Mathematical Physics and Applied Mathematics Group

The Mathematical Physics and Applied Mathematics (MPAM) group is engaged in the development of innovative analytical methods for a broad range of problems arising from engineering and physical sciences. A particular specialism is the study of complex quantum systems, including quantum chaos, random matrix theory, quantum information and computing as well as research on related fundamental questions in geometry and mathematical physics.

Contributions in the unit include the development of non-perturbative techniques for open wave chaotic systems, quantum computing and entanglement, modelling and statistical analysis of complex networks, and geometry of (higher dimensional) algebraic varieties. Another strength of the group is in the study of wave phenomena in acoustic and elastic media. Relevant contributions include the modelling of wave impacts on coastal structures, acoustic scattering in waveguides and the asymptotic theory of thin elastic structures. Research on optimal forms of bridges and structures is also a prominent direction of the group.

Specific research expertise

Random matrix theory and its applications (D. Savin, I. Smolyarenko)
Resonances and transport in open wave chaotic systems (D. Savin)
Quantum information and quantum computing (S. Virmani)
Algebraic geometry, birational geometry (A.-S. Kaloghiros)
Complex networks (G. Rodgers, I. Smolyarenko)
Statistical mechanics of complex systems and econophysics (G. Rodgers)
Waves in solids and fluids (M. Greenhow, J. Lawrie, E. Nolde, A. Pichugin)
Structural acoustics and diffraction theory (M. Greenhow, J. Lawrie)
Asymptotic theory of thin elastic structures (E. Nolde , A. Pichugin)
Layout optimization of structures (A. Pichugin)

For more detailed descriptions of research and list of individual publications, please follow the links to the web pages of individual group members.

PhD applications are welcome in all our research areas. Apply here.

Major external collaborators

Prof Gernot Akemann, Bielefeld University, Germany
Prof Alessio Corti, Imperial College London, UK
Prof Ivan Cheltsov, University of Edinburgh, UK
Prof Yan Fyodorov, KCL & Landau Institute for Theoretical Physics, Chernogolovka, Russia
Prof Julius Kaplunov, Keele University, UK
Prof Olivier Legrand, Université Côte d'Azur, Nice, France
Prof Martin Plenio, University of Ulm, Germany
Prof Ernst Wit, Università della Svizzera Italiana, Lugano, Switzerland

Externally funded projects

Calabi-Yau Pairs and Mirror Symmetry for Fano Varieties (EPSRC, 2017-2019, A.-S. Kaloghiros)
Closing the gap on the third way of computation (EPSRC, 2013-2015, S. Virmani)

Conferences

LMS Conference grants to organise Random matrix theory workshops (2014, 2016, 2018, D. Savin)
MPAM group runs the annual series of 明星八卦-Bielefeld Workshops on Random Matrix Theory and Applications, which is hosted on a rotation basis between 明星八卦 and Bielefeld University (Germany) and is the major international forum in this field.

Dr Anne-Sophie Kaloghiros

Reader in Maths /Ops

Co-director, Centre for Mathematical and Statistical modelling Algebraic geometry, Birational geometry

Professor Jane Lawrie

Professor & Deputy Dean - Academic Affairs

Structural acoustics, diffraction theory

Dr Evgeniya Nolde

Senior Lecturer

Elastic wave propagation; asymptotic models for thin structures; fluid-structure interaction.

Dr Dmitry Savin

Senior Lecturer

Dmitry is a senior lecturer in the Department of Mathematics. His research interests span applied mathematics and mathematical physics, focusing in particular on applications of random matrix theory to scattering and transport in complex quantum or wave systems. He uses statistical methods and analytical techniques to quantify chaotic behaviour in nature. Dmitry also enjoys teaching both applied and abstract subjects, reflecting on their existing and emerging connections to real world examples. Random matrix theory and its applications. Chaotic resonance scattering - quantum / wave chaos in open systems. Interference effects and collective excitations in complex systems. Applied mathematics and mathematical physics; RMT.

Dr Igor Smolyarenko

Senior Lecturer

Random matrix theory and its applications in quantum chaos, statistical mechanics and number theory; wave propagation in disordered media and mesoscopic systems.

