Related papers: Quantum Fuzzy Orbits
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…
This paper presents a novel approach to understanding the role of harmonic dynamics and gaining a deeper appreciation for its impact within and outside of quantum mechanics. This includes consequences of harmonic dynamics and the…
This study investigates the interplay between a high-frequency external forcing and the intrinsic dynamics of a quantum nonlinear parametric oscillator. To analyze this system, classical equations of motion of the averages of quantum…
Edge states of the quantum Hall fluid provide an opportunity to study mesoscopic effects in a highly correlated electron system that is both experimentally accessible and theoretically tractable. In this paper we review recent work on the…
We construct the linear and quadratic polynomial dynamical invariants for the classical and quantum time-dependent harmonic oscillator driven by a time-dependent force. To obtain them, we use exclusively the associated equations of motion…
In this paper we study some basic quantum confinement effects through investigation of a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation…
The quantization of a constant of motion for the harmonic oscillator with a time-explicitly depending external force is carried out. This quantization approach is compared with the normal Hamiltonian quantization approach. Numerical results…
In this work we address quantum vacuum amplification effects in time-varying media with an arbitrary time-modulation profile. To this end, we propose a theoretical formalism based on the concept of conjugated harmonic oscillators,…
Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the…
Effective Hamiltonians are often used in quantum physics, both in time dependent and time independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent…
The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian…
It has long been known that there exists a coordinate transformation which exactly maps the quantum free particle to the quantum harmonic oscillator. Here we extend this result by reformulating it as a unitary operation followed by a time…
We consider the quantum Hall effect induced by magnetic field and rotation, which can drive the Hall samples into the quantum Hall regime and induce fractional excitations. Both the mass and the charge of the Laughlin quasiparticles are…
We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schr\"odinger equation by using squeeze operators. Finally we give…
If spacetime undergoes quantum fluctuations, an electromagnetic wavefront will acquire uncertainties in direction as well as phase as it propagates through spacetime. These uncertainties can show up in interferometric observations of…
Understanding the observer-dependent nature of quantum entanglement has been a central question in relativistic quantum information. In this paper we will review key results on relativistic entanglement in flat and curved spacetime and…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…
Quantum effects arising from manifestly broken time-reversal symmetry are investigated using time-dependent perturbation theory in a simple model. The forward time and the backward time Hamiltonians are taken to be different and hence the…
The magnetic response of strongly localized electrons to a time-dependent vector potential is considered. The orbital magnetic moment of the system, away from steady-state conditions, is obtained. The expression involves the tunneling and…