Dynamical properties of one dimensional strongly correlated many-particle systems

Lead Research Organisation: University of Oxford
Department Name: Oxford Physics

Abstract

At present two lines of work are envisaged. The first programme is concerned with non-equilibrium dynamics in open many-particle quantum systems. These can be conveniently described by so-called Lindblad equations. A general problem is that LE are difficult to analyse by either numerical or analytical means. It has been recently demonstrated that in particular examples Lindblad equations can be mapped onto non-hermitian integrable models. This opens up the possibility to bring integrable model techniques to bear on such problems and establish exactly solved paradigms of open interacting many-particle quantum systems. This project is squarely in the EPSRC grand challenge area "Emergence and Physics Far From Equilibrium". In the first part of the project exact results for the time evolution of two and four point functions will be obtained for the previously studied example imaginary-U Hubbard model. In the second part of the project other Lindblad equations will be analyzed with the objective of mapping them to non-herminitian integrable Hamiltonians, that have non-trivial steady states.
The second line of work is concerned with the theoretical modelling of inelastic neutron scattering experiments on the quasi-one dimensional quantum magnet SrCo2V2O8, which has been recently shown to exhibit confinement of topological excitations into meson-like bound states. An open problem are the effects of the weak three-dimensional couplings. Forthcoming experiments will measure the dispersion relations perpendicular to the chain direction, which will make it possible to determine the functional form of the interchain couplings. Once this has been achieved, the interchain coupling effects can be analyzed by combining existing results with a matrix random phase approximation. The result of such a theoretical analysis can then be compared to available inelastic neutron scattering data.

Publications

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Ziolkowska Aleksandra A. (2019) Yang-Baxter integrable Lindblad equations in arXiv e-prints

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509711/1 01/10/2016 30/09/2021
1947733 Studentship EP/N509711/1 01/10/2017 31/03/2021 Aleksandra Agnieszka Ziolkowska
 
Description In this research project we have concentrated on discovering the properties of open quantum systems, meaning the systems which are dissipatively coupled to their environment. They can be found in the atomic and molecular physics, circuit QED and optomechanical systems. Despite their relevance, the mathematical methods used to approach them are far less developed than for the closed systems. Our research aimed at finding a way to study Markovian open quantum systems, which are a special subset of this broader problem. We have succeeded in finding a method, through which we can analytically find exact information about a large group of such models. We have also identified the cases in which alternative methods have to be developed. We have developed a systematic way in which one can establish a connection between an open system, either bosonic or fermionic, and an integrable Hamiltonian model. The latter are a widely studied class of models with particular properties, which allow us to calculate a lot of their features analytically. In this way we have opened an entire new avenue of exploration of open systems and on the other hand expanded the applicability of integrability methods to another field.

Through this project I had an opportunity to get involved in a wider community of physicists in the field of integrability. I have been one of the main organisers of now an annual event "Student Workshop on Integrability", which takes place at a different European institution every year. The workshop is an opportunity to discuss the research outcomes with other early career academics in the field and fosters international collaborations.
Exploitation Route Open quantum systems appear in a plethora of contexts such as atomic and molecular physics and mesoscopic physics. Their properties introduce unwanted decoherence in quantum information processing, but can be utilised in quantum computing, quantum simulations, entanglement generation and state preparation. Understanding the physical principles underlying open quantum systems is a crucial step in the advancement of these fields and aids the design of new technologies. With our results we have contributed towards this understanding in highly non-trivial cases of many-body, interacting models.
Sectors Other

 
Description Conference for Undergraduate Women in Physics (CUWiP) UK 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Undergraduate students
Results and Impact Around 100 undergraduate female physics students have participated in Conference for Undergraduate Women in Physics (CUWiP) UK. Apart from being a part of the organising committee of the event, I have participated in a panel discussion during which I have explained the students my research and described the life of a PhD student. Many undergraduate students have told me, that they felt inspired to pursue physics thanks to seeing me on the panel.
Year(s) Of Engagement Activity 2019
URL http://www.physics.ox.ac.uk/confs/cuwip2019
 
Description Science Polish Perspectives - Outreach Talk 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Around 200 participants attended the popular science talk I delivered on quantum technologies. After the talk there were many questions from the audience members, both with and without a scientific background. I have been privately contacted with further questions from Polish policy makers who wanted to consult my opinion on scientific matters. As a result, I have been invited to participate in scientific and policy making related events at the Polish Embassy in the UK, where I contributed my opinions to the discussions.
Year(s) Of Engagement Activity 2018
URL https://poloniumfoundation.org/sppoxford2018
 
Description St. John's College Oxford - Lecture Supper 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact I have been invited to give a talk about my research at St. John's College, University of Oxford. Around 30 academics and research students from various fields attended the talk. I have received many follow up questions and a few comments, that the audience members found my reasoning to be a particularly accessible explanation of quantum phenomena.
Year(s) Of Engagement Activity 2019