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Tobias Kippenberg
This course covers non-equilibrium statistical processes and the treatment of fluctuation dissipation relations by Einstein, Boltzmann and Kubo. Moreover, the fundamentals of Markov processes, stochastic differential and Fokker Planck equations, mesoscopic master equation, etc will be treated in detail. Prior knowledge of statistical physics is highly recommended but not required.
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What's inside
Learning objectives
- Formulate statistical processes mathematically
- Solve the quantum master equation using qutip in python
- Apply numerical simulation tools to non-equilibrium systems
- Explore the quantum optical numerical toolbox (matlab)
- Visualize non-equilibrium processes numerically using jupyter notebooks
- Elaborate modern examples from literature of non-equilibrium processes
- Apply emcee python package to bayesian statistical data analysis
- Formulate statistical processes mathematically
- Solve the quantum master equation using qutip in python
- Apply numerical simulation tools to non-equilibrium systems
- Explore the quantum optical numerical toolbox (matlab)
- Visualize non-equilibrium processes numerically using jupyter notebooks
- Elaborate modern examples from literature of non-equilibrium processes
- Apply emcee python package to bayesian statistical data analysis
Syllabus
Lecture 1: Brownian motion and 3 derivations
Lecture 2: Continuous stochastic process
Lecture 3: Stochastic differential equations
Lecture 4: Fluctuation dissipation theorem
Read more
Syllabus
Lecture 1: Brownian motion and 3 derivations
Lecture 2: Continuous stochastic process
Lecture 3: Stochastic differential equations
Lecture 4: Fluctuation dissipation theorem
Read more
Lecture 5: Fokker Planck equation
Lecture 6: Lévy flights
Lecture 7: Master equations
Lecture 8: The Crook and Jarzynski equality
Lecture 9+10: Quantum optics and quantum Langevin equation
Lecture 11+12: Quantum regression theorem
Good to know
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Know what's good ,
what to watch for , and
possible dealbreakers
Offers a comprehensive exploration of advanced statistical physics and non-equilibrium processes, suitable for experienced students and researchers seeking advanced knowledge in these areas
Involves extensive use of hands-on numerical simulations and data analysis techniques, providing practical experience in implementing these methodologies
Taught by Tobias Kippenberg, a recognized expert in the field of statistical physics and quantum optics, offering learners access to cutting-edge knowledge and insights
Emphasizes the application of advanced statistical physics concepts to real-world problems in various fields, including quantum optics, mesoscopic physics, and biological systems
Requires a solid foundation in statistical physics, making it most suitable for advanced undergraduate or graduate students, researchers, or professionals in related fields
Utilizes specialized software packages such as QuTiP and MATLAB, which may require additional setup or prior knowledge for learners who are not familiar with these tools
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Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Advanced statistical physics with these
activities:
Review non-equilibrium statistical processes.
Show steps
Reviewing non-equilibrium statistical processes will strengthen your foundational knowledge and refresh your memory, making the course materials easier to understand.
Show steps
-
Re-read your notes or textbooks on non-equilibrium statistical processes.
-
Review lecture slides or videos on the topic.
-
Work through practice problems or exercises.
Review the book 'Quantum Optics' by Scully and Zubairy.
Show steps
This book provides a comprehensive overview of quantum optics, which will supplement the course materials and enhance your understanding.
Show steps
-
Read the book chapters that cover the topics covered in the course.
-
Take notes and summarize the key concepts.
-
Discuss the book with classmates or the instructor.
Participate in online forums and discussions related to non-equilibrium processes.
Show steps
Participating in discussions with peers will expose you to different perspectives and help you clarify your own understanding.
Show steps
-
Find online forums or discussion groups dedicated to non-equilibrium processes.
-
Join the discussions and ask questions.
-
Share your own insights and knowledge.
-
Connect with other students or researchers in the field.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Solve problems using the quantum master equation in QuTip.
Show steps
By practicing solving problems using the quantum master equation in QuTip, you will improve your problem-solving skills and gain a deeper understanding of the concepts.
Show steps
-
Use QuTip to solve the problems.
-
Install QuTip on your computer.
-
Find practice problems or exercises online or in textbooks.
-
Check your solutions against known results or ask for help on forums.
