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Dr Marcin Szyniszewski

Research student

Research overview

Analytical and numerical solutions for many-body quantum systems. Dynamics of systems out of equilibrium. Quantum phase transitions. Investigating the massless and massive Schwinger model using various approaches.

Thesis Title

Non-equilibrium dynamics of many-body quantum systems

Thesis Outline

The purpose of this project is to investigate the time evolution of integrable and non-integrable many-body quantum systems driven out of equilibrium. We will start with a simplest yet highly non-trivial realization of such systems: dynamics of a single impurity injected into a superfluid, which is relevant to both recent experiments with ultracold quantum gases [1, 2] and more established field of study of properties of 3He impurities in 4He superfluids. Despite a long history, the dynamics of a single impurity interacting with the background superfluid is not completely understood, especially the transition from subsonic to supersonic regime [3, 5].

In a special case of an integrable dynamics in one spatial dimension, normally exact solution exists [4]. Still, extracting the physical predictions from this solution is on-trivial and has not been entirely successful so far. We will start by extending the techniques of [4, 3] and coupling them with contemporary numerical techniques in order to construct a computational methodology capable of producing experimentally testable results or both subsonic and supersonic impurities.

We will then move on to investigating the role of integrability — which is of paramount importance for synergy between experiment and theory: while most theoretical methods only work in an integrable case, real-world experiments are made in the non-integrable regime (one of the requirements for integrability is that the mass of an impurity equals that of the host particles, which does holds or neither 3He contaminants in 4He nor 87Rb/41K mixtures typically used in present-day ultracold gas experiments).

During the work on this project, a student will master the aspects of theory of integrable systems and many-body techniques, statistical mechanics of low-dimensional systems, and state-of-the- art high-performance computing including Monte Carlo simulations and parallel programming techniques using Lancaster High-End Computing facilities.

Under the supervision of E Burovski, a student will employ analytical and numerical techniques for studying the dynamics of impurities in low-dimensional strongly correlated systems. Results will then be used for interpreting results of experiments made in Cambridge, Innsbruck and elsewhere.


  1. C. Zipkes, S. Palzer, C. Sias, M. Köhl, Nature 464, 388 (2010); C. Zipkes, L. Ratschbacher, C. Sias, M. Köhl, New J. Phys. 13, 053020 (2011).
  2. J. Catani et al. Phys. Rev. A 85, 023623 (2012)
  3. Charles J. M. Mathy, Mikhail B. Zvonarev, and Eugene Demler, Nature Physics (2012), published online 21 Oct 2012.
  4. H. Castella and X. Zotos Phys, Rev. B 47, 47 (1993).
  5. Michael Schecter, Alex Kamenev, Dimitri Gangardt, Austen Lamacraft, Phys. Rev. Lett. 108, 207001 (2012).

Research Grants

Marcin Szyniszewski is funded by EPSRC NoWNano DTC grant number EP/G03737X/1.

His participation in SCES2014 conference is possible due to Graduate School Travel Grant.

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