Refine
Document Type
- Article (1)
- Conference Proceeding (1)
- Doctoral Thesis (1)
Language
- English (3) (remove)
Has Fulltext
- yes (3)
Is part of the Bibliography
- no (3)
Keywords
- phase transitions (3) (remove)
Institute
- Biochemie und Chemie (1)
- Mathematik (1)
- Physik (1)
By running a temperature series of molecular dynamics (MD) simulations starting from the known low-temperature phase, the experimentally observed phase transition in a `jumping crystal' was captured, thereby providing a prediction of the unknown crystal structure of the high-temperature phase and clarifying the phase-transition mechanism. The phase transition is accompanied by a discontinuity in two of the unit-cell parameters. The structure of the high-temperature phase is very similar to that of the low-temperature phase. The anisotropic displacement parameters calculated from the MD simulations readily identified libration as the driving force behind the phase transition. Both the predicted crystal structure and the phase-transition mechanism were verified experimentally using TLS (translation, libration, screw) refinement against X-ray powder diffraction data.
In this thesis we explore the characteristics of strongly interacting matter, described by Quantum Chromodynamics (QCD). In particular, we investigate the properties of QCD at extreme densities, a region yet to be explored by first principle methods. We base the study on lattice gauge theory with Wilson fermions in the strong coupling, heavy quark regime. We expand the lattice action around this limit, and carry out analytic integrals over the gauge links to obtain an effective, dimensionally reduced, theory of Polyakov loop interactions.
The 3D effective theory suffers only from a mild sign problem, and we briefly outline how it can be simulated using either Monte Carlo techniques with reweighting, or the Complex Langevin flow. We then continue to the main topic of the thesis, namely the analytic treatment of the effective theory. We introduce the linked cluster expansion, a method ideal for studying thermodynamic expansions. The complex nature of the effective theory action requires the development of a generalisation of the linked cluster expansion. We find a mapping between generalised linked cluster expansion and our effective theory, and use this to compute the thermodynamic quantities.
Lastly, various resummation techniques are explored, and a chain resummation is implemented on the level of the effective theory itself. The resummed effective theory describes not only nearest neighbour, next to nearest neighbour, and so on, interactions, but couplings at all distances, making it well suited for describing macroscopic effects. We compute the equation of state for cold and dense heavy QCD, and find a correspondence with that of non-relativistic free fermions, indicating a shift of the dynamics in the continuum.
We conclude this thesis by presenting two possible extensions to new physics using the techniques outlined within. First is the application of the effective theory in the large-$N_c$ limit, of particular interest to the study of conformal field theory. Second is the computation of analytic Yang Lee zeros, which can be applied in the search for real phase transitions.
Based on a non-rigorous formalism called the “cavity method”, physicists have made intriguing predictions on phase transitions in discrete structures. One of the most remarkable ones is that in problems such as random k-SAT or random graph k-coloring, very shortly before the threshold for the existence of solutions there occurs another phase transition called condensation [Krzakala et al., PNAS 2007]. The existence of this phase transition seems to be intimately related to the difficulty of proving precise results on, e. g., the k-colorability threshold as well as to the performance of message passing algorithms. In random graph k-coloring, there is a precise conjecture as to the location of the condensation phase transition in terms of a distributional fixed point problem. In this paper we prove this conjecture, provided that k exceeds a certain constant k0.