Explore the Quantum Optical Numerical Toolbox (MATLAB).
Show steps
Getting hands-on experience with the Quantum Optical Numerical Toolbox will familiarize you with the tools and techniques used in quantum optics.
Browse courses on
MATLAB
Show steps
-
Find a project idea or problem to work on.
-
Learn the basics of MATLAB and the Quantum Optical Numerical Toolbox.
-
Implement your project using MATLAB and the toolbox.
-
Test and debug your code.
-
Present your results or share your project.
Create a collection of Jupyter Notebooks demonstrating non-equilibrium processes.
Show steps
Creating a collection of Jupyter Notebooks will provide you with a valuable resource for reviewing and visualizing non-equilibrium processes.
Show steps
-
Choose a variety of non-equilibrium processes to demonstrate.
-
Find or create code to simulate or model these processes.
-
Create Jupyter Notebooks that combine the code with explanations and visualizations.
-
Share your notebooks with others or use them for your own reference.
Create a video tutorial on a specific aspect of non-equilibrium processes.
Show steps
Creating a video tutorial will help you solidify your understanding of the concept and share your knowledge with others.
Show steps
-
Choose a specific aspect of non-equilibrium processes to focus on.
-
Research the topic and gather information.
-
Create a script or outline for your tutorial.
-
Record and edit your video.
-
Share your tutorial on YouTube or other video-sharing platforms.
Develop a software tool to simulate or model non-equilibrium processes.
Show steps
Developing a software tool will provide you with practical experience and a valuable resource for further study.
Show steps
-
Design the software tool and define its functionality.
-
Choose a programming language and development environment.
-
Implement the software tool and test it thoroughly.
-
Document the software tool and make it available to others.
Review non-equilibrium statistical processes.
Show steps
Reviewing non-equilibrium statistical processes will strengthen your foundational knowledge and refresh your memory, making the course materials easier to understand.
Show steps
Show steps
Show steps
- Re-read your notes or textbooks on non-equilibrium statistical processes.
- Review lecture slides or videos on the topic.
- Work through practice problems or exercises.
Review the book 'Quantum Optics' by Scully and Zubairy.
Show steps
This book provides a comprehensive overview of quantum optics, which will supplement the course materials and enhance your understanding.
Show steps
Show steps
Show steps
- Read the book chapters that cover the topics covered in the course.
- Take notes and summarize the key concepts.
- Discuss the book with classmates or the instructor.
Participate in online forums and discussions related to non-equilibrium processes.
Show steps
Participating in discussions with peers will expose you to different perspectives and help you clarify your own understanding.
Show steps
Show steps
Show steps
- Find online forums or discussion groups dedicated to non-equilibrium processes.
- Join the discussions and ask questions.
- Share your own insights and knowledge.
- Connect with other students or researchers in the field.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Solve problems using the quantum master equation in QuTip.
Show steps
By practicing solving problems using the quantum master equation in QuTip, you will improve your problem-solving skills and gain a deeper understanding of the concepts.
Show steps
Show steps
Show steps
- Use QuTip to solve the problems.
- Install QuTip on your computer.
- Find practice problems or exercises online or in textbooks.
- Check your solutions against known results or ask for help on forums.
Explore the Quantum Optical Numerical Toolbox (MATLAB).
Show steps
Getting hands-on experience with the Quantum Optical Numerical Toolbox will familiarize you with the tools and techniques used in quantum optics.
Browse courses on
MATLAB
Show steps
Show steps
Show steps
- Find a project idea or problem to work on.
- Learn the basics of MATLAB and the Quantum Optical Numerical Toolbox.
- Implement your project using MATLAB and the toolbox.
- Test and debug your code.
- Present your results or share your project.
Create a collection of Jupyter Notebooks demonstrating non-equilibrium processes.
Show steps
Creating a collection of Jupyter Notebooks will provide you with a valuable resource for reviewing and visualizing non-equilibrium processes.
Show steps
Show steps
Show steps
- Choose a variety of non-equilibrium processes to demonstrate.
- Find or create code to simulate or model these processes.
- Create Jupyter Notebooks that combine the code with explanations and visualizations.
- Share your notebooks with others or use them for your own reference.
Create a video tutorial on a specific aspect of non-equilibrium processes.
