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Physics: Basic Statistical Physics and Quantum Statistics

Course7.5 credits

What is Statistical Mechanics? To answer, we need to have a little detour and start to talk about another topic, namely Thermodynamics.

Thermodynamics is interested in the relationship among a small number of macroscopic quantities of a body. e.g. pressure, volume, temperature, magnetisation, etc. As such, the basic concepts in thermodynamics rely directly on empirical, experimental confirmation. The power and appeal of thermodynamics is that its predictions are general and robust, and without reference to the microscopic nature of a system: Einstein, once asked about a theory of matter that would change very little or not at all over the next two hundred years, stated that he would make his bet on Thermodynamics.

In a mathematical perspective, thermodynamics has to do with mathematical identities involving derivatives of well defined function. In a physical sense,  it has to do first and foremost with the equilibrium properties of a systems, but also transformations such as heating, cooling, melting, volume compression, (de)-magnetisation, etc, chemical reactions, conversion of mechanical work into heat, conversion of heat into mechanical work, etc. 

Statistical mechanics is concerned with explaining how such properties and transformation occur as a consequence of the microscopic properties of a system. At small scales, e.g. at the quantum scale, things change incessantly in time, due to electronic, atomic and molecular motion and collisions. How to reconcile the micro- and macro- pictures?  For example, how to understand that, while both Newton’s and Schrodinger’s equations appear to be reversible in time at the microscopic level (i.e. without preferred direction of time), on the macroscopic scale we often observe irreversible changes, like at the breaking of a glass, or the mixing of coffee with milk in a cup ? Why does a broken glass not recompose spontaneously? Why do not coffee and milk in a cappuccino mutually separate spontaneously? Or, how is it possible that in thermodynamical equilibrium, the temperature, the pressure, etc. of a body stay constant, given the never-ending motion of the micro-constituents of the body? 

Statistical mechanics provides answers and explanations to these fascinating and deep questions, reconciling microscopic world and macroscopic observations. But the number of microscopic degrees of freedom of a macroscopic body is enormous. So one has to abandon a deterministic approach to the dynamics of each individual particle, and adopt a statistical perspective. Thus concepts like probability, averages, fluctuation become centerstage, and yet in this way a clear connection with the thermodynamical level of description can be established. This program can be accomplished both at the classical and quantum level.

What has been just described constitutes the essence of the course in statistical mechanics, where starting from a microscopic description of matter,

  1. the central concept of entropy is introduced,
  2. a connection with thermodynamical quantities is established, and
  3. paradigmatic systems such as the ideal (quantum an classical) gases are studied.

The overall topic is truly fascinating, since it shows in a beautiful way how what we experience in everyday life naturally emerges from the behavior of matter down at the fundamental space, time, and energy scales.

 

 

 

 

More information can be found at http://liveatlund.lu.se/departments/physics-N/FYSB12/Pages/default.aspx

Contact

Undergraduate Programme of Studies in Physics within Faculty of Science
Sölvegatan 14 C, 223 62 Lund
Box 118, 221 00 Lund
+46 46 222 77 21

Johan Knutsson

Study advisor

+46 46 222 38 48

johan [dot] knutsson [at] sljus [dot] lu [dot] se

Mathieu Gisselbrecht

Study advisor

mathieu [dot] gisselbrecht [at] sljus [dot] lu [dot] se

Entry requirements

Entry requirements

General and FYSA01 General Physics, 30 hp, and 45 hp Mathematics, including NUMA01 7.5 hp, MATB22 7.5 hp and MATB21 7.5 hp, or equivalent.

Selection criteria

Seats are allocated according to: The general average (GPA) of your higher secondary school leaving certificate: 20 %, The Swedish national university aptitude test: 10 %, Previous college/university studies (APGR): 70 %.

English language requirements

Most of Lund University’s programmes require English Level 6 (unless otherwise stated under "Entry requirements"). This is the equivalent of an overall IELTS score of 6.5 or a TOEFL score of 90. There are several ways to prove your English language proficiency - check which proof is accepted at the University Admissions in Sweden website. All students must prove they meet English language requirements by the deadline, in order to be considered for admission.

Country-specific requirements

Check if there are any country-specific eligibility rules for you to study Master's studies or Bachelor's studies in Sweden.

Apply

Important dates

This programme or course is currently not open in an international application round.

How to apply

Lund University uses a national application system run by University Admissions in Sweden. It is only possible to apply during the application periods.
 

Step 1: Apply online

  • Check you meet the entry requirements of the programme or course you are interested in
  • Start your application – go to www.universityadmissions.se where you create an account and select programmes/courses, during the application period
  • Rank your programme/course choices in order of preference and submit them before the application deadline
     

Step 2: Submit documents

  • Read about how to document your eligibility and how to submit your documents at www.universityadmissions.se. Follow any country-specific document rules for Master's studies or Bachelor's studies
  • Get all your documents ready: official transcripts and high school diploma (Bachelor's applicants), official transcripts and degree certificate or proof of expected graduation (Master's applicants), passport/ID and proof of English proficiency (all applicants)
  • Prepare programme-specific documents if stated on this page
  • Upload or send all required documents to University Admissions before the document deadline
  • Pay the application fee (if applicable) before the document deadline

*Note that the process if different if you are applying as an exchange student or as a part of a cooperation programme (such as Erasmus +).
*If you have studied your entire Bachelor's programme in Sweden and all of your academic credits are in Ladok, you do not have to submit transcripts or your diploma when applying for a Master's programme.

*Svensk student? Läs instruktionerna om att söka till ett internationellt masterprogram på lu.se.

Tuition fees

Non-EU/EEA citizens

Full programme/course tuition fee: SEK 18 125

First payment: SEK 18 125

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Citizens of a country outside of the European Union (EU), the European Economic Area (EEA) and Switzerland are required to pay tuition fees. You pay one instalment of the tuition fee in advance of each semester.

Read more about tuition fees, payments and exemptions

EU/EEA citizens and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.

Application fee

If you are required to pay tuition fees, you are generally also required to pay an application fee of SEK 900 (approximately EUR 100) when you apply at www.universityadmissions.se. You pay one application fee regardless of how many programmes or courses you apply to.

Read more about paying the University Admissions in Sweden application fee and exemptions


*Note that there are no tuition or application fees for exchange students or PhD students, regardless of their nationality.

Scholarships & funding

Lund University Global Scholarship programme

The Lund University Global Scholarship programme is a merit-based and selective scholarship targeted at top academic students from countries outside the EU/EEA.

Lund University Global Scholarship

Swedish Institute Scholarships

The Swedish Institute offers scholarships to international students applying for studies in Sweden at Bachelor's, Master's, PhD and post-doctoral levels.

Scholarship options at the Swedish Institute website

Country-specific scholarships and funding options

Lund University has agreements with scholarship organisations and funding bodies in different countries, which may allow applicants to apply for funding or scholarships in their home countries for their studies at Lund University.

External scholarships

Information about scholarships from external organisations