Physics at different scales
• My main research focus is on the macroscopic fluctuation theory. The recently developed macroscopic fluctuation theory deals with diffusive processes driven out of equilibrium. In equilibrium, the probability of obtaining a certain state is given by the Boltzmann distribution, irrespective of the system's dynamics. When a system is driven out of equilibrium, it cannot be described in general by the Boltzmann distribution as the dynamics of the system plays a major role. I am interested in finding universal properties of out of equilibrium systems. One example of such a universality is discussed in Europhys. Lett. 2013, where we have shown that the integrated current probability density of a system coupled to two reservoirs (e.g. heat or particle reservoirs) is independent of the geometry of the system. Another example is described in the next bullet.
• The macroscopic fluctuation theory was developed to account for out-of-equilibrium fluctuations in classical statistical mechanics models. However, we have found that it also allows to fully describe transport properties of mesoscopic systems such as coherent light in disordered medium and electron transport in a wire. This description is both surprising and appealing. Mesoscopic transport models are typically quantum mechanical problems as the system is held at zero temperature, and Aharonov Bohm effects are present. However, it turns out that one can capture the quantum mechanical nature of the problem by a coarse grained classical theory, namely the macroscopic fluctuation theory. The correspondence between the macroscopic fluctuations theory and such mesoscopic processes allows to borrow ideas and results from one to supplement the other. One especially interesting result is the Gallavotti-Cohen relation, which generalizes the Einstein relation and fluctuation-dissipation theorem for systems completely out of equilibrium. The Gallavotti-Cohen relation was only glimpsed for a certain mesoscopic system, with no deep understanding of the origin of this relation.
• Open quantum systems can be described by stochastic tools due to the probabilistic nature of measurements in quantum mechanics. Recently, there has been significant progress in the experimental realization and stabilization of quantum systems. Together with the understanding that many mesoscopic systems can be described by stochastic equations, I find ample motivation to work in this fast evolving field. Using a quantum Langevin equation is one of the promising leads to describe simple open quantum systems with quantum dissipation. Currently, I am interested in how the equivalent of Fick's law becomes manifest in diffusive open quantum systems and what are the possible corrections at finite time and finite system size.
• Thermal and athermal uncertainty relations: The thermodynamic uncertainty relation is a recent result characterising a transport efficiency for thermal transport systems. An interesting question is whether other stochastic systems have the equivalent of a transport efficiency. Coherent light propagating through a disordered medium indeed has such a transport efficiency [in preparation]. We use statistical mechanics methods to describe this stochastic, but athermal system and provide the mesoscopic physics equivalent of the thermodynamic uncertainty bound. Exploring this transport efficiency can lead to an optimal control theory of mesoscopic devices.
• Energy forms is a mathematical tool. It is a natural way to study dynamical properties of random walkers in a fractal geometry. Moreover, I have found that Energy forms describes also open stochastic systems, via a similarity to the macroscopic fluctuation theory description. This mapping, allows describe open systems, using potential theory. Among the benefits of this method we find, Kirchhoff rules for stochastic processes on graphs and the use of Green functions to understand out-of-equilibrium fluctuations. In fractals, random walkers usually exhibit anomalous diffusion. Therefore, Energy forms should be a useful tool to try and explore interacting systems known to display such anomalous diffusion.
• Directed polymers in a random media : In recent years, new methods were developed in order to manipulate single vortices in type II superconductors by means of magnetic force microscopy (MFM). The vortex moves in a series of jumps when it is dragged using the magnetic tip of the MFM. Theoretically, it is possible to relate the physics of vortices in type II superconductors (within Ginzburg Landau theory) to the theory of polymers in random media. We find that, as suggested by theory, the jump-size distribution does not depend on the applied force and is consistent with power-law behavior. The measured exponent of the power law is found to be much larger than widely accepted theoretical calculations.
• The macroscopic fluctuation theory was developed to account for out-of-equilibrium fluctuations in classical statistical mechanics models. However, we have found that it also allows to fully describe transport properties of mesoscopic systems such as coherent light in disordered medium and electron transport in a wire. This description is both surprising and appealing. Mesoscopic transport models are typically quantum mechanical problems as the system is held at zero temperature, and Aharonov Bohm effects are present. However, it turns out that one can capture the quantum mechanical nature of the problem by a coarse grained classical theory, namely the macroscopic fluctuation theory. The correspondence between the macroscopic fluctuations theory and such mesoscopic processes allows to borrow ideas and results from one to supplement the other. One especially interesting result is the Gallavotti-Cohen relation, which generalizes the Einstein relation and fluctuation-dissipation theorem for systems completely out of equilibrium. The Gallavotti-Cohen relation was only glimpsed for a certain mesoscopic system, with no deep understanding of the origin of this relation.
• Open quantum systems can be described by stochastic tools due to the probabilistic nature of measurements in quantum mechanics. Recently, there has been significant progress in the experimental realization and stabilization of quantum systems. Together with the understanding that many mesoscopic systems can be described by stochastic equations, I find ample motivation to work in this fast evolving field. Using a quantum Langevin equation is one of the promising leads to describe simple open quantum systems with quantum dissipation. Currently, I am interested in how the equivalent of Fick's law becomes manifest in diffusive open quantum systems and what are the possible corrections at finite time and finite system size.
• Thermal and athermal uncertainty relations: The thermodynamic uncertainty relation is a recent result characterising a transport efficiency for thermal transport systems. An interesting question is whether other stochastic systems have the equivalent of a transport efficiency. Coherent light propagating through a disordered medium indeed has such a transport efficiency [in preparation]. We use statistical mechanics methods to describe this stochastic, but athermal system and provide the mesoscopic physics equivalent of the thermodynamic uncertainty bound. Exploring this transport efficiency can lead to an optimal control theory of mesoscopic devices.
• Energy forms is a mathematical tool. It is a natural way to study dynamical properties of random walkers in a fractal geometry. Moreover, I have found that Energy forms describes also open stochastic systems, via a similarity to the macroscopic fluctuation theory description. This mapping, allows describe open systems, using potential theory. Among the benefits of this method we find, Kirchhoff rules for stochastic processes on graphs and the use of Green functions to understand out-of-equilibrium fluctuations. In fractals, random walkers usually exhibit anomalous diffusion. Therefore, Energy forms should be a useful tool to try and explore interacting systems known to display such anomalous diffusion.
• Directed polymers in a random media : In recent years, new methods were developed in order to manipulate single vortices in type II superconductors by means of magnetic force microscopy (MFM). The vortex moves in a series of jumps when it is dragged using the magnetic tip of the MFM. Theoretically, it is possible to relate the physics of vortices in type II superconductors (within Ginzburg Landau theory) to the theory of polymers in random media. We find that, as suggested by theory, the jump-size distribution does not depend on the applied force and is consistent with power-law behavior. The measured exponent of the power law is found to be much larger than widely accepted theoretical calculations.