Classical and Quantum Dissipative Systems

Abstract

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Trajectory approach to the Schrödinger–Langevin equation with linear dissipation for ground states

“…(5) [1,8,13]. First, the norm of the wave function is conserved; thus, the dissipative potential does not change the normalization of the wave function.…”

“…This approach leads to various nonlinear Schrödinger equations. Related developments and applications of these formulations for quantum dissipative systems are presented in review articles and monographs [1][2][3][4][5][6].…”

“…In this approach, a dissipative potential and a random potential are incorporated into the timedependent Schrödinger equation (TDSE), and these terms describe the thermal and statistical influence of the environment. The nonlinear Schrödinger-Langevin equation and its solutions have been discussed and analyzed for several quantum systems [1,6,[9][10][11][12]. In addition, this equation has been propagated for obtaining the ground states of several one-dimensional quantum systems [13].…”

Novel dissipative Lagrange-Hamilton formalism for LC/van der pol oscillator with new implication on phase noise dependency on quality factor

“…First we give a procedure for finding T 1 . Again taking derivative in (8), but this time without expanding using chain rule (as in (9)), and substituting (7), we have…”

Anelastic acoustic impedance and the correspondence principle

“…Rigorously, the attenuation is described not by modifying λ and μ but by adding an external dissipation force to the right‐hand side of Lagrange's equations (Bourbié et al 1987; Razavy 2005) Here, D is a (usually) second‐order functional describing energy dissipation (not to be confused with the ‘specific dissipation function’ Q −1 used by Bland (1960), Anderson and Archambeau (1964) and others). Several realistic examples of dissipation functionals for porous fluid‐filled rock were given by Bourbié et al (1987).…”