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# Reduced Density Matrices in Quantum Physics and Role of Fermionic Exchange Symmetry

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The interdisciplinary workshop brings together experts in quantum science, as e.g. quantum information theory, quantum chemistry, solid state physics and mathematical physics. The aim is to explore from a conceptual viewpoint the influence of the fermionic exchange symmetry and its consequences for the reduced 1-and 2-fermion picture. In particular, a better understanding should be developed of how the conflict of energy minimization and antisymmetry of the N-fermion quantum state leads to simplified descriptions of fermionic ground states.

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# | Episode Title | Description | People | Date | |
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1 | DMRG in Quantum Chemistry: From its relation to traditional methods to n-orbital density matrices and beyond | In my talk I will attempt to provide an overview on the application of the density matrix renormalization group (DMRG) algorithm in quantum chemistry. | Markus Reiher | 21 Oct 2016 | |

2 | (Almost) 25 Years of DMRG - What Is It About? | In this talk, I will introduce DMRG both from the historical (statistical) and modern (matrix product state) perspective, highlighting why it has become the method of choice for one-dimensional quantum systems in and out of equilibrium. | Ulrich Schollwöck | 21 Oct 2016 | |

3 | Openness of a Many-fermion Quantum System from the Generalized Pauli Principle | Information about the interaction of a many-electron quantum system with its environment is encoded within the one-electron density matrix (1-RDM). | Romit Chakraborty | 21 Oct 2016 | |

4 | Generalized Pauli Constraints in Reduced Density Matrix Functional Theory | Reduced Density Matrix Functional Theory is a method that relies on the 1-1 correspondence between the ground state wavefunction of many electron systems and the first order reduced density matrix(1RDM) and uses the second one as its fundamental valuable. | Iris Theophilou | 21 Oct 2016 | |

5 | Quasipinning and Extended Hartree-Fock Method based on Generalized Pauli Constraints | It is now known that fermionic natural occupation numbers (NON) do not only obey Pauli’s exclusion principle but are even stronger restricted by the so-called generalized Pauli constraints (GPC). | Carlos Benavides-Riveros | 21 Oct 2016 | |

6 | Fermionic Exchange Symmetry: Quantifying its Influence beyond Pauli’s Exclusion Principle | The Pauli exclusion principle has a strong impact on the properties and the behavior of most fermionic quantum systems. Remarkably, even stronger restrictions on fermionic natural occupation numbers follow from the fermionic exchange symmetry. | Felix Tennie | 21 Oct 2016 | |

7 | Pinning of Fermionic Occupation Numbers | The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. | Matthias Christandl | 21 Oct 2016 | |

8 | Calculation Of Generalized Pauli Constraints | In the talk I am planning to explain two different solutions of N-representability problem and then give the algorithm to calculate GPCs. | Murat Altunbulak | 21 Oct 2016 | |

9 | Derivation of the time-dependent Hartree(-Fock)-equation | In the talk I will present recent progress in proving closeness of the microscopic and effective description for systems of many fermions. | Peter Pickl | 21 Oct 2016 | |

10 | Physical Meaning of Natural Orbitals and Natural Occupation Numbers | We show that the success of reduced density-matrix functional theory in describing molecular dissociation lies in the flexibility provided by fractional occupation numbers while the role of the natural orbitals is minor. | Nicole Helbig | 21 Oct 2016 | |

11 | Introduction and Overview of the Reduced Density Matrix Functional Theory | In this presentation, we review the theoretical foundations of RDMFT the most successful approximations and extensions, we assess present-day functionals on applications to molecular and periodic systems and we discuss the challenges and future prospect | Nektarios N. Lathiotakis | 21 Oct 2016 | |

12 | Quantum Marginal Problem and Generalized Pauli Constraints | I will give an introduction to the univariate quantum marginal problem using an elementary mathematical point of view. In particular, I will explain how extremality of the local spectrum carries structural information about the global wave function. | David Gross | 21 Oct 2016 | |

13 | Two-electron Reduced Density Matrices in Quantum Chemistry and Physics | Strongly correlated quantum systems are not easily described with conventional quantum chemistry formalism because the number of non-negligible configurations grows exponen- tially with the number of orbitals actively participating in the correlation. | David A. Mazziotti | 11 Oct 2016 | |

14 | Entanglement Spectroscopy and its application to the fractional quantum Hall phases | In this talk, we will give an overview of the entanglement spectroscopy with a focus on to the fractional quantum Hall phases. | Nicolas Regnault | 11 Oct 2016 | |

15 | Why should anyone care about computing with anyons? | In this talk Jiannis Pachos discusses a variety of different topics starting from characterizing knot invariants, their quantum simulation with exotic particles called anyons and finally the possible realization of anyons in the laboratory. | Jiannis Pachos | 11 Oct 2016 | |

16 | Quantum Geometry, Exclusion Statistics, and the Geometry of "Flux Attachment" in 2D Landau levels | Duncan Haldane talks about Quantum Geometry, Exclusion Statistics, and the Geometry of "Flux Attachment" in 2D Landau levels. | Duncan Haldane | 11 Oct 2016 | |

17 | Exchange symmetry and anyon virial coefficients | This talk mentions some aspects of the theory of identical particles, for example, treating neutrons and protons as identical particles distinguished by a quantum number called isotopic spin. | Jan Myrheim | 11 Oct 2016 | |

18 | Exchange statistics - Basic concepts | In this talk Jon Magne Leinaas from University of Oslo reviews some of the basic ideas and questions related to the exchange symmetry of identical particles. | Jon Magne Leinaas | 11 Oct 2016 |