Show steps
Creating a video tutorial will help you solidify your understanding of the concept and share your knowledge with others.
Show steps
Show steps
Show steps
- Choose a specific aspect of non-equilibrium processes to focus on.
- Research the topic and gather information.
- Create a script or outline for your tutorial.
- Record and edit your video.
- Share your tutorial on YouTube or other video-sharing platforms.
Develop a software tool to simulate or model non-equilibrium processes.
Show steps
Developing a software tool will provide you with practical experience and a valuable resource for further study.
Show steps
Show steps
Show steps
- Design the software tool and define its functionality.
- Choose a programming language and development environment.
- Implement the software tool and test it thoroughly.
- Document the software tool and make it available to others.
Career center
Learners who complete Advanced statistical physics will develop knowledge and skills
that may be useful to these careers:
Statistician
Statistician
Statisticians collect, analyze, interpret, and present data. They work in a variety of fields, including government, business, and healthcare. This course can help build a foundation for this role by deepening your knowledge of statistical processes and fluctuation dissipation relations. Furthermore, the tools to solve the quantum master equation using QuTip in Python, visualizing non-equilibrium processes numerically using Jupyter Notebooks, and applying the EMCEE Python package to Bayesian statistical data analysis are directly applicable to many statistician roles.
Physicist
Physicist
Physicists study matter and energy and the interactions between them. It is an interdisciplinary field that connects multiple scientific fields. They use a variety of tools and techniques to study the physical world, from the smallest subatomic particles to the largest structures in the universe. This course covers topics directly relevant to many subfields of physics, including statistical physics, quantum optics, and condensed matter physics.
Data Scientist
Data Scientist
Data Scientists combine expertise in statistical and mathematical modeling to extract meaningful insights and trends from data. This course can help build a foundation for this role by deepening your knowledge of Non-Equilibrium Statistical Processes and fluctuation dissipation relations by Einstein, Boltzmann, and Kubo. Furthermore, the tools to solve the quantum master equation using QuTip in Python, visualizing non-equilibrium processes numerically using Jupyter Notebooks, and applying the EMCEE Python package to Bayesian statistical data analysis are directly applicable to many data science roles.
Research Scientist
Research Scientist
Research Scientists conduct research in a variety of fields, including physics, chemistry, biology, and computer science. They use a variety of methods and techniques to study the natural world and develop new technologies. This course may be useful for developing the research skills needed for a career in research science, particularly when working with complex systems and non-equilibrium processes.
Data Analyst
Data Analyst
Data Analysts collect, clean, and analyze data to help organizations make better decisions. They use a variety of tools and techniques to extract meaningful insights from data. This course can help build a foundation for this role by deepening your knowledge of Non-Equilibrium Statistical Processes and fluctuation dissipation relations. Furthermore, the tools to solve the quantum master equation using QuTip in Python, visualizing non-equilibrium processes numerically using Jupyter Notebooks, and applying the EMCEE Python package to Bayesian statistical data analysis are directly applicable to many data analyst roles.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts apply analytical methods to help organizations make better decisions. They use mathematical modeling, simulation, and optimization to solve problems in a variety of areas, including supply chain management, healthcare, and finance. A background in statistical physics can be beneficial for this role, particularly when dealing with complex systems and non-equilibrium processes.
Economist
Economist
Economists study how individuals, businesses, and governments make decisions in the face of scarcity. They use a variety of tools and techniques to analyze economic data and develop policies to improve economic outcomes. This course may be useful for developing the analytical skills needed for economics, particularly when dealing with complex systems and non-equilibrium processes.
Software Engineer
Software Engineer
Software Engineers design, build, and maintain computer systems and applications. They use a variety of programming languages and tools to create software that meets the needs of users. This course may be useful for developing the programming skills needed for software engineering, particularly when working with numerical simulation tools, data analysis, and scientific computing.
Financial Analyst
Financial Analyst
Financial Analysts use quantitative methods to evaluate the performance of companies, stocks, bonds, and other investments. They make recommendations for investments and manage portfolios. This course may be useful for developing the mathematical skills needed for financial analysis, particularly when working with stochastic processes and non-equilibrium systems.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical models to analyze financial data and make predictions about future trends. This course may be useful for developing the mathematical skills needed for financial analysis, particularly when working with stochastic processes and non-equilibrium systems.
