Toward understanding non-equilibrium and non-perturbative phenomena (December 1st 2017 - March 31, 2021)
One of the most important concepts in modern physics is symmetry. We can classify equilibrium phases of matter (including vacuum) based on symmetry, and systematically construct the low-energy effective field theory (EFT) by the use of which we can describe what we are interested in within our (energy) scale. Furthermore, as is usual for practical applications of EFT, it is crucial to put an assumption of scale separations since it gives us small parameters which enables us to use the perturbative expansion. Based on these, we can discuss equilibrium phase transitions and the Standard Model for elementary particles in the unified same language. Then, a lot of unsolved problems in modern physics stay beyond the above regimes where the equilibrium state is not realized and/or the perturbative calculation does not work. In fact, we cannot even non-perturbatively define quantum field theory in a mathematically rigorous way, and do not know the reason why we experience one-way direction of “Arrow of Time”. Therefore, non-equilibrium and non-perturbative phenomena both occupy frontiers of theoretical physics. In this working group, we will work on non-equilibrium and non-perturbative problems and extend our knowledge beyond the current limitation of theoretical physics. To accomplish this goal, we are planning to have three research subjects: (1) Classification of non-equilibrium state of matter and phase transition, (2) Generalization and application of EFT for non-equilibrium phenomena, and (3) Non-perturbative analysis and resurgence theory in physic and mathematics. Below, we will briefly explain backgrounds and objectives of these research subjects in order.
1. Classification of non-equilibrium state of matter and phase transition
Classification of phases of matter and phase transitions based on symmetry is one of the most prominent achievements in modern physics. For example, while liquid and gas are symmetric phases, crystal (liquid crystal) is regarded as a phase whose translational (rotational) symmetry is spontaneously broken. Also, some novel topological phases are understandable with the help of a generalization of symmetry. Furthermore, some kinds of phase transitions are described based on the symmetry principle, and we have a well-established theoretical formulation to deal with dynamics of equilibrium phase transitions. Nevertheless, this clear view based on symmetry has been restricted to equilibrium states of matter though there exist many non-equilibrium states of matter and phase transitions. For example, there are several results in experiments and numerical simulations that some phase transitions realized in non-equilibrium situations appear to have a kind of universality. Indeed, the non-equilibrium turbulent transition in the liquid crystal and quantum fluid shows the universal behaviour described by the same effective model. The underlying reason for this universality however remains unclear due to the lack of theoretical attempts. Also, although it has been known that non-equilibrium steady state driven by external force (e.g. electric fields) shows a phase transition, theoretical model from the phenomenological viewpoint is still unknown. In this research, considering these non-equilibrium phase transitions, we will clarify a symmetry principle and theoretical formulation which enable us to classify the non-equilibrium states of matter and phase transitions.
2. Generalization and application of EFT for non-equilibrium phenomena
The notion of effective field theory (EFT) is one of the most striking concepts in modern physics. EFT is only based on symmetry and assumptions on scale separations, and thus provide a universal technique applicable to various physical phenomena. Indeed, EFT covers broad branches of physics from particle/nuclear physics and cosmology to condensed-matter physics. Nevertheless, the application of EFT has been mainly restricted to vacuum states of systems, and it is just recent that EFT is applied to the non-equilibrium real-time dynamics. While one simplest example for non-equilibrium EFT is hydrodynamics which captures spacetime evolution of conserved charge densities, we have a lot of non-equilibrium phenomena which can be described by the use of non-equilibrium EFT. However, the structure of non-equilibrium EFT becomes more complicated than usual vacuum EFT, and we need to clarify its theoretical basis before possible fruitful applications. In this research, we will first lay out a general way to construct non-equilibrium EFT based on the Schwinger-Keldysh formalism of quantum field theory, and then, apply it to various physical systems; for example, usual and unusual transport phenomena, exotic materials in condensed-matter physics, inflation in cosmology, and collective motions of active matters (e.g. schools of fish, flocks of birds) in biology.
3. Non-perturbative analysis and resurgence theory in physic and mathematics
Except for some simple examples, we cannot exactly solve most problems encountered in physics. Although some of such cases allow us to use first-principle numerical simulations, there are situations where we cannot obtain meaningful results from numerical simulations. In such cases, giving up exact calculations, we often use the perturbation theory－an expansion with respect to small parameters－and it has provided fruitful results in physics. However, there exist many interesting non-perturbative phenomena uncaptured by the perturbation theory. One example is real-time dynamics of quantum systems under strong external fields. They show interesting behaviours such as the Schwinger mechanism and Hawking radiation, both of which represent the particle production driven by external electric/gravitational fields. Also, there are topological objects such as the instanton in quantum field theory which cannot be captured by the usual perturbation theory. Contrary to the situation where we can simply apply the perturbation theory, little is known in the non-perturbative regimes since the perturbative analytic calculation was thought to be useless. However, there recently appears interesting advances in the perturbation theory known as the resurgence. In the resurgence theory, divergent parts of the naïve perturbative expansion is related to the non-perturbative properties of systems. We can thus obtain the non-perturbative information from the perturbative expansion. Nevertheless, its application is still restricted to simple systems such as low-dimensional quantum systems, or quantum mechanics. Thus, we have to establish the generalization of the resurgence theory to systems composed of quantum fields in order to apply it to realistic systems. In this research, we will clarify a mathematical basis of the resurgence theory, and pursue the possibility to apply the resurgence theory to quantum field theory.
As a group activity, we are planning to have a regular STAMP seminar at least once a month and an internal study group－e.g. study group on “resurgence” which is already running－, and, moreover, organize an intensive lecture (typically using 2-3 days) once in a few months. In addition, we will organize the domestic/international workshops－the first domestic workshop “Frontiers of nonequilibrium physics－Particle physics, cosmology, and condensed matter－” will be held during December 6th-8th in this year (2017).
- Tomoki Ozawa (RIKEN)
- Keiji Saito (Keio Univ.)