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We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that…
Quantum interactions exchanging different types of particles play a pivotal r\^{o}le in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two fermions…
The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the…
Amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during periodic pacing of one- and two-dimensional homogeneous tissue and one-dimensional anatomical reentry in a ring of homogeneous tissue.…
We analytically derive the diffusion coefficients that drive a system of $N$ coupled harmonic oscillators to an equilibrium state exhibiting persistent correlations. It is shown that the main effect of the latter consists in a…
We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical…
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate…
We explore the zero-temperature behavior of an assembly of bosons interacting through a zero-range, attractive potential. Because the two-body interaction admits a bound state, the many-body model is best described by a Hamiltonian that…
We derive analytically the spatial correlation functions for gap fluctuations in two-band scenario with intra- and interband pair-transfer interactions. These functions demonstrate the changes in spatial functionality due to the presence of…
We report two phenomena, induced by dynamical correlations, that occur during the free cooling of a two-dimensional mixture of inelastic hard disks. First, we show that, due to the onset of velocity correlations, the ratio of the kinetic…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
It is well known that systems with long-range interactions may exhibit different phase diagrams when studied within two different ensembles. In many of the previously studied examples of ensemble inequivalence, the phase diagrams differ…
We study the spectral statistics of interacting spinless fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle-systems, we compute the low-energy many-body states numerically. While at weak…
We discuss a diagonal representation of a reduced density matrix determined within the framework of the complex scaling method. We also discuss a possible measure of bipartite correlations in quantum resonance states. As an example, we…
We give a pedagogical introduction to the theory of resonances, focusing specifically on the spectrum of excited strongly interacting particles. After providing historical context starting from the atomic theory, we summarize the status of…
Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlations effects in the two-dimensional case, with a focus on systems with…
In this paper we consider a system of identical three two-level atoms interacting at resonance with a single-mode of the quantized field in a lossless cavity. The initial cavity field is prepared in the coherent state while the atoms are…
Interacting quantum many-body systems are usually expected to thermalise, in the sense that the evolution of local expectation values approach a stationary value resembling a thermal ensemble. This intuition is notably contradicted in…
Collective phenomena in the Tavis-Cummings model has been widely studied, focusing on the phase transition features. In many occasions, it has been used variational approaches that consider separated radiation-matters systems. In this…
Via computer simulations we study kinetics of pattern formation in a two-dimensional active matter system. Self-propulsion in our model is incorporated via the Vicsek-like activity, i.e., particles have the tendency of aligning their…