i am a theoretical physicist working in the theory of quantum information and computation. my research to date has covered aspects of entanglement theory, architectures for quantum computing, quantum channel capacities, classical simulation of quantum systems, and the construction of local hidden variable models. for more details on my research, please see my research tab. my research concerns quantum information theory and all things related to the complexity of quantum systems. preprints to all my publications can be found on the quant-ph arxiv (here) or on brunel's research archives. here are short summaries of my research work, loosely organised into various themes: entanglement theory and entanglement measures i started out my scientific career as a graduate student at imperial college under the supervision of martin plenio (now at ulm) and peter knight, working on entanglement theory. results include statements about the relative ordering of entanglement measures, bounds on the relative entropy of entanglement, and computation of an asymptotic entanglement measure (a paper for which most credit goes to coauthor koenraad audenaert for his quite heroic contribution). since my phd i have often revisited the topic of entanglement measures with the fortunate assistance of many insightful coauthors, e.g. here and here. quantum computation with triplet/singlet measurements in a collaboration with terry rudolph that seems to become active with approximately the same period as a typical species of cicada, i established the "stpbqp" conjecture of michael freedman, matt hastings, and modjtaba shokrian-zini. we did this by building upon the insights of their paper which proposed and evidenced the conjecture, and our own other work on a related question from many years ago. the published proof of the conjecture is available at this link. loosely speaking, the work demonstrates that using only measurements of two qubit total angular momentum, one can perform quantum computation given almost any initial state that is not completely symmetric. this brings natural robustness to a certain form of error, and has interesting fundamental connections to the study of quantum reference frames. it is also perhaps surprising that quantum computation is possible with a single combined dynamical/measurement operation of such a simple and physically natural form, in a way that is almost completely agnostic about the initialisation of the qubits. locc discrimination of quantum states i had an early interest in the locc discrimination of quantum states (loosely speaking - how to distinguish quantum states of many quantum subsystems when you can only measure the subsystems in a distributed way). in collaboration with various colleagues i showed that two pure states can be optimally discriminated even in the locc setting, and obtained bounds on when discrimination is possible given more states, and obtained optimal locc protocols in some settings with high symmetry. correlated error quantum information i was introduced to this topic while i was a postdoc with chiara macchiavello at pavia. we investigated the effect of correlations on the information carrying capacity of two correlated quantum channels. motivated by some intriguing non-analyticity in that example, together with martin plenio i developed connections between correlated error quantum channel capacities and many-body physics, see here and here for details. classical simulation of quantum systems motivated by the ever increasing buzz concerning quantum computing, i became interested in how well classical computers can efficiently simulate quantum systems. together with various coauthors i've developed bounds (e.g. here and here) on the noise that quantum computers can tolerate before losing their advantage over classical computers. in more recent work have shown how ideas from the foundations of physics can be used to develop efficient simulations of some complex quantum systems, even without noise. perhaps the most surprising example of this arises in certain pure entangled modifications of cluster state quantum computing, which we have shown can be efficiently simulated classically (see also here for more explicit examples). some of this work was supported by an epsrc "bright ideas" grant and an epsrc dtp.

Dr Shash Virmani

Senior Lecturer

I am a theoretical physicist working in the theory of quantum information and computation. My research to date has covered aspects of entanglement theory, architectures for quantum computing, quantum channel capacities, classical simulation of quantum systems, and the construction of local hidden variable models. For more details on my research, please see my research tab. My research concerns quantum information theory and all things related to the complexity of quantum systems. Preprints to all my publications can be found on the quant-ph arXiv (here) or on 明星八卦's research archives. Here are short summaries of my research work, loosely organised into various themes: Entanglement theory and entanglement measures I started out my scientific career as a graduate student at Imperial College under the supervision of Martin Plenio (now at Ulm) and Peter Knight, working on entanglement theory. Results include statements about the relative ordering of entanglement measures, bounds on the relative entropy of entanglement, and computation of an asymptotic entanglement measure (a paper for which most credit goes to coauthor Koenraad Audenaert for his quite heroic contribution). Since my PhD I have often revisited the topic of entanglement measures with the fortunate assistance of many insightful coauthors, e.g. here and here. Quantum Computation with Triplet/Singlet measurements In a collaboration with Terry Rudolph that seems to become active with approximately the same period as a typical species of cicada, I established the "STPBQP" conjecture of Michael Freedman, Matt Hastings, and Modjtaba Shokrian-Zini. We did this by building upon the insights of their paper which proposed and evidenced the conjecture, and our own other work on a related question from many years ago. The published proof of the conjecture is available at this link. Loosely speaking, the work demonstrates that using only measurements of two qubit total angular momentum, one can perform quantum computation given almost any initial state that is not completely symmetric. This brings natural robustness to a certain form of error, and has interesting fundamental connections to the study of quantum reference frames. It is also perhaps surprising that quantum computation is possible with a single combined dynamical/measurement operation of such a simple and physically natural form, in a way that is almost completely agnostic about the initialisation of the qubits. LOCC discrimination of quantum states I had an early interest in the LOCC discrimination of quantum states (loosely speaking - how to distinguish quantum states of many quantum subsystems when you can only measure the subsystems in a distributed way). In collaboration with various colleagues I showed that two pure states can be optimally discriminated even in the LOCC setting, and obtained bounds on when discrimination is possible given more states, and obtained optimal LOCC protocols in some settings with high symmetry. Correlated error quantum information I was introduced to this topic while I was a postdoc with Chiara Macchiavello at Pavia. We investigated the effect of correlations on the information carrying capacity of two correlated quantum channels. Motivated by some intriguing non-analyticity in that example, together with Martin Plenio I developed connections between correlated error quantum channel capacities and many-body physics, see here and here for details. Classical simulation of quantum systems Motivated by the ever increasing buzz concerning quantum computing, I became interested in how well classical computers can efficiently simulate quantum systems. Together with various coauthors I've developed bounds (e.g. here and here) on the noise that quantum computers can tolerate before losing their advantage over classical computers. In more recent work have shown how ideas from the foundations of physics can be used to develop efficient simulations of some complex quantum systems, even without noise. Perhaps the most surprising example of this arises in certain pure entangled modifications of cluster state quantum computing, which we have shown can be efficiently simulated classically (see also here for more explicit examples). Some of this work was supported by an EPSRC "Bright Ideas" grant and an EPSRC DTP.