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

A Study on the Interaction between Gender Morality and Free Love in Early 20th Century China : Centered on Du Cheng Shu&Qu Jiang\u27s Love Letter

This article attempts to answer the question of "love" and why it has been prohibited from entering the public sphere in Chinese history. This article takes the "Love Letter Incident" as a case study and uses the process tracking method to analyze the love letter incident between Du Chengshu (杜成淑) and Qu Jiang (屈疆). In this event, various social groups interacted on this matter, so this article horizontally compared the thinking and self-expression of young men and women in the face of love issues and vertically explored the premature and delayed disclosure of love issues under the trend of gender equality in China since the early 20th century. Examining and evaluating love issues by various parties in the public sphere is necessary for private love writing to move toward the public sphere. Through various evaluations of love letters, the issue of love has entered the public sphere. However, in China at the beginning of the 20th century, the issue of love still faced scrutiny from traditional Chinese gender morality and morality, making it difficult for love issues to be made public. This article finds that in early 20th-century China. The concept of "gender equality" accompanied by China\u27s modernization movement (May Fourth Movement) was valued by society, and the morality of "gender equality" has never been established. However, Chinese society still maintains an unfriendly attitude towards women, and the perception of gender inequality is still considered normal