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The singularity of quantum correlations, such as quantum entanglement(QE) and quantum discord(QD), has been widely regarded as a valuable indicator for quantum phase transition(QPT) in low-dimensional quantum systems. In this paper, for a…
This lecture is a tutorial introduction to coherent effects in disordered electronic systems. Avoiding technicalities as most as possible, I present some personal points of view to describe well-known signatures of phase coherence like weak…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…
We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal…
Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of…
A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite…
We overview the concept of dynamical phase transitions in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal…
Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness"…
The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum…
We investigate the effect of classical singularities in the quantum properties of non-random Hamiltonians. We present explicit results for the case of a kicked rotator with a non-analytical potential though extensions to higher…
Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…
An effective field theory is derived for the ferromagnetic transition of diffusive electrons at T=0. The static disorder which leads to diffusive electron dynamics induces an effective long-range interaction between the spins of the form…
Out of equilibrium, the lack of reciprocity is the rule rather than the exception. Non-reciprocal interactions occur, for instance, in networks of neurons, directional growth of interfaces, and synthetic active materials. While wave…
The behavior of the conductivity and the density of states, as well as the phase relaxation time, of disordered itinerant electrons across a quantum ferromagnetic transition is discussed. It is shown that critical fluctuations lead to…
Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility…
We review some recent work on the occurrence of coalescing eigenstates at exceptional points in non-Hermitian systems and their influence on physical quantities. We particularly focus on quantum dynamics near exceptional points in open…
We study measurement-induced phase transitions in quantum circuits consisting of kicked Ising models with postselected weak measurements, whose dynamics can be mapped onto a classical dynamical system. For a periodic (Floquet) non-unitary…
Relaxor ferroelectrics are complex oxide materials which are rather unique to study the effects of compositional disorder on phase transitions. Here, we study the effects of quenched cubic random electric fields on the lattice instabilities…
Gauge effects on the fluctuation properties of the normal-to-superconducting phase transition in bulk and thin film superconductors are reviewed. Similar problems in the description of other natural systems (liquid crystals, quantum field…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…