ECTS - University of Pisa
| Modules | Area | Type | Hours | Teacher(s) | |
| QUANTUM LIQUIDS S | FIS/03 | LEZIONI | 36 |
|
Obiettivi di apprendimento
Al termine dell’insegnamento, la/lo studente avrà sviluppato conoscenze concettuali, procedurali e fattuali nella fisica dei liquidi quantistici. In particolare, avrà imparato a:
Conoscere la fenomenologia dei liquidi quantistici nelle principali piattaforme sperimentali in cui vengono correntemente ingegnerizzati e utilizzati;
At the course end, the student will have developed conceptual, procedural, and factual knowledge on the physics of quantum liquids and fluids. In particular, the student will have developed:
(a) Understanding and knowledge in operating the toolbox useful to conceive and realize in highly controlled and accurate manner conditions of extreme quantum degeneracy and correlations in the properties of charge/density and/or spin in quantum liquids, acting on temperature, dimensionality, strength and range of the interactions, introduction of synthetic gauge fields and dimensions;
(b) Knowledge and understanding of basic elements of theoretical methods aimed to predict and characterize the ground state and the excitations in quantum liquids, link them in a conceptual map, and classify them according to their functionality to solve specific types of problems. Among the developed theoretical methods are the linear response theory, the theory of measurements and correlation functions, quantum hydrodynamics, density functional theory, essential concepts of Green's functions theory, elements to relate these theoretical methods to the simulational methods treated in the course Laboratory for Numerical Methods.
(c) Knowledge of the phenomenology of quantum liquids in selected experimental platforms where they are currently engineered, such as: quantum gases, superconducting circuits, light fluids in optical cavities, 2D semiconductor systems;
La verifica è realizzata discutendo in una prova orale una dissertazione su un problema di fisica dei liquidi quantistici tra quelli non specificamente discussi nel corso e che faccia uso delle conoscenze e dei metodi teorici sviluppati durante il corso.
The assessment is performed by oral discussion of an essay on problem in the physics of quantum liquids, selected among those that have not specifically treated within the course and that uses understanding and methods developed in the course.
Al termine dell’insegnamento lo/a studente avrà appreso a
At the end of the course, the student will have learned to
(a) Recognize and appreciate in the complexity of the physical behavior of quantum liquids, the simplicity of their macroscopic properties, as governed by conservation laws and symmetry breaking accompanied by the appearence of new elasticities, low-frequency dynamical modes and defects
(b) Organize and link in a relationship this disciplinary knowledge in a same conceptual map with thermodynamics, statistical mechanics and phase transitions, quantum mechanics, field theory, and structure of matter in its different realizations
(c) Connect the conceptual comprehension and formal setting of the problem with the available phenomenology and experimental, and envisage the applications; intepret the phenomenology in terms of a few essntial concepts and ideas, and infer the understanding
(d) Formalize the concepts and treat them according to the different methods and related procedures developed in the course
(e) Evaluate with critical thinking specialized research articles on the course topics
(f) Create understanding on phenomena in quantum liquids implemented in different experimental platforms
(g) Communicate in effective and efficient manner the developed ideas and knowledge, using elementary physics concepts
(h) Work in autonomous manner, developing awarness of the conceptual learning map, and build self-evaluation capacity
(i) Work in team
La verifica è realizzata discutendo in una prova orale una dissertazione individuale e - in modo facoltativo - un lavoro di gruppo.
La dissertazione individuale è su un problema di fisica dei liquidi quantistici tra quelli non specificamente discussi nel corso e che faccia uso delle conoscenze e dei metodi teorici sviluppati durante il corso. Si richiede alla/o studente di individuare il problema oggetto della dissertazione:
La verifica individuale è concepita in modo da valutare lo stato delle conoscenze dello/a studente, e di sviluppo di competenze nelle seguenti aree:
(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.
