Path integral for a pair of time-dependent coupled and driven oscillators

Path Integrals and Their Application to Dissipative Quantum Systems

Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time Path Integral Dissipative Systems - Introduction - Environment as Collection of Harmonic Oscillators - Effective Action Damped Harmonic Oscillator - Partition Function - Ground State Energy and Density of States - Position Autocorrelation Function

Husimi Parametric Oscillator in Frame of Symplectic Group and Q-oscillators

Time--dependent integrals of motion which are linear forms in position and momentum are discussed for Husimi parametric forced oscillator. Generalization of these integrals of motion for q--oscillator is presented. Squeezing and quadrature correlation phenomena are discussed on the base of Schrödinger uncertainty relation. The properties of the generalized correlated states, squeezed states, even and odd coherent states (the Schrödinger cat states) are reviewed. The relation of the constructed nonclassical states to representations of the symplectic symmetry group and finite symmetry groups is…

谐振子路径积分蒙特卡洛热力学能与哈密顿能量的解析评估

Analytical evaluations of the Path Integral Monte Carlo thermodynamic and Hamiltonian energies for the harmonic oscillator

本文利用谐振子的普适离散虚时传播子解析评估热力学能与哈密顿能量，证明哈密顿能量可优化至十二阶并在三个珠子内收敛，同时揭示二阶原始近似传播子计算热力学能时收敛极慢。

Relaxation of two coupled quantum oscillators to quasi-equilibrium states based on path integrals

The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths of oscillators. The expression for density matrix was found in the linear regime with respect to the coupling constant between selected oscillators. Time-dependent spatial variances and covariance were investigated analytically and numerically. It was shown that asymptotic variances in the long-time limit are always in accordance with the fluctuation dissipat…

Finite oscillator obtained through finite frame quantization

The Hamiltonian of the harmonic oscillator is usually defined as a differential operator, but an integral representation can be obtained by using the coherent state quantization. The finite frame quantization is a finite counterpart of the coherent state quantization and it allows us to define a finite oscillator by starting from the integral representation of the harmonic oscillator. Our purpose is to investigate the oscillator obtained in this way, and to present a possible application to the discrete fractional Fourier transform.

Oscillatory path integrals for radio astronomy

We introduce a new method for evaluating the oscillatory integrals which describe natural interference patterns. As an illustrative example of contemporary interest, we consider astrophysical plasma lensing of coherent sources like pulsars and fast radio bursts in radioastronomy. Plasma lenses are known to occur near the source, in the interstellar medium, as well as in the solar wind and the earth's ionosphere. Such lensing is strongest at long wavelengths hence it is generally important to go beyond geometric optics and into the full wave optics regime. Our computational method is a spinoff …