Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userProof that Half-Harmonic Oscillators become Full-Harmonic Oscillators after the Wall Slides Away
95
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Normally, the half-harmonic oscillator is active when $x>0$ and absent when $x<0$. From a canonical quantization perspective, this leads to odd eigenfunctions being present while even eigenfunctions are absent. In that case, only the usual odd eigenfunctions will appear if the wall slides to negative infinity. However, if an affine quantization is used, sliding the wall away shows that all the odd and even eigenfunctions are encountered, exactly like any full-harmonic oscillator. We provide numerical support for this.
rate research
Read More
In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the $SU(2)$ coherent states, where these are then used as the basis of expansion for Schrodinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density functions in configuration space.
We study the spontaneous decoherence of the coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the hidden couplings between the center-of-mass and relative degrees of freedoms, which actually originates from the symmetries of the ring geometry and corresponding nontrivial boundary conditions. Especially, such spontaneous decoherence completely vanishes at the thermodynamical limit because the nontrivial boundary conditions become trivial Born-von Karman boundary conditions when the perimeter of the ring container tends to infinity. Our investigation shows that a thermal macroscopic object with certain symmetries has chance to degrade its quantum properties even without applying an external symmetry breaking field or surrounding environment.
Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some systems are not separable into independent modes by a point transformation. For these coupled systems 2D invariants may still guide the Hamiltonian design. The theory to perform the inversion and two application examples are provided: (i) We control the deflection of wave packets in transversally harmonic waveguides; and (ii) we design the state transfer from one coupled oscillator to another.
In this communication we investigate the quantum statistics of three harmonic oscillators mutually interacting with each other considering the modes are initially in Fock states. After solving the equations of motion, the squeezing phenomenon, sub-Poissonian statistics and quasiprobability functions are discussed. We demonstrate that the interaction is able to produce squeezing of different types. We show also that certain types of Fock states can evolve in this interaction into thermal state and squeezed thermal state governed by the interaction parameters.
In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperature, which are coupled to opposite ends of the lattice, with focus on the validity of Fouriers law of heat conduction. We provide analytical solutions of the heat current through the quantum system in the non-equilibrium steady state using the rotating-wave approximation and bath interactions described by a master equation of Lindblad form. The influence of local dephasing in the transition of ballistic to diffusive transport is investigated.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
