## Final Report Summary - NEDFOQ (Non-equilibrium dynamics of quantum fluids in one dimension)

Perhaps, the best way to introduce someone to the fascinating the world of non-equilibrium quantum dynamics in one dimension (1D) is by means of a simple example. Imagine a tiny particle suspended in a glass of water. Given some initial velocity such a particle will soon be stopped by viscous friction -- a fact that for centuries prevented humans from discovering inertia. If, however, a particle were to move in a glass of superfluid 4He it would have travelled an enormous distance without any hindrance. In contrast, in cryogenic Fermi liquid 3He a particle would experience strong friction obeying, though, a different force-velocity law than in water. Obviously, studying the motion of a particle is a fun way to discriminate different types of fluid environment.

Now, imagine a particle inserted into an extremely narrow channel containing a one-dimensional quantum fluid.Will it be stopped by viscous forces will it move on forever? The answer to this innocent question, as well as to many other similar questions, turns out to be surprisingly complex.

The reason is, absolutely everything in a 1D space is not the way it is in higher dimensions.

For example, a 1D space is the only Cartesian space where a sphere consists of two disconnected pieces (points). It can be shown, that for this reason one-dimensional superfluid cannot exist. Nor can there exist 1D shear viscosity. Understanding one-dimensional fluids requires alternative tools and approaches. In search for those one encounters beautiful mathematics connecting to such fields as random matrix theory, conformal field theory and classical and quantum integrability.

It was the purpose of put such mathematical concepts to practical use by addressing "simple" questions motivated by experiment. The main results obtained within the project include the theory of motion of mobile probe in a one-dimensional degenerate quantum fluid, the mathematical description of the decay of solitary waves in out-of equilibrium condensates with suddenly quenched parameters, a theory of mesoscopic conductance fluctuations in one-dimensional helical metals and the description of non-equilibrium current noise in chiral Luttinger liquids. Theoretical analysis of experimentally relevant questions is not a one-way process. Within this project practical questions drove purely mathematical research generating new results in, e.g. the theory of Painleve transcendents as well as touching upon fundamental issues in quantum statistical mechanics such as the adiabatic theorem and typicality hypothesis.

We do, however, remember that it is observable physics that we are interested in.

So, going back to the original "simple" question will a moving particle be stopped by a one-dimensional quantum fluid? Kinetic theory developed within this project can, in particular, answer this question. And, the answer is "No." Contrary to intuition, the particle will move perpetually, however the steady-state velocity may depend on the initial velocity in a non-trivial way and even have the opposite sign.

Now, imagine a particle inserted into an extremely narrow channel containing a one-dimensional quantum fluid.Will it be stopped by viscous forces will it move on forever? The answer to this innocent question, as well as to many other similar questions, turns out to be surprisingly complex.

The reason is, absolutely everything in a 1D space is not the way it is in higher dimensions.

For example, a 1D space is the only Cartesian space where a sphere consists of two disconnected pieces (points). It can be shown, that for this reason one-dimensional superfluid cannot exist. Nor can there exist 1D shear viscosity. Understanding one-dimensional fluids requires alternative tools and approaches. In search for those one encounters beautiful mathematics connecting to such fields as random matrix theory, conformal field theory and classical and quantum integrability.

It was the purpose of put such mathematical concepts to practical use by addressing "simple" questions motivated by experiment. The main results obtained within the project include the theory of motion of mobile probe in a one-dimensional degenerate quantum fluid, the mathematical description of the decay of solitary waves in out-of equilibrium condensates with suddenly quenched parameters, a theory of mesoscopic conductance fluctuations in one-dimensional helical metals and the description of non-equilibrium current noise in chiral Luttinger liquids. Theoretical analysis of experimentally relevant questions is not a one-way process. Within this project practical questions drove purely mathematical research generating new results in, e.g. the theory of Painleve transcendents as well as touching upon fundamental issues in quantum statistical mechanics such as the adiabatic theorem and typicality hypothesis.

We do, however, remember that it is observable physics that we are interested in.

So, going back to the original "simple" question will a moving particle be stopped by a one-dimensional quantum fluid? Kinetic theory developed within this project can, in particular, answer this question. And, the answer is "No." Contrary to intuition, the particle will move perpetually, however the steady-state velocity may depend on the initial velocity in a non-trivial way and even have the opposite sign.