Project Manager
Project Manager
Project Managers plan and execute projects to achieve specific goals. They use a variety of tools and techniques to manage projects on time, within budget, and to the required quality standards. This course may be useful for developing the project management skills needed for this role, particularly when managing complex projects with multiple stakeholders and dependencies.
Science Writer
Science Writer
Science Writers communicate complex scientific information to a general audience. They use a variety of writing styles and formats to make scientific topics accessible and engaging. This course may be useful for developing the writing skills needed for science writing, particularly when writing about complex scientific topics such as Non-Equilibrium Statistical Processes.
Technical Writer
Technical Writer
Technical Writers create instruction manuals, training materials, and other technical documents. They use a variety of writing styles and formats to communicate complex technical information to a specific audience. This course may be useful for developing the writing skills needed for technical writing, particularly when writing about complex scientific topics.
Consultant
Consultant
Consultants provide expert advice to businesses and organizations on a variety of topics. They use their knowledge and expertise to help clients solve problems and make better decisions in a variety of subject matter areas. Often a consultant will need to have deep expertise in multiple domains, which can include knowledge of statistical processes and Non-Equilibrium Statistical Processes. This course may be useful for gaining exposure to advanced statistical physics principles.
Teacher
Teacher
Teachers plan and deliver instruction to students in a variety of settings. They use a variety of methods and techniques to help students learn and grow. This course may be useful for developing the communication and teaching skills needed for teaching, particularly when teaching physics or other STEM disciplines at the college level.
For more career information including salaries, visit:
OpenCourser.com/course/iawrzg/advanced
Reading list
We've selected nine books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Advanced statistical physics.
Provides a comprehensive overview of statistical mechanics, both from a theoretical and a computational perspective. It would be a valuable reference for students who want to delve deeper into the mathematical foundations of statistical physics.
Save
Provides a comprehensive overview of quantum optics, with a focus on the theoretical foundations of the field. It includes extensive discussions of topics such as quantum measurement, quantum entanglement, and quantum information theory. It would be a valuable resource for students who are interested in learning more about the quantum aspects of light-matter interactions.
Save
Provides a comprehensive overview of the statistical physics of particles. It would be a valuable resource for students who are interested in learning more about the statistical properties of matter.
Provides a comprehensive overview of Bayesian data analysis. It would be a valuable resource for students who are interested in learning more about the statistical techniques used to analyze data from complex systems.
Provides a gentle introduction to quantum statistical mechanics, making it accessible to students with a background in classical statistical mechanics. It would be a good starting point for students who are interested in learning more about the quantum aspects of statistical physics.
Provides a comprehensive overview of Python for data analysis. It would be a valuable resource for students who are interested in learning more about the programming techniques used to analyze data from complex systems.
Provides a comprehensive overview of mesoscopic physics, a field that studies the behavior of electrons in small devices. It would be a valuable resource for students who are interested in learning more about the physics of nanoscale devices.
Provides a clear and concise introduction to quantum field theory. It would be a good starting point for students who are new to the field.
Provides a clear and concise introduction to statistical and thermal physics. It would be a good starting point for students who are new to the field.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/iawrzg/advanced
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Effort
3 to 5 hours per week for 10 weeks
Level
Advanced
Via
edX
Institution
École Polytechnique Fédérale de Lausanne
Instructor
Tobias Kippenberg
Language
English
Transcript
English
Good to know
Offers a comprehensive exploration of advanced statistical physics and non-equilibrium processes, suitable for experienced students and researchers seeking advanced knowledge in these areas
Involves extensive use of hands-on numerical simulations and data analysis techniques, providing practical experience in implementing these methodologies
Taught by Tobias Kippenberg, a recognized expert in the field of statistical physics and quantum optics, offering learners access to cutting-edge knowledge and insights
Emphasizes the application of advanced statistical physics concepts to real-world problems in various fields, including quantum optics, mesoscopic physics, and biological systems
Requires a solid foundation in statistical physics, making it most suitable for advanced undergraduate or graduate students, researchers, or professionals in related fields
Utilizes specialized software packages such as QuTiP and MATLAB, which may require additional setup or prior knowledge for learners who are not familiar with these tools
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