Wave Function Evolution of a Dissipative System
نویسنده
چکیده
For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner line width theory follows easily. ∗Permanent Address: Department of Physics, Notheast Normal University, Changchun 130024, P.R.China
منابع مشابه
Finite temperature correlation function of two dissipative massive scalar fields: Thermofield approach
The present paper aims at investigating the manner of two dissipative massive scalar fields. Two massive scalar fields that interact with a reservoir were considered and a reservoir was modeled by continuum Klein-Gordon fields. The Lagrangian of the total system was canonically quantized and the dynamics of the system was determined using the Euler-Lagrange equation. Then, the explicit form of the...
متن کاملDilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems
In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...
متن کاملRayleigh Wave in an Initially Stressed Transversely Isotropic Dissipative Half-Space
The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the surface wave solutions. The appropriate solutions satisfy the required boundary conditions at the stress-free surface to obtain the frequency equation of Rayleigh wave. The numerical values of the non-dimensional speed of Rayleigh wave speed are computed for different values of frequency...
متن کاملQuantum Statistical Mechanics. II. Stochastic Schrödinger Equation
The stochastic dissipative Schrödinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the density matrix, which is an explicit, stochastic form of the Lindblad master equation. A quantum fluctuation-dissipation theorem is also derived. The time co...
متن کاملOn the evolution of localized wave packets governed by a dissipative wave equation
The present paper deals with the effect of dissipation on the propagation of wave packets governed by a wave equation of Jeffrey type. We show that all packets undergo a shift of the central frequency (the mode with maximal amplitude) towards the lower frequencies (‘‘redshift’’ in theory of light or ‘‘baseshift’’ in acoustics). Packets with Gaussian apodization function do not change their shap...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1993