Quantum effects in plasmas

Abstract

The year 2025 had been designated by UNESCO as the International Year of Quantum Science and Technology. 125 years ago Max Planck's discovery of radiation quanta started the quantum era and 100 years ago quantum mechanics was discovered by Schroedinger, Heisenberg, Bohr, Pauli, Dirac, Born, Fermi and many others. By now, quantum mechanics is the theoretical foundation of most fields of physics and chemistry, and it is the basis for modern nanotechnology. How about plasma physics? How important are quantum effects in plasmas? In what experiments quantum effects are observed and where do they govern the behavior of plasmas? How can these effects be treated theoretically and via computer simulations? Starting with a brief historical overview we discuss the broad parameter range that is characteristic for plasmas and outline where quantum effects are relevant. This is the case primarily for warm dense matter and inertial fusion plasmas. We provide an overview on the theoretical quantum methods that are available for these dense plasmas and how their respective advantages can be combined in order to achieve predictive capability. The key is a downfolding approach that is based on first principles simulations.

Figures (41)

• Figure 1: Radiation energy versus wavelength (in $\mu m$) for 7 temperatures. Upper curves (crosses): measurements by Lummer and Pringsheim, lower curves (dashed lines with circles): Wien's theory. From Ref. lummer_vhdpg_99
• Figure 2: Illustration of Planck's second derivation by comparing Fermi (left) and Bose statistics (right). Each of the four energy levels $E_i$ hosts a total number $N_i$ of particles (in Planck's model $N_i \to P$ and particles [dots] correspond to energy units). Energy $E_i$ is $g_i$-fold degenerate (e.g. four horizontal bars for $E_1$). In the right part, each of the $g_i$ states can host between $0$ and $N_i$ particles, and the number of realizations is given by Eq. (\ref{['eq:kombi-mit-wdh']}) which is characteristic for Bose statistics. In contrast, for fermions, due to the Pauli principle, each of the $g_i$ states can only host $0$ or $1$ particles which leads to a completely different partition sum (\ref{['eq:z-fermi']}) and entropy (\ref{['eq:entropy-fermi']}). Left and right figures show a possible configuration (microstate).
• Figure 3: Illustration of the key quantum effect -- spatial delocalization -- for the example of an atom. A classical point particle (electron) would unavoidably collapse into the nucleus, as this lowers its energy $W$ (top figure). This is in contrast to the known stability of atoms. Nature provides a simple solution (bottom): during its approach of the nucleus the electron increases its size (grey circle), giving rise to a finite value of the interaction energy $W$. In quantum mechanics the finite extension is connected with a statistical interpretation.
• Figure 4: Illustration when quantum effects are relevant. Top: for one particle encountering an obstacle (a double slit) with extension $d$ quantum effects will be relevant when the quantum extension $\lambda$ exceeds $d$, as in the right picture giving rise to diffraction and interference. For two particles at a distance $d$, quantum effects will dominate if $\lambda$ exceeds $d$ resulting in coherence and entanglement. Finally, for many particles (bottom), $\lambda$ has to be compared to the statistical mean of the interparticle distances which scales with the density as $\langle d\rangle \sim n^{-1/3}$.
• Figure 5: Illustration of N-particle quantum effects that arise from spin statistics of fermions. In the top left part we indicate the strong density dependence of the Fermi energy that leads to a decrease nonideality effects with density, cf. Sec. \ref{['ss:qp_parameters']}. The top right graphic shows a scattering process of two electrons entering from below with momenta $p_1$ and $p_2$ and exiting with $p'_1$ and $p'_2$. Quantum exchange gives rise to an additional (negative) scattering contribution where $p'_1$ and $p'_2$ are exchanged. Finally, the probability of a scattering process (scattering rate) is reduced by Pauli blocking.