Boltzmann equation with double-well potentials
نویسندگان
چکیده
منابع مشابه
Energy splitting in symmetric double-well potentials
The quantum mechanical tunnelling in a smooth symmetric double-well potential is a long-standing and well-known problem. Three methods have been proposed to calculate the energy splitting: the instanton method @1,2#, the WKB approximation @3,4# and numerical calculation @4–6#. The instanton method is helpful to understand the physical insight of quantum tunnelling, but the validity is restricte...
متن کاملRate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials
For the spatially homogeneous Boltzmann equation with hard potentials and Grad’s cutoff (e.g. hard spheres), we give quantitative estimates of exponential convergence to equilibrium, and we show that the rate of exponential decay is governed by the spectral gap for the linearized equation, on which we provide a lower bound. Our approach is based on establishing spectral gaplike estimates valid ...
متن کاملExact Solution of the Poisson-Boltzmann Equation for Two Spheres with Fixed Surface Potentials 1
The Poisson-Boltzmann (PB) equation has been a major theoretical tool (1-5) in understanding and interpreting properties of colloidal systems immersed in electrolitic solutions. The most elementary geometry of two particles consists of two parallel plates, since the PB equation for such system becomes a classical ordinary differential equation. This simplification enables one to obtain a useful...
متن کاملOn Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials
This paper concerns Lconvergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials (−4 ≤ γ < 0), with and without angular cutoff. We prove the time-averaged L-convergence to equilibrium for all weak solutions whose initial data have finite entropy and finite moments up to order greater than 2 + |γ|. For the usual L-convergence we prove that th...
متن کاملSimulated quantum annealing of double-well and multiwell potentials.
We analyze the performance of quantum annealing as a heuristic optimization method to find the absolute minimum of various continuous models, including landscapes with only two wells and also models with many competing minima and with disorder. The simulations performed using a projective quantum Monte Carlo (QMC) algorithm are compared with those based on the finite-temperature path-integral Q...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review A
سال: 2016
ISSN: 2469-9926,2469-9934
DOI: 10.1103/physreva.94.043643