Related papers: Scale Invariance Breaking and Discrete Phase Invar…
We introduce models of one-dimensional $n(\geq3)$-body problems that undergo phase transition from a continuous scale-invariant phase to a discrete scale-invariant phase. In this paper, we focus on identical spinless particles that interact…
The Efimov effect (in a broad sense) refers to the onset of a geometric sequence of many-body bound states as a consequence of the breakdown of continuous scale invariance to discrete scale invariance. While originally discovered in…
We re-consider the quantum mechanics of scale invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We…
We provide a review on the physics associated with phase transitions in which continuous scale invariance is broken into discrete scale invariance. The rich features of this transition characterized by the abrupt formation of a geometric…
Efimov states are known to have a discrete real space scale invariance, working in momentum space we identify the relevant discrete scale invariance for the scattering amplitude defining its Weierstrass function as well. Through the use of…
Scale invariance emerges and plays an important role in strongly correlated many-body systems such as critical regimes nearby phase transitions and the unitary Fermi gases. Discrete scaling symmetry also manifests itself in quantum few-body…
One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale…
We study a one-dimensional quantum problem of two particles interacting with a third one via a scale-invariant subcritically attractive inverse square potential, which can be realized, for example, in a mixture of dipoles and charges…
When the scattering length is proportional to the distance from the center of the system, two particles are shown to be trapped about the center. Furthermore, their spectrum exhibits discrete scale invariance, whose scale factor is…
Because of the absence of indistinguishability constraint, interparticle interactions between nonidentical particles have in general much more variety than those between identical particles. In particular, it is known that there exists a…
The use in the action integral of totally divergent densities in generally coordinate invariant theories can lead to interesting mechanisms of spontaneous symmetry breaking of scale invariance. With dependence in the action on a metric…
When two non-relativistic particles interact resonantly in three dimensions, an infinite tower of three-body bound states emerges, exhibiting a discrete scale invariance. This universal phenomenon, known as the Efimov effect, has garnered…
We study scale invariance at the quantum level (three loops) in a perturbative approach. For a scale-invariant classical theory the scalar potential is computed at three-loop level while keeping manifest this symmetry. Spontaneous scale…
We argue that scale invariance is not anomalous in quantum field theory, provided it is broken cosmologically. We consider a locally scale invariant extension of the Standard Model of particle physics and argue that it fits both the…
We construct a class of theories which are scale invariant on quantum level in all orders of perturbation theory. In a subclass of these models scale invariance is spontaneously broken, leading to the existence of a massless dilaton. The…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating complexity of turbulent flows. Here we challenge the concept of broken scale invariance by establishing a hidden…
We show that scale invariance provides a solution to the fine tuning problem of the cosmological constant. We construct a generalization of the standard model of particle physics which displays exact quantum scale invariance. The matter…
In this work we develop a general formalism that categorizes the action of broken scale invariance on the non-equilibrium dynamics of non-relativistic quantum systems. This approach is equally applicable to both strongly and weakly…
A scenario based on the scale invariance for explaining the vanishing cosmological constant (CC) is discussed. I begin with a notice on the miraculous fact of the CC problem that the vacuum energies totally vanish at each step of…