Related papers: Coherent states for time dependent harmonic oscill…
We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry.…
The theory of adiabatic invariants has a long history and important applications in physics but is rarely rigorous. Here we treat exactly the general time-dependent 1-D harmonic oscillator, $\ddot{q} + \omega^2(t) q=0$ which cannot be…
We present a nonperturbative, first-principles numerical approach for time-dependent problems in the framework of quantum field theory. In this approach the time evolution of quantum field systems is treated in real time and at the…
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
The general theory of time-dependent frequency and time-dependent mass ('effective mass') is described.The general theory for time-dependent harmonic- oscillator is applied in the present research for studying certain quantum effects in the…
We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or nonstationary quantum states. In particular we discuss the stationary states of quantum systems with singular velocity fields. We introduce a…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
We study the convergence properties of state estimates of an oscillating qubit being monitored by a sequence of \textit{discrete}, unsharp measurements. Our method derives a differential equation determining the evolution of the estimation…
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…
The time evolution of anharmonic molecular wave packets is investigated under the influence of the environment consisting of harmonic oscillators. These oscillators represent photon or phonon modes and assumed to be in thermal equilibrium.…
We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to…
We develop a complete analytical description of the time evolution of squeezed states of a charged particle under the Fock-Darwin Hamiltonian and a time-dependent electric field. This result generalises a relation obtained by Infeld and…
We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set -- mass, frequency, driving strength, and parametric pumping -- is time-dependent. Our…
We treat quantum back-reaction in time dependent processes for quantum field theory in various simplified models. The first example is a harmonic oscillator whose frequency depends on a second quantum variable $x$. Beginning with a…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
Chimera states have been a vibrant subject of research in the recent past, but the analytical treatment of transitions from chimeras to coherent states remains a challenge. Here we analytically derive the necessary conditions for this…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
Using operator ordering techniques based on BCH-like relations of the su(1,1) Lie algebra and a time-splitting approach,we present an alternative method of solving the dynamics of a time-dependent quantum harmonic oscillator for any initial…
A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass…