Related papers: Critical scattering in a time-dependent harmonic o…
The crystallographic restriction theorem constrains two-dimensional nematicity to display either Ising ($Z_{2}$) or three-state-Potts ($Z_{3}$) critical behaviors, both of which are dominated by amplitude fluctuations. Here, we use group…
We have systematically studied both classical and quantum chaotic behaviors of two colliding harmonic oscillators. The classical case falls in Kolmogorov-Arnold-Moser class. It is shown that there exists an energy threshold, above which the…
A critical transition for a system modelled by a concave quadratic scalar ordinary differential equation occurs when a small variation of the coefficients changes dramatically the dynamics, from the existence of an attractor-repeller pair…
Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by sudden parameter changes. We discuss the characterization of such dynamical phase transitions based on the statistics of produced…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
The transition from the quantum Hall state to the insulator is considered for non-interacting electrons in a two-dimensional disordered lattice model with perpendicular magnetic field. Using correlated random disorder potentials the…
The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay…
The effects of quantum and thermal corrections on the dynamics of a damped nonlinearly kicked harmonic oscillator are studied. This is done via the Quantum Langevin Equation formalism working on a truncated moment expansion of the density…
In this paper we study the focusing cubic wave equation in 1+5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the model target manifolds $\mathbb{S}^3$ and $\mathbb{H}^3$. In…
The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The…
We consider the Cauchy problem of a dissipative nonlinear Schr\"odinger equation with a time dependent harmonic potential. We find a critical situation that the $L^2$-norm of dissipative solutions decays or not and which is decided by a…
We investigate the evolution of the density-density correlations in the isoscalar critical condensate formed at the QCD critical point. The initial equilibrium state of the system is characterized by a fractal measure determining the…
We explore the critical properties of the recently discovered finite-time dynamical phase transition in the non-equilibrium relaxation of Ising magnets after a temperature quench. The transition is characterized by a sudden switch in the…
We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in…
An Ising spin system under the critical temperature driven by a dichotomous Markov noise (magnetic field) with a finite correlation time is studied both numerically and theoretically. The order parameter exhibits a transition between two…
The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…
We study the asymptotic development at infinity of an integral operator. We use this development to give sufficient conditions in order to upper bound the number of critical periodic orbits that bifurcate from the outer boundary of the…
When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This article reviews the general theory of such temporal fluctuations. We first survey some results on the…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
Quantum criticality of open many-body systems has attracted lots of interest for emergent phenomena and universality. Here we present the exact steady state of the quantum van der Pol oscillator using the complex $P$-representation. We show…