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This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
Atomic gases confined in curved geometries are characterized by distinctive features that are absent in their flat counterparts, such as periodic boundaries, local curvature, and nontrivial topologies. The recent experiments with…
In closed quantum systems, a dynamical phase transition is identified by nonanalytic behaviors of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a…
Chaotic many-body dynamics typically generates volume-law entanglement from initially low-entangled states. We reveal an intricate, hierarchical entanglement structure in local quantum quenches, both in the canonical purification of locally…
We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival…
The quantum dynamics generated by time-dependent variational calculations is discussed from the perspective of geometric quantization. On examples, it is shown that approximate energy eigenstates can be associated to the quantized periodic…
The dynamics of an individual magnetic moment is studied through the Landau-Lifshitz equation with a periodic driving in the direction perpendicular to the applied field. For fields lower than the anisotropy field and small values of the…
We study the energy function of the Kuramoto model in random geometric graphs defined in the unit circle as the number of nodes diverges. We prove the existence of at least one local minimum for each winding number $q \in \mathbb{Z}$ with…
A host of dynamical measures of quantum correlations -- out-of-time ordered correlators (OTOC), Loschmidt echo, generalized entanglement and observational entropy -- are useful to infer the underlying classical chaotic dynamics in quantum…
Spin dynamics in a quantum well made of diluted-magnetic semiconductor is studied theoretically. The exchange interaction of the ensemble of localized spins with two-dimensional heavy-hole gas is shown to affect time evolution of the spin…
While electric power grids play a key role in the decarbonization of society, it remains unclear how recent trends, such as the strong integration of renewable energies, can affect their stability. Power oscillation modes, which are key to…
Driven mesoscopic system is a topic of great recent interest. The temporal evolution of the fluxes(particle and energy) are studied in a system of a driven single level quantum dot. At a very low reservoir temperature $T\rightarrow 0$ and…
It was experimentally found that quantum magnetoresistive hc/2e periodic oscillations of the Little-Parks type in a superconducting mesoscopic ring with decreasing temperature and increasing applied dc current are modified to the sum of…
We investigate the role of topology in the space-time scaling limit of quantum quench dynamics, where both time and system size tend to infinity at a constant ratio. There, while the standard topological characterization relying on local…
Slow variations (quenches) of the magnetic field across the paramagnetic-ferromagnetic phase transition of spin systems produce heat. In systems with short-range interactions the heat exhibits universal power-law scaling as a function of…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
Caustics occur widely in dynamics and take on shapes classified by catastrophe theory. At finite wavelengths they produce interference patterns containing networks of vortices (phase singularities). Here we investigate caustics in quantized…
Quenched thermodynamic states of an amorphous ferromagnet are studied. The magnet is a countable collection of point particles chaotically distributed over $\mathbb{R}^d$, $d\geq 2$. Each particle bears a real-valued spin with symmetric a…
Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins…
Quantum Phase slips are dual process of particle tunneling in coherent networks. Besides to be of central interest for condensed matter physics, quantum phase slips are resources that are sought to be manipulated in quantum circuits. Here,…