Il lavoro di gruppo è su un problema pratico relativo all’applicazione di idee e metodi appresi nel corso in una particolare piattaforma sperimentale per le tecnologie quantistiche – concordata con gli e le studenti. Il problema viene discusso in gruppo in una apposita sessione di esame utilizzando tecniche del team-based learning (questa sessione avrà luogo alla fine del corso). Si richiede di discutere la metodologia più funzionale di trattamento, sviluppare la comprensione del problema, e comunicare i risultati, conducendo le diverse attività attraverso una suddivisione di compiti, condivisione dei risultati, e gestione autonoma del gruppo.
The assessment is performed by oral discussion of an essay on problem in the physics of quantum liquids, selected among those that have not specifically treated within the course and that uses understanding and methods developed in the course. The student is required to identify the essay subject:
The individual testing is conceived to assess the development of student’s knowledge and competences in the following areas:
(a) understand ideas and concepts and be able to communicate them also after using basic physics tools (besides advanced);
(b) be able to express concepts in formal manner and manage them via the methods developed during the course, along with the corresponding procedures;
(c) be able to connect the conceptual understanding of the problem and its formal expression with the phenomenology and experimental fact that are available, and envision possible applications;
(d) autonomy, awareness of the course conceptual map and of the learning outcomes, effectiveness and efficiency in scientific communication.
The group work is conceived to be on practical problem related to the application of ideas and methods learned during the course to either one among the different experimental platforms for quantum technologies. The problem will be selected by the students with the supervision of the lecturer. The problem will be discussed within the participating group in an on-purpose examination session operated by means of team-based learning techniques (this session will take place at the end of the course). It is required to discuss the methodology that is best suited to the problem, develop the comprehension of the problem, communicate the results, conduct the different activities by distributing the different assignments among the group members, sharing the results, and managing the group in autonomy.
Ci si attende che la/lo studente sviluppi:
(a) Interesse per le idee a fondamento della scienza e tecnologie quantistiche
(b) Curiosità e spirito critico
(c) Spirito di iniziativa e partecipazione attiva
(d) Correttezza al momento della valutazione
It is expected that the student will develop:
La verifica del comportamenti viene operata in aula nel corso e in sede di prova d’esame mediante osservazione, e mediante possibili attività di valutazione formativa in itinere sul portale elearning.
The behaviors’ evaluation is performed during classroom activities and at the assessment time via observation, and by means of possible activities of formative evaluation on the elearning portal.
Prerequisito 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 sebbene non indispensabili sono conoscenze di fisica dei solidi.
Prerequisite is a base knowledge of classical dynamics, thermodynamics and elements of statistical mechanics, electromagnetism, structure of matter and quantum mechanics.
Useful, though, not indispensable, are notions of solid-state physics.
Le attività d’aula e online sono disegnate attorno agli obiettivi di apprendimento. In particolare:
(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, anche utilizzando slides e spezzoni di seminari di esperti/e qualificati disponibii online ;
(b) formalizzare i concetti (conoscenza concettuale);
(c) ovunque possibile discutere il problema complesso attraverso semplici modelli che usano la fisica di base;
(d) sviluppare e classificare la conoscenza di metodi teorici e di simulazione per le predizioni quantitative (conoscenza procedurale e fattuale), avendo cura di sviluppare alla lavagna tutti i passaggi per ogni tipologia di calcolo;
(e) al termine di ogni macro-argomento, costruire in modo interattivo una mappa concettuale che lo rappresenta, evidenziando concetti e relazioni tra questi;
(f) l’ultima parte del corso è dedicata a studi di casi in differenti piattaforme per le tecnologie quantistiche, allo scopo di acquisire pratica d'applicazione della conoscenza procedurale e fattuale
Classroom and online activities are tailored on the expected learning outcomes. In particular:
A. Introduction and conceptual map of the essential ideas qualitatively discussed via examples anticipated from the course itself
B. Measurements and correlation functions [4 h]
Generalities and essential concepts. Measurements and Correlation functions, Response functions, Quantum Hydrodynamics via a simple model.
C. TheoreticalMethods for strongly correlated quantum fluids [28h]. 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. The methods will be first developed in C1 for systems with maximal symmetry and then, after bridging in C2 with a crash dictionary on broken symmetries and quantum phase transitions, completed in C3-C4 by introducing their peculiarities in correspondence of phase transitions driven by tuning interactions strength, disorder, temperature, and dimensionality.
C1 Systems with maximal symmetry [20h]
C1.1 Formal development of the Theory of Linear Response: Definitions and properties- Fluctuation Dissipation Theorem - Sum rules - Applications: calculation of response functions within the Random-Phase Approximation (fermions and bosons) and concept of local-field factor [6 h]
C1.2 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 - A dictionary with response functions - Wick's theorem [4 h]
C1.3 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 thermodynamic derivatives of conserved quantities. Relationship with Linear Response. Relationship with experiments: Landau-Placzek ratio and examples. [8 h]
C1.4 A crash dictionary of (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 linear response theory – Hints on current functionals and TDDFT, relationship with Linear Response and microscopic formulation of Navier-Stokes equations. [2 h]
During the development of the formal tools, care will be taken to establish and discuss links between the learned theoretical methods and simulational/numerical methods on one side and experimental methods on the other, with examples from different spectroscopies (matter, spin, and optical probes) and from transport measurements.
C2 A crash dictionary on broken symmetries and (quantum) phase transitions [2 h]
- 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 – Introduction to the concepts of scaling, critical exponents and universality- Dynamical effects: Anderson-Higgs mechanism and Goldstone modes - Analogy between superconductivity and electroweak theory- Conditions of validity for mean-field theories and thermal and quantum (as e.g. due to correlations and reduced dimensionality) fluctuations
C3. Superfluidity/superconductivity and Bose-Einstein Condensation of neutral and charged Fermi and Bose systems [4 h].
Application of the theory of linear response to the microscopic calculation of the superfluid density/moment of inertia and the relationship between superfluid and condensate fraction – Peculiarities in hydrodynamic treatment and microscopic two-fluid equations.
C4. Effects of reduced dimensionality: the very special 1D case [2 h]-Specialty of 1D systems: always strongly correlated and collectivization of excitations. Luttinger Liquids: structure and thermodynamic properties. Typical phase diagrams in 1D systems with Charge/density and Spin-Density Waves. Essentials on bosonization techniques.
D. Cases study, selected in each of the following four different platforms for quantum technologies [6 h]:
D0. The basic toolbox (2 or 3-levels systems, interactions, gauge fields, and dimensionality) in the following quantum technologies platforms: quantum gases and trapped ions, superconducting circuits, matter and optical cavities, fluids of light [6 h].
A. Introduction and conceptual map of the essential ideas qualitatively discussed via examples anticipated from the course itself
B. Measurements and correlation functions [4 h]
Generalities and essential concepts. Measurements and Correlation functions, Response functions, Quantum Hydrodynamics via a simple model.
C. TheoreticalMethods for strongly correlated quantum fluids [28h]. 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. The methods will be first developed in C1 for systems with maximal symmetry and then, after bridging in C2 with a crash dictionary on broken symmetries and quantum phase transitions, completed in C3-C4 by introducing their peculiarities in correspondence of phase transitions driven by tuning interactions strength, disorder, temperature, and dimensionality.
C1 Systems with maximal symmetry [20h]
C1.1 Formal development of the Theory of Linear Response: Definitions and properties- Fluctuation Dissipation Theorem - Sum rules - Applications: calculation of response functions within the Random-Phase Approximation (fermions and bosons) and concept of local-field factor [6 h]
C1.2 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 - A dictionary with response functions - Wick's theorem [4 h]
C1.3 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 thermodynamic derivatives of conserved quantities. Relationship with Linear Response. Relationship with experiments: Landau-Placzek ratio and examples. [8 h]
C1.4 A crash dictionary of (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 linear response theory – Hints on current functionals and TDDFT, relationship with Linear Response and microscopic formulation of Navier-Stokes equations. [2 h]
During the development of the formal tools, care will be taken to establish and discuss links between the learned theoretical methods and simulational/numerical methods on one side and experimental methods on the other, with examples from different spectroscopies (matter, spin, and optical probes) and from transport measurements.
C2 A crash dictionary on broken symmetries and (quantum) phase transitions [2 h]
- 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 – Introduction to the concepts of scaling, critical exponents and universality- Dynamical effects: Anderson-Higgs mechanism and Goldstone modes - Analogy between superconductivity and electroweak theory- Conditions of validity for mean-field theories and thermal and quantum (as e.g. due to correlations and reduced dimensionality) fluctuations
C3. Superfluidity/superconductivity and Bose-Einstein Condensation of neutral and charged Fermi and Bose systems [4 h].
Application of the theory of linear response to the microscopic calculation of the superfluid density/moment of inertia and the relationship between superfluid and condensate fraction – Peculiarities in hydrodynamic treatment and microscopic two-fluid equations.
C4. Effects of reduced dimensionality: the very special 1D case [2 h]-Specialty of 1D systems: always strongly correlated and collectivization of excitations. Luttinger Liquids: structure and thermodynamic properties. Typical phase diagrams in 1D systems with Charge/density and Spin-Density Waves. Essentials on bosonization techniques.
D. Cases study, selected in each of the following four different platforms for quantum technologies [6 h]:
D0. The basic toolbox (2 or 3-levels systems, interactions, gauge fields, and dimensionality) in the following quantum technologies platforms: quantum gases and trapped ions, superconducting circuits, matter and optical cavities, fluids of light [6 h].
Note:
5.1 Generali:
– P.C. Martin, Measurements and Correlation Functions, Gordon and Breach (1968) [Con riferimento al Programma: Parte B]
- G. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid, Cambridge University Press (2010) [Con riferimento al Programma: Parte C1]
- Piers Coleman, Introduction to Many-Body Physics, Cambridge University Press (2015) [Con riferimento al Programma: Parte C2 e C3]
- L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics, Benjamin (1962) [Con riferimento al Programma: Parte C1- Nonequilibrium methods]
– Baym, Microscopic Description of Superfluidity, Math. Methods in Solid-State&Superfluid Theory, Clark&Derrick Eds., Oliver&Boyd (1969) [Con riferimento al Programma: Parte C4]
– P.C. Hohenberg and P.C. Martin, Microscopic Theory of Superfluid Helium, Annals of Physics 34, 291-359 (1965) [Con riferimento al Programma: Parte C4]
– Giamarchi, Quantum Physics in One Dimension, Oxford Science Pub. (2006) [Con riferimento al Programma: Parte C5]
- G. Iadonisi, G. Cantele, and M.L. Chiofalo, Introduction to Solid State Physics and Crystalline Nanostructures, Springer (2014) [Con riferimento al Programma: Background in solid-state physics]
- M. L. Chiofalo, L. Salvi, G. Tino, La Fisica della Materia, in Lezioni di Fisica, Corriere della Sera (2018) [Overview semi-divulgativa sulle quantum technologies]
5.2 Parti specifiche del corso (materiale facoltativo, in aggiunta alle note di lezione disponibili sul portale)
– 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)
-- A. Daley, Quantum trajectories and open many-body quantum systems, Adv. Phys. 63, 77 (2014)
Altre letture, per studenti particolarmente interessati/e:
– 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)
– 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)
– L. A. Bloomfield, How Things Work, Wiley (2013)
Notes:
5.1 General:
– P.C. Martin, Measurements and Correlation Functions, Gordon and Breach (1968) [Referring to Programme: Part B]
- G. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid, Cambridge University Press (2010) [Referring to Programme: Part C1]
- Piers Coleman, Introduction to Many-Body Physics, Cambridge University Press (2015) [Referring to Programme: Parts C2 and C3]
- L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics, Benjamin (1962) [Referring to Programme: Part C1- Nonequilibrium methods]
