Related papers: Unitary relations in time-dependent harmonic oscil…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
In this paper we analyze a recent application of perturbation theory by the moment method to a family of two-dimensional anharmonic oscillators. By means of straightforward unitary transformations we show that two of the models studied by…
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model…
The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models.…
By using dynamical invariants theory, Hassoul et al. [1,2] investigate the quantum dynamics of two (2D) and three (3D) dimensional time-dependent coupled oscillators. They claim that, in the 2D case, introducing two pairs of annihilation…
The commutators of the Poincar\'e group generators will be unchanged in form if a unitary transformation relates the free generators to the generators of an interacting relativistic theory. We test the concept of unitary transformations of…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
The dynamics of qubits coupled to a harmonic oscillator with time-periodic coupling is investigated in the framework of Floquet theory. This system can be used to model nonadiabatic phenomena that require a periodic modulation of the…
The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero divisors. Starting with the commutator of the bicomplex position…
It is shown that, in the framework of non-relativistic quantum mechanics, any conserved Hermitian operator (which may depend explicitly on the time) is the generator of a one-parameter group of unitary symmetries of the Hamiltonian and…
The paper deals with the problem of dynamics of externally driven open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two externally driven coupled quantum oscillators…
We investigate the energy distribution and quantum thermodynamics in periodically driven polaritonic systems in the stationary state at room temperature. Specifically, we consider an exciton strongly coupled to a harmonic oscillator and…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example,…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…
A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary…
Different from the usual harmonic oscillator, the time-decaying harmonic oscillator accelerates particles and generates scattering states. We study one of the multidimensional inverse scatterings in this two-body quantum system perturbed by…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
A quantum Otto engine based on a three-dimensional harmonic oscillator is proposed. One of the modes of this oscillator functions as the working fluid, while the other two play the role of baths. The coupling between the working fluid and…