Related papers: Quasi-integrability and nonlinear resonances in co…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
We consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasi-soliton" pulses, which have fixed stable structure but can reflect from…
We study the semiclassical dynamics of a spinor condensate with the magnetic dipole-dipole interaction included. The time evolution of the population imbalance and the relative phase among different spin components depends greatly on the…
The discovery of topological matter has revolutionized the field of condensed matter physics giving rise to many interesting phenomena, and fostering the development of new quantum technologies. In this thesis we study the quantum dynamics…
The fields of cavity quantum electrodynamics and magnetism have recently merged into \textit{`cavity spintronics'}, investigating a quasiparticle that emerges from the strong coupling between standing electromagnetic waves confined in a…
We study the spectral function of two-leg Hubbard ladders with the time-dependent density matrix renormalization group method (tDMRG). The high-resolution spectrum displays features of spin-charge separation and a scattering continuum of…
The paradigm of the two-level atom is revisited and its perturbative analysis is discussed in view of the principle of duality in perturbation theory. The models we consider are a two-level atom and an ensemble of two-level atoms both…
We consider two qubits interacting with local and collective thermal reservoirs. Each spin-reservoir interaction consists of an energy exchange and an energy conserving channel. We prove a resonance representation of the reduced dynamics of…
Nonlinear spin systems exhibit rich and exotic dynamical phenomena, offering promising applications ranging from spin masers and time crystals to precision measurement. Recent theoretical work [T. Wang et al., Commun. Phys. 8, 41 (2025)]…
We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed…
The conditions under which an open quantum mechanical system may be described by mixed quantum-classical dynamics are investigated. Decoherence is studied using influence functional methods in a model composite quantum system comprising two…
We present a system of $N$-coupled Li\'enard type nonlinear oscillators which is completely integrable and possesses explicit $N$ time-independent and $N$ time-dependent integrals. In a special case, it becomes maximally superintegrable and…
Employing the non-perturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with spectral density J(omega) propto omega^s. We show that,…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…
A dynamical quantum phase transition can occur during time evolution of sudden quenched quantum systems across a phase transition. It corresponds to the nonanalytic behavior at a critical time of the rate function of the quantum state…
Analytical results on the correlation functions of strongly correlated many-body systems are rare in the literature and their importance cannot be overstated. We present determinant representations for the space-, time-, and…
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasi-energy which is…
The space- and time-dependent response of many-body quantum systems is the most informative aspect of their emergent behaviour. The dynamical structure factor, experimentally measurable using neutron scattering, can map this response in…
The topological properties of the one-dimensional interacting systems with spatially modulated interaction in two-particle regime are theoretically investigated. Taking the boson-Hubbard model and spinless fermion interacting model as…