To offer an introduction to the modern physics of liquids, understood as the study of the phenomenology of fluids starting from interatomic force laws. We will study the theoretical methods based on integral equations that allow us to describe the structure of the liquid. Computer numerical simulation methods applied to the physics of liquids will be introduced. Then we will study the correlation functions and the theory of linear response with applications to the study of the dynamics of liquids in the hydrodynamic limit and in the visco-elastic limit. The memory functions will be introduced. The physics of supercooled liquids and the study of the glass transition will be discussed
Curriculum
teacher profile teaching materials
Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Programme
1- Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
Core Documentation
J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Type of delivery of the course
The exposition of the theories is carried out on the blackboard to allow students to understand the necessary analytical developments. In particular, it is shown how microscopic models can yield results to be compared with experiments. The methods are based either on the approximate resolution of integral equations or on numerical calculation by computer simulation- Experimental methods are then introduced which allow to observe the properties of the various systems of interest. For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation
The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student among those scheduled. This part allows us to highlight how much the student is able to to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to expose the topic as if it were a seminar, this is useful for his future as a graduating student. The second part of the oral exam consists of a question on another scheduled topic. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to expose shortly a topic in a comprehensible way is also important in the different branches of Physics. teacher profile teaching materials
Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Programme
1- Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
Core Documentation
J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Type of delivery of the course
The exposition of the theories is carried out on the blackboard to allow students to understand the necessary analytical developments. In particular, it is shown how microscopic models can yield results to be compared with experiments. The methods are based either on the approximate resolution of integral equations or on numerical calculation by computer simulation- Experimental methods are then introduced which allow to observe the properties of the various systems of interest. For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation
The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student among those scheduled. This part allows us to highlight how much the student is able to to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to expose the topic as if it were a seminar, this is useful for his future as a graduating student. The second part of the oral exam consists of a question on another scheduled topic. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to expose shortly a topic in a comprehensible way is also important in the different branches of Physics. teacher profile teaching materials
Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Programme
1- Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
Core Documentation
J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Type of delivery of the course
The exposition of the theories is carried out on the blackboard to allow students to understand the necessary analytical developments. In particular, it is shown how microscopic models can yield results to be compared with experiments. The methods are based either on the approximate resolution of integral equations or on numerical calculation by computer simulation- Experimental methods are then introduced which allow to observe the properties of the various systems of interest. For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation
The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student among those scheduled. This part allows us to highlight how much the student is able to to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to expose the topic as if it were a seminar, this is useful for his future as a graduating student. The second part of the oral exam consists of a question on another scheduled topic. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to expose shortly a topic in a comprehensible way is also important in the different branches of Physics. teacher profile teaching materials
Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Programme
1- Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
Core Documentation
J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Type of delivery of the course
The exposition of the theories is carried out on the blackboard to allow students to understand the necessary analytical developments. In particular, it is shown how microscopic models can yield results to be compared with experiments. The methods are based either on the approximate resolution of integral equations or on numerical calculation by computer simulation- Experimental methods are then introduced which allow to observe the properties of the various systems of interest. For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation
The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student among those scheduled. This part allows us to highlight how much the student is able to to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to expose the topic as if it were a seminar, this is useful for his future as a graduating student. The second part of the oral exam consists of a question on another scheduled topic. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to expose shortly a topic in a comprehensible way is also important in the different branches of Physics. teacher profile teaching materials
Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Programme
1- Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamics functions. Equilibrium conditions. Legendre transforms and thermodynamic potentials. Stability conditions for the phases. Phase transitions and their classification. Van der Waals equation. Recall theory of ensembles in Statistical Mechanics. Fluctuations.
2- Atomic interactions and short range order.
Characterization of the liquid state of matter. Forces between atoms and effective potentials. Distribution functions in canonical and grand canonical ensembles. Radial distribution function and relationship with thermodynamics. The static structure factor. Measurement of the structure of a liquid by diffusion techniques. Hierarchical equation for distribution functions. Mean force potential. Ornstein-Zernike equation. Direct correlation function. Static response function. Closure relations. Approximation of hypernetted chains (HNC). Approximation of Percus-Yevick (PY). PY Solution for hard sphere liquid. State equation for hard spheres. Thermodynamic inconsistency. Modified HNC theory. Structure factor of liquid mixtures and molecular fluids.
3- Computer simulation of fluid systems.
Stochastic and deterministic simulation methods. Method of Molecular Dynamics. Algorithms à la Verlet. Molecular dynamics at constant temperature and constant pressure. The Monte Carlo method. Monte Carlo simulation in different ensembles.
4- Liquid dynamics.
Time dependent correlation functions. Anelastic diffusion of neutrons and measure of the dynamic structure factor. Van Hove's correlation functions. Principle of detailed balance. Linear response theory. Response function. Fluctuation-dissipation theorem. Particle diffusion. Diffusion coefficient. Velocity correlation function. Hydrodynamics and collective modes. Brillouin scattering.
5- Metastable states, supercooled liquids and glass transtion.
Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and behavior of the correlation functions close to the critical point. Supercooled liquids and glass transition. Angell diagram. Outline of the dynamics and the Mode Coupling theory. Configurational entropy and the Kauzmann's temperature.
Core Documentation
J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.
P. G. Debenedetti, Metastable Liquids, Princeton University Press.
Supplementary notes.
Type of delivery of the course
The exposition of the theories is carried out on the blackboard to allow students to understand the necessary analytical developments. In particular, it is shown how microscopic models can yield results to be compared with experiments. The methods are based either on the approximate resolution of integral equations or on numerical calculation by computer simulation- Experimental methods are then introduced which allow to observe the properties of the various systems of interest. For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation
The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student among those scheduled. This part allows us to highlight how much the student is able to to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to expose the topic as if it were a seminar, this is useful for his future as a graduating student. The second part of the oral exam consists of a question on another scheduled topic. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to expose shortly a topic in a comprehensible way is also important in the different branches of Physics.