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We consider a hierarchy of the natural type Hamiltonian systems of $n$ degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. We give a Lax representation in terms of $2\times 2$…
Evolution of quantum fidelity for two-level systems is studied in the context of periodic echo. From a general treatment for time independent case, we obtain a simple condition on the governing Hamiltonians under which the systems display…
The interaction among the components of a hybrid quantum system is often neglected when considering the coupling of these components to an environment. However, if the interaction strength is large, this approximation leads to unphysical…
In this work, the entanglement dynamics of a moving-biparticle system driven by an external classical field are investigated, where the moving-biparticle system is coupled with a zero temperature common environment. The analytical…
We consider the motion of a light sail that is accelerated by a powerful laser beam. We derive the equations of motion for two proof-of-concept sail designs with damped internal degrees of freedom. Using linear stability analysis we show…
Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…
We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential with state-dependent time-delayed feedback. In the limit of small time-delays, we show that the oscillator is equivalent to a Li\'enard system.…
We are interested in optimally driving a dynamical system that can be influenced by exogenous noises. This is generally called a Stochastic Optimal Control (SOC) problem and the Dynamic Programming (DP) principle is the natural way of…
We compare two approaches to open quantum systems, namely, the non-Hermitian dynamics and the Lindblad master equation. In order to deal with more general dissipative phenomena, we propose the unified master equation that combines the…
The Maxwell-Bloch dissipative equations describe laser dynamics. Under a simple condition on the parameters there exist two time dependent first integrals, that allow a nonstandard separation of variables in the equations. That condition…
Nuclear spin systems in manganites, having separation of ferromagnetic and antiferromagnetic phases, which are manifested as two lines in the NMR spectrum, are studied. Taking into account the Ising nuclear interaction, we obtain an…
We present a quantized model of harmonically confined dot atom with inherent damping in the presence of a transverse magnetic field. The model leads to a non hermitian Hamiltonian in real coordinate. We have analytically studied the effects…
Using the Hubbard representation for $SU(2)$ we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of non-linear coupled equations. In order to…
The Rabi oscillations of a two-level atom illuminated by a laser on resonance with the atomic transition may be suppressed by the atomic motion through averaging or filtering mechanisms. The optical analogs of these velocity effects are…
The question of decoupling and freeze-out is reinvestigated and analysed in terms of transparent semi-classical decoupling formulae, which provide a smooth decoupling in time both, for single and two particle inclusive spectra. They…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
Dissipative phase transitions (DPTs) are traditionally characterized through the spectral properties of a time-independent Liouvillian superoperator. However, this definition cannot be applied to time-periodic (Floquet) systems that cannot…
We investigate how an external driving field can control the amount of extractable work from a quantum emitter, a two-level quantum system (TLS) interacting with a photonic environment. In this scenario, the TLS functions as a quantum…
We investigate the Magnus expansion for a generic time-dependent two-level system under single-axis driving.By virtue of the su(2) Lie algebra, the expansion is decomposed into a commutator-free form. To illustrate the usefulness of the…
Coupled relaxation oscillators, realized via chemical or other means, can exhibit a multiplicity of steady states, characterized by spatial patterns resulting from lateral inhibition. We show that perturbation-initiated transformations…