In this paper we survey the topic of time-reversal symmetry in dynamical systems. We begin with a brief discussion of the position of time-reversal symmetry in physics. After defining time-reversal symmetry as it applies to dynamical systems, we then introduce a major theme of our survey, namely the relation of time-reversible dynamical sytems to equivariant and Hamiltonian dynamical systems. W...

We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems. We give sufficient conditions for symmetry breaking in both cases.

We investigate topological signatures in the short-time non-equilibrium dynamics of symmetry protected (SPT) systems starting from initial states which break protecting symmetry. Na\"ively, one might expect that topology loses meaning when a is broken. Defying this intuition, we illustrate, an interacting Su-Schrieffer-Heeger (SSH) model, how combination breaking and quench can give rise to bot...

In this paper, we study the influence of quantum effects to chaotic dynamics, especially the influence of Pauli effect and dynamical symmetry breaking to chaotic motions. We apply the semiquantal theory to the Sp(6) fermion symmetry model in nuclear collective motion. We demonstrate that quantum chaos appears when dynamical symmetry is broken. We further show that dynamical Pauli effect enhance...

Mirror fermions with masses around the weak scale could break dynamically the electro-weak symmetry if they were coupled with a new strong interaction. The purpose of this talk is to show what sort of dynamics are needed in order to render such theories phenomenologically viable.

We show that supersymmetry and R-symmetry can be dynamically broken in a longlived metastable vacuum of SQCD with massive and massless flavors. The vacuum results from a competition of a (leading) two-loop effect and small “Planck” suppressed higher-dimension operators. This mechanism provides a particularly simple realization of dynamical SUSY and R-symmetry breaking, and as such it is a good ...

The possibility of the appearance of the C4 symmetry in the rotational bands is studied within the particle-rotor model. The role of the triaxiality of the rotor is analized.