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Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
Quantum confinement, magnetic-field effects, and laser coupling with the two low-lying states of electrons bound to donor impurities in semiconductors may be used to coherently manipulate the two-level donor system in order to establish the…
Non-Markovian effects arising in open quantum systems evolution have been a subject of increasing interest over the past decade. One of the most appealing features of non-Markovianity (NM) is that it captures scenarios where loss of…
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…
We consider the phase-transition-like behaviour in the Rabi model containing a single two-level system, or qubit, and a single harmonic oscillator. The system experiences a sudden transition from an uncorrelated state to an increasingly…
The non-equilibrium spin dynamics of a one-dimensional system of repulsively interacting fermions is studied by means of density-matrix renormalization-group simulations. We focus on the short-time decay of the oscillation amplitudes of the…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of…
We study the real-time dynamics of multi-party entanglement signals in chaotic quantum many-body systems including but not necessarily restricted to holographic conformal field theories. We find that scrambling dynamics generates multiparty…
The standard weak-coupling approximations associated to open quantum systems have been extensively used in the description of a two-level quantum system, qubit, subjected to relatively weak dissipation compared with the qubit frequency.…
We demonstrate theoretically the parametric oscillator behavior of a two-level quantum system with broken inversion symmetry exposed to a strong electromagnetic field. A multitude of resonance frequencies and additional harmonics in the…
The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using recently derived…
Dissipative structures are localized, stable patterns that arise due to the intricate balance among dissipation, dispersion, interaction, and external drive. Their creation and manipulation are of great interest in fields as diverse as…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
We investigate on a unified basis tunneling and vibrational relaxation in driven dissipative multistable systems described by their N lowest lying unperturbed levels. By use of the discrete variable representation we derive a set of coupled…
We apply the effective approach to evaluating semiclassical relational dynamics to the closed Friedman--Robertson--Walker cosmological model filled with a minimally coupled massive scalar field. This model is interesting for studying…
In this paper we treat the 2--level system interacting with external fields without the rotating wave approximation and construct some approximate solutions in the strong coupling regime.
We discuss a model for non-linear quantum evolution based on the idea of time displaced entanglement, produced by taking one member of an entangled pair on a round trip at relativistic speeds, thus inducing a time-shift between the pair. We…
The real time evolution of quantum field theory models can be calculated order by order in perturbation theory. For $\lambda \phi^4$ models, the perturbative series have a zero radius of convergence which in part motivated the design of…