Quantum Marginal Problem and Generalized Pauli Constraints

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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.

The talk will also give some quantum information background, touching e.g. on the computational complexity of general quantum marginal problems and relations to entanglement.

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Oxford Physics Academic Lectures

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Department: Department of Physics

Date Added: 11/10/2016

Duration: 00:59:02

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Two-electron Reduced Density Matrices in Quantum Chemistry and Physics

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Oxford Physics Academic Lectures

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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.

In this lecture we will introduce the concept of reduced density matrices for systems of identical fermions and comment on their relevance to problems in quantum chemistry and physics, especially the description of strongly correlated quantum systems. We will discuss Coulsons challenge in which Coulson highlighted the potential advantages of a direct calculation of the two-electron reduced density matrix without the many-electron wave function and cautioned against the difficulty of ensuring that the two-electron reduced density matrix represents an N-electron quantum system, known as the N-representability problem. We will present recent advances for the direct calculation of the two-electron reduced density matrix including the implementation of N-representability conditions by semidefinite programming. Two-electron reduced density matrix (2-RDM) methods can accurately approximate strong electron correlation in molecules and materials at a computational cost that grows non-exponentially with system size [5]. In an application we will treat a quantum chemical system with sextillion (1021) quantum degrees of freedom to reveal the important role of quantum entanglement in its oxidation and reduction.

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Oxford Physics Academic Lectures

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Department: Department of Physics

Date Added: 11/10/2016

Duration: 00:59:10

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Entanglement Spectroscopy and its application to the fractional quantum Hall phases

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Oxford Physics Academic Lectures

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In this talk, we will give an overview of the entanglement spectroscopy with a focus on to the fractional quantum Hall phases.

We will show how much information is encoded within the ground state and how different partitions probe different types of excitations. The entanglement spectroscopy, initially introduced by Li and Haldane in the context of the fractional quantum Hall effects, has stimulated an extensive range of studies. The entanglement spectrum is the spectrum of the reduced density matrix, when we partition the system into two. For many quantum systems, it unveils a unique feature: Computed from the bulk ground state wave function, the entanglement spectrum give access to the physics of edge excitations.

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Oxford Physics Academic Lectures

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Department: Department of Physics

Date Added: 11/10/2016

Duration: 00:51:32

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Why should anyone care about computing with anyons?

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Oxford Physics Academic Lectures

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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.

Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding field of research focused on the exploration of quantum evolutions that are resilient to errors.

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Oxford Physics Academic Lectures

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Department: Department of Physics

Date Added: 11/10/2016

Duration: 00:55:12

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Quantum Geometry, Exclusion Statistics, and the Geometry of "Flux Attachment" in 2D Landau levels

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Oxford Physics Academic Lectures

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

The degenerate partially-filled 2D Landau level is a remarkable environment in which kinetic energy is replaced by "quantum geometry" (or an uncertainty principle) that quantises the space occupied by the electrons quite differently from the atomic-scale quantisation by a periodic arrangement of atoms. In this arena, when the short-range part of the Coulomb interaction dominates, it can lead to "flux attachment", where a particle (or cluster of particles) exclusively occupies a quantised region of space. This principle underlies both the incompressible fractional quantum Hall fluids an the composite fermion Fermi liquid states that occur in such systems.

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Oxford Physics Academic Lectures

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Department: Department of Physics

Date Added: 11/10/2016

Duration: 01:16:53

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Exchange symmetry and anyon virial coefficients

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Oxford Physics Academic Lectures

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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.

He will also review studies of systems of three or more anyons. In particular, the virial expansion shows that the free anyon gas approximates exclusion statistics, with a correspondence between the anyon parameter and the exclusion parameter which is different from the case of anyons in a magnetic field, discussed in the talk by Jon Magne Leinaas.

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Oxford Physics Academic Lectures

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Department: Department of Physics

Date Added: 11/10/2016

Duration: 01:07:27

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Exchange statistics - Basic concepts

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Oxford Physics Academic Lectures

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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.

This talks begins with discussing the braid description of particle exchange and some of the interesting question this raises with respect to geometry and topology. A particularly interesting question is whether the geometric understanding of particle exchange means that the spin-statistics theorem can be given a purely geometric formulation. Even if that so far has not been done, the correct relation between spin and statistics seems in some ways natural from the geometric point of view, as he will discuss. In the last part he will focus on the dynamics of systems of anyons in condensed matter systems, where the physical space has the character of a phase space rather than a configuration space. A semi-classical description is discussed, where the anyon parameter is coupled to an exclusion effect, which in the quantum description is known as exclusion statistics.

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Oxford Physics Academic Lectures

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Department: Department of Physics

Date Added: 11/10/2016

Duration: 01:18:26

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Local communities: first and last providers of protection (Forced Migration Review 53)

It is often people’s immediate community that provides the first, last and perhaps best tactical response for many people affected by or under threat of displacement. In the 23 feature theme articles in this issue of FMR, authors from around the world – including authors who are themselves displaced – explore the capacity of communities to organise themselves before, during and after displacement in ways that help protect the community. See more at http://www.fmreview.org/community-protection.html.

CNS remyelination: from mechanisms to medicines

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Nuffield Department of Clinical Neurosciences

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NDCN Departmental Seminar

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Nuffield Department of Clinical Neurosciences

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Robin Franklin

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neuroscience

Department: Nuffield Department of Clinical Neurosciences

Date Added: 07/10/2016

Duration: 00:48:07

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Dark Matter(s) Discussion

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The Physics of Fine-Tuning

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Celine Boehm, Rocky Kolb, and Justin Read discuss fine-tuning in dark matter models, how we judge astrophysical parameters to be fine-tuned, how we get evidence for dark matter, supersymmetry, and our prospects for finding the dark matter particle.

This discussion was conducted at the Dennis Sciama Theatre at the Denys Wilkinson Building, Oxford, on September 8, 2016.