Feynman propagator is calculated for the time dependent harmonic oscillator by converting the problem into a free particle motion

Background/introduction Harmonic motion imaging (HMI) is a radiation forcebased elasticity imaging technique that estimates tissue harmonic displacements induced by an oscillatory ultrasonic radiation force to assess tissue stiffness. The objective of this study was to evaluate the feasibility of applying HMI on pancreatic tumor detection and high-intensity focused ultrasound (HIFU) treatment m...

We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propa...

We demonstrate experimentally a gating ratchet with cold rubidium atoms in a driven near-resonant optical lattice. A single-harmonic periodic modulation of the optical potential depth is applied, together with a single-harmonic rocking force. Directed motion is observed as a result of the breaking of the symmetries of the system.

We introduce Harmonic Motion, a free open source toolkit for artists, musicians and designers working with gestural data. Extracting musically useful features from captured gesture data can be challenging, with projects often requiring bespoke processing techniques developed through iterations of tweaking equations involving a number of constant values – sometimes referred to as ‘magic numbers’...

This paper discusses the problem of motion processing and proposes the use of a mathematical model, which describes a motion signal as a path with variable harmonic components. We show that this model is quite suited to representing a motion path as a periodic part with additional motion texture (noise), as described in [18]. This provides a good mathematical formulation to the idea of “motion ...

Several ultrasound-based imaging modalities have been proposed for image guidance and monitoring of High-Intensity Focused Ultrasound (HIFU) surgery. However, accurate localization and characterization of the effective region of treatment (thermal lesion) remain the obstacles in the clinical implementation of HIFU ablation. Harmonic motion imaging for focused ultrasound (HMIFU) is a novel HIFU ...

We compute the influence of the quantum zero-point motion of a vortex on the electronic quasiparticle spectra of s-wave superconductors. The vortex is assumed to be pinned by a harmonic potential, and its coupling to the quasiparticles is computed in the framework of BCS theory. Near the core of the vortex, the motion leads to a shift of spectral weight away from the chemical potential, and the...

In the present work the classical problem of harmonic oscillator in the hyperbolic space H 2 : z 2 0+z 2 1−z 2−z 3 = R has been completely solved in framework of Hamilton–Jacobi equation. We have shown that the harmonic oscillator on H 2 , as in the other spaces with constant curvature, is exactly solvable and belongs to the class of maximally superintegrable system. We have proved that all the...

Introduction Tagging has shown great promise for analyzing cardiac motion patterns [1]. Two different methods have been proposed to utilize the phase associated with harmonic modulation of magnetization to enable tissue tracking. Using Displacement ENcoding with Stimulated Echoes (DENSE) [2] tagged magnetization is demodulated by decoding gradients permitting motion tracking from the signal pha...