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

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.

# Episode Title Description People Date
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