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In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a…
The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radiofrequency pulses that repetitively flip the state of the system, a technique that…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics with…
We consider the problem of metastability for stochastic reversible dynamics with exponentially small transition probabilities. We generalize previous results in several directions. We give an estimate of the spectral gap of the transition…
Motivated by the spin self-rephasing recently observed in an atomic clock, we introduce a simple dynamical model to study the competition between dephasing and synchronization. Two spins $S$ are taken to be initially parallel and in the…
The paper is devoted to the connection between integrability of a finite quantum system and degeneracies of its energy levels. In particular, we analyze in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb demonstrated…
We perform molecular dynamics simulation of a small number of particles in a box with periodic boundary conditions from a view point of chaotic dynamical systems. There is a transition at a critical energy E_c that each particle is confined…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
Current fluctuations in a dissipative two-state system have been studied using a novel quantum dynamics simulation method. After a transformation of the path integrals, the tunneling dynamics is computed by deterministic integration over…
The dark energy crossing of the cosmological constant boundary (the transition between the quintessence and phantom regimes) is described in terms of the implicitly defined dark energy equation of state. The generalizations of the models…
Using flow equations, equilibrium and non-equilibrium dynamics of a two-level system are investigated, which couples via non-commuting components to two independent oscillator baths. In equilibrium the two-level energy splitting is…
We propose a dynamical mechanism of the two-way switching between the metastable state and the stable state, which has been found in experiments of photoinduced reversible magnetization and photoinduced structural phase transition. We find…
We investigate the influence of nearby two-level systems on the dynamics of a qubit. The intrinsic decoherence is given by a coupling of both the qubit and the two-level systems to a heat bath. Assuming weak interactions between the qubit…
A three-state system subjected to a time-dependent Hamiltonian whose bare energies undergo one or more crossings, depending on the relevant parameters, is considered, also taking into account the role of dissipation in the adiabatic…
We show a hitherto unexplored consequence of the property of identicity in quantum mechanics. If two identical objects, distinguished by a dynamical variable A, are in certain entangled states of another dynamical variable B, then, for such…
Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements…
We study quantum entanglement and its relation to transport in a non-equilibrium interacting double dot system connected to electronic baths. The dynamical properties in the non-interacting regime are studied using an exact numerical…
The classical Monte Carlo method is used to study the properties of the ground state and phase transitions of the spin-pseudospin model, which describes a two-dimensional Ising magnet with competing charge and spin interactions. This…
Dynamical supersymmetry breaking is considered in models which admit descriptions in terms of electric, confined, or magnetic degrees of freedom in various limits. In this way, a variety of seemingly different theories which break…
To understand the onset of collective motion, we investigate active systems where particles switch on and off their self-propulsion. We prove that even when the only possible transition is off$\to$on, an active 2-state system behaves as an…