– Baym, Microscopic Description of Superfluidity, Math. Methods in Solid-State&Superfluid Theory, Clark&Derrick Eds., Oliver&Boyd (1969) [Referring to Programme: Part C4]
– P.C. Hohenberg and P.C. Martin, Microscopic Theory of Superfluid Helium, Annals of Physics 34, 291-359 (1965) [Referring to Programme: Part C4]
– Giamarchi, Quantum Physics in One Dimension, Oxford Science Pub. (2006) [Referring to Programme: Part C5]
- G. Iadonisi, G. Cantele, and M.L. Chiofalo, Introduction to Solid State Physics and Crystalline Nanostructures, Springer (2014) [Referring to Programme: Background in solid-state physics]
- M. L. Chiofalo, L. Salvi, G. Tino, La Fisica della Materia, in Lezioni di Fisica, Corriere della Sera (2018) [Semi-popularized overview on quantum technologies]
5.2 Specific course parts (optional material, in addition to the lecture notes on the portal)
– 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)
-- A. Daley, Quantum trajectories and open many-body quantum systems, Adv. Phys. 63, 77 (2014)
More readings, for especially interested students:
– 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)
– 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)
– L. A. Bloomfield, How Things Work, Wiley (2013)
Utilizzare al massimo le potenzialità del portale elearning e del materiale messo a disposizione online anche sul canale Teams del corso.
Use at best the resources on the elearning website and on the Teams page of the course.
La valutazione finale è il risultato della valutazione sull’essay e (in modo facoltativo) sul lavoro di gruppo. Per chi decide di partecipare al lavoro di gruppo, il 75% della valutazione è sull’essay, e il 25% sul lavoro di gruppo. Per chi non desidera partecipare al lavoro di gruppo, il 100% della valutazione è sull’essay.
Per entrambe le prove, la valutazione è formulata per competenze. Con riferimento alle aree (a)-(d) illustrata nella sezione Modalità di verifica delle capacità:
– 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 l’Area (d)
The final assessment results from evaluating the essay and (optionally) the group work. For those who choose to participate to the group work, 75% of the evaluation is performed on the essay, and %25 on the group work. Who chooses to not participate to the group work, 100% of the evaluation is on the essay.
For both types of tests, the assessment is operated by evaluating competences. Referring to areas (a)-(d) in section Assessment of competences:
– up to 18 points for Area (a)
– up to 6 punti for Area (b)
– up to 4 punti for Area (c)
– up to 5 punti for Area (d)
Il corso è concepito sia per studenti che vogliano specializzarsi nella fisica teorica della materia condensata che a studenti che vogliano acquisire una cassetta degli attrezzi concettuale e metodologica per comprendere la fisica dei liquidi quantistici e il funzionamento delle tecnologie quantistiche e apprendere a concepirne di nuove. Poiché diverse sono le piattaforme sperimentali dove le tecnologie quantistiche possono essere utilmente realizzate in forme differenti con funzionalità simili, la scelta del corso è privilegiare l'ampiezza di visione concettuale e metodologica nei primi circa 2/3 del corso, dedicando l’ultima parte alle implementazioni pratiche, che pure possono essere sempre approfondite all’occorrenza.
The course is conceived for students who wish to refine their knowledge and competences on theoretical condensed-matter physics and for students who wish to acquire a conceptual and methodological toolbox to understand the physics of quantum liquids, comprehend how quantum technologies work, and learn the essentials needed to conceive them. Since quantum technologies have been developed in different experimental platforms, with different forms and similar functionalities, the course choice is to privilege a wide-open conceptual and methodological vision in the first 2/3 part of the course, and devote the last part to practical implementations, which can always be deepened whenever needed.
