The main purpose of theoretical physics is to understand physical phenomena. Accurate understanding is possible only using mathematical models. In the best case, experimental observations can be explained using only a small number of basic assumptions. Using the models it is possible to calculate the properties of the system under different conditions and predict new phenomena.

The figure shows different length scales in the universe. Every division in the scale corresponds to a length scale that is ten times larger than the one below. The length scales from the atomic size to the human size are shown as enlarged on the right hand side.

Atoms and its constituent particles are described by laws of quantum mechanics. On the human scale these phenomena are averaged, and the averages obey laws of classical physics. Between these scales there is a *mesoscopic* region, where the behavior is partly classical but partly quantum mechanical.

Research of theoretical physics in Oulu concentrates on the scale from atomic to mesoscopic physics. This range shows many interesting phenomena, and some examples are given below.

#### Superconductivity

Several metals transform to superconducting state at temperatures near the absolute zero. We study quantum phenomena in contacts of superconducting metals. Using such contacts it is possible to construct a circuit, which could be used as a component in a potential quantum computer.

It is common that the electrical resistivity decreases with decreasing temperature. In superconductors the resistivity drops abruptly and vanishes below a critical temperature *T*_{c} (figure on the left). In superconducting contacts the dependence of the current on the voltage differs from Ohm´s law *I=V/R* (figure on the right). Note that the electric current *I* (smaller than *I*_{c}) is possible in the absence of voltage, *V*=0.

#### Quantum fluids

One of the main problems of theoretical physics is to solve the behavior of many interacting particles. One pure example of this is liquid helium at low temperatures, where the atomic motions have to be calculated using quantum mechanics. The figure shows the calculated density of a thin film of helium on a solid substrate.

Helium superfluid wets magnesium surface with a monolayer film. If the wetting is restricted then the second atomic layer begins to form and the film grows layer by layer. In the figure we present results of a many-body calculation for the film density profiles as a function of surface density and distance from the Mg substrate. In the thickest films the third atomic layer begins to form.

Liquid helium transforms to a superfluid state at low temperatures. One distinguishing property of this state is that in a rotating container, the rotation of the liquid is not uniform but is concentrated on vortex lines. In the figure the yellow lines mark vortex lines, and the liquid circulates around the lines. Simultaneously the vortex lines rotate together with the container.

#### Quantum dots

The junction between two different semiconductors can trap electrons so that they can move only on the plane parallel to the heterojunction. In quantum dots, for example using electrodes even the planar motion of electrons can be restricted and the electrons start to behave like the ones in atoms. Unlike atoms quantum dots are artificial devices and consequently it is possible to control their properties. This makes them, as well as other nanostructures very promising components for future electronics.

Electron density in a double quantum dot. The density has maxima (white color) at the basins of the wells forming the dot and gets the smaller (blue color) the further we go. The structure of the wells can be seen here. To go around the dot click on the picture.

#### Superlattice

Growing alternating thin layers of two different substances forms a *superlattice*. In a superlattice the electrons are not accelerated without limit by a constant electric field but start to oscillate back and forth because of quantum mechanics. Using this Bloch oscillation it might be possible to construct a device that can produce high frequency THz radiation, which is not easy to produce by other means.

The figure shows a wave function that describes the probability of an electron being in different potential minima *n* of the superlattice. A strong constant electric field tends to accelerate the electron to the right (which shows up as rapid oscillations of the wave function on the right hand side). However, because of the quantum mechanical interference the electron cannot escape to the right but remains oscillating back and forth. One way to understand this is that the electron is bound to an energy band (shaded area), which is tilted because of the strong electric field. The electron oscillates in a region that is of approximately the same size as the horizontal width of the energy band (the wave function is nonzero essentially only in this region).

Last updated: 25.4.2017