMC): Variational, Diffusion, Reptation, Path-Integral QMC.
E.2 Implementations of DFT.
E.3 Density Matrix Renormalization Group (DMRG).
E.4 Theoretical laboratories.
F. Defects: a dictionary [if time allows it]
Carachterization according to broken-symmetry properties. Generalities on topological defects, examples and applications: vortices and dislocations, Kosterlitz-Thouless transition. Generalities on domains, walls, and solitons, examples and applications.
A. Introduction and conceptual map of the essential ideas...
...qualitatively discussed via examples anticipated from the course itself
B. Structure and scattering
Generalities and essential concepts. Measurements and Correlation functions, Response functions, Quantum Hydrodynamics via a simple model.
C. Theoretical Methods for strongly correlated many-body systems
C.1 Systems with maximal symmetry. Development of theoretical methods, starting from the measurement of correlation functions which have been phenomenologically introduced in B. Discussion of the relationships among the different methods, enlightening goods and bads.
C.2 Systems with broken symmetry
C.3 Effects of reduced dimensionality: the 1D case
D. Applications of the methods via two case studies:
D.1 Case stuudy: superfluidity and Bose-Einstein Condensation of neutral and charged Fermi and Bose systems. Applying: Theory of linear response to the microscopic calculation of the superfluid density/moment of inertia and the relationship between superfluid and condensate fraction - DFT and TD extension - Hydrodynamics and microscopic two-fluid equations - Green's functions treatment (peculiarities: Ward identities and conseving vs. gapless approximations).
D.2 Case study: Typical phase diagrams in 1D systems with Charge/density and Spin-Density Waves. 1D systems and bosonization techniques.
In addition, the following parts can be discussed after specific agreement and planning:
E. Principles for Simulational methods for strongly correlated systems
[Via ad hoc seminars within collaborations with other courses and teachers]
E.1 Quantum Monte Carlo (QMC): Variational, Diffusion, Reptation, Path-Integral QMC.
E.2 Implementations of DFT.
E.3 Density Matrix Renormalization Group (DMRG).
E.4 Theoretical laboratories.
F. Defects: a dictionary [if time allows it]
Carachterization according to broken-symmetry properties. Generalities on topological defects, examples and applications: vortices and dislocations, Kosterlitz-Thouless transition. Generalities on domains, walls, and solitons, examples and applications.
Manuali di studio e articoli sono disponibili presso la Biblioteca di Fisica e/o online. Materiale addizionale è sul portale elearning del corso, dove è anche una guida ragionata all'uso dei differenti libri e articoli.
5.1 Generali:
– Piers Coleman, Introduction to Many-Body Physics, Cambridge University Press (2015)
– L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics, Benjamin (1962)
– P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press (1995)
– G. Iadonisi, G. Cantele, and M.L. Chiofalo, Introduction to Solid State Physics and Crystalline Nanostructures, Springer (2014)
– G. Grosso and G. Pastori Parravicini, Solid State Physics, Academic Press (2000)
5.2 Parti specifiche del corso
– P.C. Martin, Measurements and Correlation Functions, Gordon and Breach (1968)
– G. Vignale, C. A Ullrich, S. Conti, Time-Dependent Density Functional Theory and beyond the Adiabatic Local Density Approximation, Phys. Rev. Lett. 79, 4878 (1997)
– Baym, Microscopic Description of Superfluidity, Math. Methods in Solid-State&Superfluid Theory, Clark&Derrick Eds., Oliver&Boyd (1969)
– P.C. Hohenberg and P.C. Martin, Microscopic Theory of Superfluid Helium, Annals of Physics 34, 291-359 (1965)
– Giamarchi, Quantum Physics in One Dimension, Oxford Science Pub. (2006)
– W.M. Foulkes, L. Mitas, R.J. Needs, and G. Rajagopal, Quantum Monte Carlo Simulations of Solids, Revue of Modern Physics 73, 33 (2001)
– U. Schollwok and S.R. White, Methods for Time Dependence in DMRG, in Effective Models for Low-Dimensional Strongly Correlated Systems, G.G. Batrouni and D. Poilblanc Eds., p. 155 AIP, Melville, New York (2006)
Additional suggested reading:
– P. Nozières and D. Pines, Theory of Quantum Liquids I – II, Westview Press (1999); Pines, The Many-Body Problem, Wiley (1997)
– D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, And Correlation Functions, Adv. Books Classics (1995)
– L. A. Bloomfield, How Things Work, Wiley (2013)
Textbooks and articles are available at the Physics Library and/or online. Additional material is on the elearning website of the course, where a guided tour of the different textbooks and papers is provided.
