Related papers: Two Dimensional Isotropic Harmonic Oscillator on a…
This work addresses the problem of relaxation of open systems to quasi-equilibrium states. Time-dependent density matrix of two arbitrary coupled quantum oscillators of arbitrary properties interacting with separate reservoirs is derived…
The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is…
Based on chiral soliton models, the quantum fluctuation energies of quarks over a spatially inhomogeneous meson field background have been thoroughly studied. We have used a systematic calculation scheme initiated by Schwinger, in which the…
Properties of the response functions for a two-dimensional quartic oscillator are studied based on the diagonalization of the Hamiltonian in a large model space. In particular, response functions corresponding to a given momentum transfer…
We prove that the $1-d$ quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their…
A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue. This analogue does not factor. The two dimensional case is…
This work is mainly based on some theoretical surveys on two dimensional quantum gravitational well, considering harmonic oscillator potential causes an effective plank constant. We find that there is a similarity between two different…
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…
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…
We study the time evolution of two coupled quantum harmonic oscillators interacting through nonlinear optomechanical-like Hamiltonians that include cross-Kerr interactions. We employ techniques developed to decouple the time-evolution…
The Heisenberg model on a triangular lattice is a prime example for a geometrically frustrated spin system. However most experimentally accessible compounds have spatially anisotropic exchange interactions. As a function of this anisotropy,…
We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding…
The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two…
The eigenfunctions and eigenenergies for a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials are derived. Equal scalar and vector potentials may be applicable to the spectrum of an antinucleion imbedded in a…
Real, time-dependent scalar fields can form oscillating, self-gravitating configurations-oscillatonsthat are viable candidates for scalar-field dark matter (SFDM). We revisit oscillatons with an exponential self-interaction and develop a…
In this proceeding, we study time evolution of a complex scalar field, in symmetry broken phase, in presence of oscillating spacetime metric background. We show that spacetime oscillations lead to parametric resonance of the field. This…
This study explores the time-dependent Dunkl-Pauli oscillator in two dimensions. We constructed the Dunkl-Pauli Hamiltonian, which incorporates a time-varying magnetic field and a harmonic oscillator characterized by time-dependent mass and…
We analyze recent results for a harmonic oscillator in an environment with a pointlike defect. We show that the allowed oscillator frequencies predicted by the authors stem from a misinterpretation of the exact solutions of a conditionally…
In a Quantum Field Theory with a time-dependent background, time-translational symmetry is broken. We therefore expect time-dependent loop corrections to cosmological observables after renormalization for an interacting field, with the…
We calculate transition amplitudes and probabilities between the coherent and Fock states of a quantum harmonic oscillator with a moving center for an arbitrary law of motion. These quantities are determined by the Fourier transform of the…