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Statistical Physics of Nanoparticles (2015)

Name of course: Statistical Physics of Nanoparticles

ECTS credits: 2.5 or 5, depending on project option is selected. 

Course parameters:

Language: English

Level of course: PhD course

Time of year: Spring 2015

No. of contact hours/hours in total incl. preparation, assignment(s) or the like: Option without project: 30 contact hours/70 hours total. Option with project: 35 contact hours/140 hours total.

Capacity limits: 20 students

Objectives of the course:

To provide the students with the tools to understand the literature in the field and enable them to independently establish physically realistic models and solve them.

Learning outcomes and competences:

At the end of the course, the student should be able to:

  • Calculate thermal properties of particles with a variety of different excitation spectra and understand the size dependence.
  • Identify the differences in finite vs. infinite sizes of phenomena/systems such as melting, molecular beams, thermal electrons.
  • Understand phenomena such as non-exponential decay, negative heat capacities and their connection to canonical vs. microcanonical ensembles.


Compulsory programme:

The only compulsory part will be the project report.

Course contents:

Topics covered in the lectures and the exercise classes will include 10 out of the following 11 (one topic will be deselected in consultation with the students at the first lecture):

  • Introduction; ensembles, degrees of freedom and all that
  • The relation between classical and quantum statistics; phase space, examples
  • Microcanonical temperature; definition, applications
  • Thermal properties of vibrations; useful relations
  • Rate constants for emission of atoms, electrons and photons; (almost) all you need to know
  • The evaporative ensemble; non-exponential decays, abundances and energies
  • Abundance distributions; large scale features, critical sizes, nucleation
  • Molecular dynamics and Monte Carlo simulations; the starting kit
  • Thermal excitation of valence electrons; exactly solvable models and realistic models
  • He droplets; excitation spectra and thermal properties
  • Melting and freezing of nanoparticles; the finite size phase transition

The subject of the (optional) project is chosen by the student. Groups of up to three students are can submit a single report if it is accompanied by a statement signed by all that specifies the contribution of each student.


Basic quantum mechanics, thermal physics and mathematical skills.

Name of lecturer:

Klavs Hansen

Type of course/teaching methods:

There will be 10 lectures, 20 classroom exercise hours. The project students will get a additional 5 hours of consultation time.


Klavs Hansen, Statistical Physics of Nanoparticles in the Gas Phase, Springer, Dordrecht (2013).

Course homepage:


Course assessment:

30 minutes oral exam plus the report of the optional project. The oral exam for the project students will include questions on the report.


Department of Physics


Q4, F2015




For registration and if you have any questions, please contact:

Klavs Hansen, e-mail:, phone 87156332



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Revised 20.06.2016