Uncertainty Relation for a Quantum Open System

We derive the uncertainty relation for a quantum open system comprised of a Brownian particle interacting with a bath of quantum oscillators at finite temperature. We examine how the quantum and thermal fluctuations of the environment contribute to the uncertainty in the canonical variables of the system. We show that upon contact with the bath (assumed ohmic in this paper) the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is the same as the decoherence time in similar models in the discussion of quantum to classical transition. This offers some insight into the physical mechanisms involved in the environment-induced decoherence process. We obtain closed analytic expressions for this generalized uncertainty relation under the conditions of high temperature and weak damping separately. We also consider under these conditions an arbitrarily-squeezed initial state and show how the squeeze parameter enters in the generalized uncertainty relation. Using these results we examine the transition of the system from a quantum pure state to a nonequilibrium quantum statistical state and to an equilibrium quantum statistical state. The three stages are marked by the decoherence time and the relaxation time respectively. With these observations we explicate the physical conditions when the two basic postulates of quantum statistical mechanics become valid. We also comment on the inappropriateness in the usage of the word classicality in many decoherence studies of quantum to classical transition.Comment: 36 pages,Tex,umdpp93-162,(submitted to Phys. Rev. A

SiamVGG: Visual Tracking using Deeper Siamese Networks

Recently, we have seen a rapid development of Deep Neural Network (DNN) based visual tracking solutions. Some trackers combine the DNN-based solutions with Discriminative Correlation Filters (DCF) to extract semantic features and successfully deliver the state-of-the-art tracking accuracy. However, these solutions are highly compute-intensive, which require long processing time, resulting unsecured real-time performance. To deliver both high accuracy and reliable real-time performance, we propose a novel tracker called SiamVGG. It combines a Convolutional Neural Network (CNN) backbone and a cross-correlation operator, and takes advantage of the features from exemplary images for more accurate object tracking. The architecture of SiamVGG is customized from VGG-16, with the parameters shared by both exemplary images and desired input video frames. We demonstrate the proposed SiamVGG on OTB-2013/50/100 and VOT 2015/2016/2017 datasets with the state-of-the-art accuracy while maintaining a decent real-time performance of 50 FPS running on a GTX 1080Ti. Our design can achieve 2% higher Expected Average Overlap (EAO) compared to the ECO and C-COT in VOT2017 Challenge