ABSTRACT
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the master-equation approach, which is numerically expensive for large dimensions of the Hilbert space. Here, we numerically investigate the suitability of a known stochastic Schrödinger equation that is local in time to give a description of thermal relaxation and energy transport. This stochastic Schrödinger equation can be solved with a moderate numerical cost, indeed comparable to that of a Markovian system, and reproduces the dynamics of a system evolving according to a general non-Markovian master equation. After verifying that it describes thermal relaxation correctly, we apply it for the first time to the energy transport in a spin chain. We also discuss a portable algorithm for the generation of the coloured noise associated with the numerical solution of the non-Markovian dynamics.
ABSTRACT
Stochastic methods are ubiquitous to a variety of fields, ranging from physics to economics and mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in contact with a somewhat bigger system, an environment with which it is considered in thermal equilibrium. Any small fluctuation of the environment has some random effect on the system. In physics, stochastic methods have been applied to the investigation of phase transitions, thermal and electrical noise, thermal relaxation, quantum information, Brownian motion and so on. In this review, we will focus on the so-called stochastic Schrödinger equation. This is useful as a starting point to investigate the dynamics of open quantum systems capable of exchanging energy and momentum with an external environment. We discuss in some detail the general derivation of a stochastic Schrödinger equation and some of its recent applications to spin thermal transport, thermal relaxation, and Bose-Einstein condensation. We thoroughly discuss the advantages of this formalism with respect to the more common approach in terms of the reduced density matrix. The applications discussed here constitute only a few examples of a much wider range of applicability.
Subject(s)
Physics , Quantum Theory , Algorithms , Models, StatisticalABSTRACT
In attempting to solve the problem of gastroesophageal reflux esophagitis, we tested an experimental technique in 1967. In the past 13 years we have applied that intercostal pedicle method to prevent reflux in 43 patients. Thirty-four patients had esophagogastrectomy and esophagogastrostomy for cancer. Six additional patients underwent palliative, nonresective esophagogastrostomy. In another two patients the lower esophagus was resected for complete full-wall thickness fibrous stricture. One patient had severely symptomatic reflux. Six patients treated by resection for cancer are long-term survivors. The two patients with benign stricture were followed for 2 years and the last patient with severe reflux symptoms was followed for 13 years. History, esophagography, fluoroscopy, and fiberoptic esophagoscopy were used for follow-up in 40 of 43 patients. Motility and pH studies were used for follow-up in 21 instances. There have been no symptoms of regurgitation and reflux. No stricture has been seen though one patient needed a few dilatations for the first 2 years and none in the last 2 years. The esophagogram shows a typical slinglike appearance. The lower esophageal sphincter-like pressure has been as high as 26 mm Hg in the immediate postoperative period, settling to 12 to 15 mm Hg in the long-term follow-up. The pH is definitely alkaline in the esophagus. Competence has also been observed in the only two patients who had an ephemeral anastomotic leak. We recommend the intercostal pedicle technique in all cases of esophagogastrostomy performed in the chest.
