First AGM Meeting 2019

First AGM Meeting 2019 on Geometric Quantum Mechanics

25 April 2019, University of Surrey, Mathematics Department, Room 22AA04

This one-day meeting will cover various disciplines related to geometric quantum mechanics.

Timetable:

10:00--10:40 Michael Foskett (University of Surrey)

10:40--11:10 Coffee break (in room 40AA04)

11:10--12:00 Simon Salamon (Kings College London)

12:00--12:50 Gary Gibbons (Cambridge University)

12:50--14:20 Lunch at Hillside cafeteria

14:20--15:10 Vladimir Kisil (University of Leeds)

15:10--16:00 Benjamin Doyon (Kings College London)

16:00--16:30 Coffee break (in room 40AA04)

16:30--17:20 Eva-Maria Graefe (Imperial College London)

Since many people will be returning to London after the workshop, there is no formal dinner. But informal dinner plans in Guildford will be arranged on the day of the workshop, for those who wish to stick around.

Titles and Abstracts

Michael Foskett

Geometry of nonadiabatic quantum hydrodynamics

Ever since Born and Oppenheimer’s celebrated paper in 1927 the interplay of electronic and nuclear dynamics has been an active area of study in quantum chemistry. Motivated by the current interests in capturing and modelling nonadiabatic effects, we consider the geometric perspective of quantum hydrodynamics (QHD) and apply this to the so-called 'exact factorization’ of the molecular wavefunction. In this talk I will first present a classical closure of QHD in terms of density operators before considering a generalised exact factorisation model in this setting. Performing a regularisation procedure then allows for momentum map singular solutions which reduces the problem to a finite-dimensional canonical Hamiltonian system, thus lifting the 'curse of dimensions' faced in many-body problems.

Simon Salamon

The SIC-POVM problem and moment maps

The SIC-POVM problem can be interpreted as the quest for a regular simplex in the Lie algebra su(d) whose d^2 vertices lie on complex projective space as an adjoint orbit. Moment maps defined by the action of maximal tori T^(d-1) are of special relevance in describing solutions consisting of Heisenberg orbits. We shall illustrate this theory with examples.

Gary Gibbons

The geometric quantum mechanics of ghosts

I will explore some aspects of the the geometry of the space of rays of theories in which some states have negative norm squared. In particular I will discuss some connections with Anti-de-Sitter space times and some possible connections with holography and the future tube of Minkowski space times.

Vladimir Kisil

Geometrisation of quantum mechanics and non-commutivisation of classical theory

From earliest days quantum mechanics was developed as a conceptual counterpart of classical theory. Yet, both descriptions have some notable distinctions:

1) Evolution of a classical system is given by a time flow of the phase space. In quantum mechanics such geometrisation is straightforward for a harmonic oscillator in the Fock representation only.

2) According to Dirac quantum mechanics emerges from classical theory if commuting observables are replacing by non-commuting ones. A non-zero Planck constant reflects the measure of such non-commutativity between the coordinate and momentum observables.

In this talk we discuss how these distinctions are melting if both quantum and classical mechanics are developed from common symmetries.

Benjamin Doyon

A geometric picture of (generalised) thermalisation

The geometry of states of thermodynamically large quantum systems is particularly difficult to analyse. Yet taking thermodynamically large systems is essential in order to understand the problem of thermalisation and irreversibility from a microscopic, unitary-evolution perspective. Recently, it was observed that the usual thermalisation expected to emerge after long-time evolution, is broken in integrable models by the presence of infinitely many local conserved quantities, and one obtains so-called generalised Gibbs ensembles. This has brought to the fore the importance of the concept of local charges in non-equilibrium dynamics. Based on this concept, I will provide a geometric characterisation of an infinite-dimensional family of states, which include Kubo-Martin-Schwinger states associated with short-range Hamiltonians, and explain a (generalised) thermalisation theorem which applies to integrable and non-integrable models. This gives some steps towards an understanding of many-body states and dynamics via an infinite-dimensional Riemannian geometry.

Eva-Maria Graefe

Dynamics of Gaussian states in open quantum systems in the semiclassical limit

The time evolution of the Wigner function for Gaussian states generated by non-Hermitian Schrödinger as well as Lindblad equations is investigated in the semiclassical limit of small h-bar. This yields a generalisation of the Ehrenfest theorem for the dynamics of observable expectation values. In addition to this, the Gaussian approximation yields dynamical equations for the covariances. New types of phase-space dynamics are obtained and illustrated in several examples.

Directions to Campus

At Guildford rail station, take the University exit (not the town centre exit) and turn right as soon as you get out. Then, take the second right (the first is a cul-de-sac). Walk by the parking lot until you enter campus. Keep going along the same road, which continues to the left, next to a big pond. At the end of this stretch is the Thomas Telford (AA) building, and the Mathematics Department is on the fourth floor.

The AA building is labelled Academic Building 1 on this campus map (in square D4).

You can view the entire route from the station on Google Maps here.

If you'd prefer not to walk, there is a bus stop across the road from the station University exit. Bus 1 goes to campus every 10 minutes. The nearest bus stop to the Thomas Telford building is Senate Square.

Travel Expenses

Travel expenses can be reimbursed by completing a Visitor's Expense Claim Form. You can either submit this on the day, or mail it afterwards to Paul Skerritt, Mathematics Department, University of Surrey, GU2 7XH. Please remember to include receipts. For train tickets, an email receipt or original train ticket/receipt is good. Scans of original tickets are usually not enough for our finance department, unfortunately.

Contact:

Paul Skerritt (Surrey)