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Project Area A: Many-Body Phenomena

Project Area B: Semiclassical Asymptotics

Project Area C: Effective Single-Particle Systems beyond Wigner Dyson

Project Area D: Symmetry Classes and Symmetric Spaces

Project Area A: Many-Body Phenomena

A1

Effective theories of correlated fermions
J. von Delft, ASC München, K. Efetov, TP Bochum, P. Müller, M München
In this project we study various effective theories for correlated fermion systems. In particular, we will (1) investigate bosonization in arbitrary dimensions as a tool for both analytics and Monte Carlo numerics; (2) develop effective field theories for disordered Luttinger liquids; (3) study transport properties of Josephson junctions and other granular materials; (4) study the behavior of the transmission phase through a quantum dot during the crossover from closed to open dots; (5) conduct a mathematical study of Anderson’s orthogonality catastrophe in clean and disordered fermion systems; and (6) extend the Jordan-Wigner transformation from linear structures to star geometries, allowing for an exact mapping of quantum spin chains in a star geometry to quantum impurity models.

A3

Nonlinear dynamics of strongly interacting quantum fields
A. Altland, TP Köln, K. Hornberger, TP Duisburg-Essen, S. Kehrein, ASC München, M. Kunze, M Köln, A. Rosch, TP Köln, R. Schützhold, TP Duisburg-Essen
The understanding of strongly interacting quantum many-body systems is one of the main challenges of contemporary physics. Even in those cases where the ground state of such a system is known, we are just beginning to understand their non-linear dynamics. In this project, we study the impact of particle interactions by means of archetypical processes: a) the back-reaction of quantum (or thermal) fluctuations onto the classical mean field and b) the decoherence, equilibration and thermalization dynamics of the system after a departure from the ground (or thermal equilibrium) state. Furthermore, we study the interplay of thermalization and dynamics by investigating the expansion of fermionic atoms in optical lattices where c) the breakdown of hydrodynamics is described by regularized singular diffusion equations.

A4

Nonequilibrium phenomena
R. Egger, TP Düsseldorf, S. Kehrein, ASC München, R. Schützhold, TP Duisburg-Essen
This project is devoted to the theory of nonequilibrium phenomena in interacting mesoscopic quantum systems, in particular to conceptual foundations of time-dependent transport and quantum phase transitions. Several interrelated subprojects aim at achieving progress in this important area. This includes the formulation and application of general fluctuation relations, the development of theoretical approaches for driven open quantum systems and time-dependent quantum phase transitions, as well as questions of more applied relevance, such as current-induced mechanical forces, or nonequilibrium phenomena in disordered Luttinger liquids.

A5

Mesocopic transport of Dirac fermions
E. Efetov, TP Bochum, R. Egger, TP Düsseldorf, I. Eremin, TP Bochum
Project A5 aims at a detailed understanding of Dirac fermions in mesoscopic systems. Physical realizations include graphene monolayers and the surface state of a strong topological insulator. The project is mainly concerned with interaction effects and with physics-motivated research on experimentally relevant questions concerning mesoscopic quantum transport of Dirac fermions.

A7

Fluctuations and large deviations in nonequilibrium stochastic dynamics
A. Altland, TP Köln, E. Frey, ASC München, J. Krug, TP Köln, C. Külske, M Bochum, A. Winter, M Duisburg-Essen
The project explores fluctuation-dominated behavior in interacting many-body systems originating from a variety of physical and biological contexts. A common methodological basis is provided by the use of large deviations principles in path space, which links the project to dynamical systems theory and semi-classical quantum mechanics. Specific problems to be addressed concern the structure of none-equilibrium measures in spin systems, fluctuation theorems for mesoscopic quantum systems, and effects of demographic and spatial fluctuations in models of biological population dynamics.

A8

Non-abelian symmetries in tensor networks
J. von Delft, TP München, P. Littelmann, M Köln, U. Schollwöck, TP München
In the numerical simulation of quantum-many body systems, the exploitation of symmetries is absolutely essential for the feasibility of certain calculations, in that they can provide orders of magnitude in performance gain. Given non-abelian symmetries, for example, for numerical procedures such as the diagonalization of Hamiltonians, the Wigner-Eckart theorem can be utilized to significantly reduce the number of relevant matrix elements. In particular, this allows one to focus on symmetry multiplets only, instead of separately keeping track of all states within each multiplet. Though the added symmetry structure makes numerical codes significantly more complex,finally their performance can be dramatically improved. The project thus focuses on the efficient and transparent implementation of quantum symmetry spaces. These are to be applied to tensor network algorithms such as the numerical renormalization group (NRG), the density matrix renormalization group (DMRG) for 1-dimensional quantum chain models, as well as the multiscale entanglement ansatz (MERA) and the projected entangled-pair states (PEPS) Ansatz for two-dimensional quantum lattice models. Moreover, the efficiency of algorithms for calculating the Clebsch-Gordan coefficients for nonabelian groups such as SU(N) will be increased, by exploiting the Weyl symmetry of their weight diagrams.

A9

The spectrum of interacting fermions in graphene quantum dots
R. Egger, TP Düsseldorf, H. Siedentop, M München, E. Stockmeyer, M München
The physical object of research in project A9 is defined by two-dimensional graphene monolayers, where fermions (dressed electrons) can be delocalized or confined by a locally perturbed homogeneous magnetic field defining a quantum dot. We aim at the detailed understanding of spectra of Weyl operators (massless Dirac operators) describing interacting fermions in graphene.The fermions interact directly through Coulomb forces and, possibly, indirectly via phonon fields. The prime mathematical objects to be studied will be self-adjoint operators describing these systems. More precisely, these will be suitable N-particle Hamiltonians, and those Hamiltonians coupled to phonon fields.
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