5.1 General:
– Piers Coleman, Introduction to Many-Body Physics, Cambridge University Press (2015)
– L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics, Benjamin (1962)
– P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press (1995)
– G. Iadonisi, G. Cantele, and M.L. Chiofalo, Introduction to Solid State Physics and Crystalline Nanostructures, Springer (2014)
– G. Grosso and G. Pastori Parravicini, Solid State Physics, Academic Press (2000)
5.2 For specific parts of the course:
– P.C. Martin, Measurements and Correlation Functions, Gordon and Breach (1968)
– G. Vignale, C. A Ullrich, S. Conti, Time-Dependent Density Functional Theory and beyond the Adiabatic Local Density Approximation, Phys. Rev. Lett. 79, 4878 (1997)
– Baym, Microscopic Description of Superfluidity, Math. Methods in Solid-State&Superfluid Theory, Clark&Derrick Eds., Oliver&Boyd (1969)
– P.C. Hohenberg and P.C. Martin, Microscopic Theory of Superfluid Helium, Annals of Physics 34, 291-359 (1965)
– Giamarchi, Quantum Physics in One Dimension, Oxford Science Pub. (2006)
– W.M. Foulkes, L. Mitas, R.J. Needs, and G. Rajagopal, Quantum Monte Carlo Simulations of Solids, Revue of Modern Physics 73, 33 (2001)
– U. Schollwok and S.R. White, Methods for Time Dependence in DMRG, in Effective Models for Low-Dimensional Strongly Correlated Systems, G.G. Batrouni and D. Poilblanc Eds., p. 155 AIP, Melville, New York (2006)
Additional suggested reading:
– P. Nozières and D. Pines, Theory of Quantum Liquids I – II, Westview Press (1999); Pines, The Many-Body Problem, Wiley (1997)
– D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, And Correlation Functions, Adv. Books Classics (1995)
– L. A. Bloomfield, How Things Work, Wiley (2013)
Si consiglia di utilizzare al massimo delle potenzialità il materiale e le opportunità di verifica sul portale elearning di Fisica
Follow the material organized on the elarning page of the course
La valutazione è formulata mediante prova orale. In particolare, si richiede allo/a studente di individuare, in autonomia o con l'accompagnamento del/la docente, un problema di fisica dei molti corpi non discusso nel corso ovvero approfondire aspetti dei casi di studio discussi e dimostrare:
(a) di aver compreso idee e concetti e saperli comunicare utilizzando conoscenze di fisica di base;
(b) di saper formalizzare i concetti e saperli trattare attraverso l'uso di uno o più tra i metodi sviluppati nel corso e relative procedure;
(c) di saper connettere la comprensione concettuale e la formalizzazione del problema con la fenomenologia e i fatti sperimentali disponibili, e avere un'idea delle applicazioni;
(d) autonomia, consapevolezza della mappa concettuale e di quanto appreso, efficacia ed efficienza nella comunicazione scientifica.
Assessment is performed via oral exam. The exam stems from a problem in many-body physics not discussed during the course, that the student may choose (in autonomy or accompanied by the teacher). Assessment is performed according to the following competences Areas:
(a) understanding ideas and concepts, and competence in communicating them after using basic-physics knowledge;
(b) competence in formalizing the concepts and treating them via one or more among the methods developed during the course with related procedures;
(c) competence in relating the conceptual comprehension and the problem formalization with the phenomenological and experimental available facts, and having hints about possible applications;
(d) autonomy, awareness of conceptual maps, learning process and contents, effectiveness in scientific communication.
L'intenzione è destinare il corso sia a studenti che vogliano specializzarsi nella fisica della materia condensata che a coloro che vogliano semplicemente complementare le proprie conoscenze. La scelta del corso è dunque privilegiare l'ampiezza di visione concettuale e metodologica piuttosto che il dettaglio delle tecniche, che possono poi essere sempre approfondite all'occorrenza.
The course is aimed to students who wishes to specialize their career in condensed matter physics and theoretical physics, AND to students who simply wish to complement their knowledge with respect to other specific fields. A specific choice of the course is to privilege a wider conceptual and methodological vision more than technical details, which can be deepened at any given and useful time.
