Nonuniversal Effects in Bose-Einstein Condensation :: Albert Einstein Gases Science Essays

Nonuniversal Effects in Bose-Einstein Condensation In 1924 Albert Einstein predicted the existence of a special type of matter now known as Bose-Einstein condensation. However, it was not until 1995 that simple BEC (Bose-Einstein condensation) was observed in a low-density Bosonic gas. This recent experimental breakthrough has led to renewed theoretical interest in BEC. The focus of my research is to more accurately determine basic properties of homogeneous Bose gases. In particular nonuniversal effects of the energy density and condensate fraction will be explored. The validity of the theoretical predictions obtained is verified by comparison to numerical data from the paper begin{it}Ground State of a Homogeneous Bose Gas: A Diffusion Monte Carlo Calculation end{it} by Giorgini, Boronat, and Casulleras. end{abstract} %dedicate{To my parents for their supporting me through college, %to God for all the mysteries of physics, and to Jammie for her %unconditional love.} %newpage %tableofcontents newpage section{Introduction}   Ã‚  Ã‚  Ã‚  Ã‚  The Bose-Einstein condensation of trapped atoms allows the experimental study of Bose gases with high precision. It is well known that the dominant effects of interactions between the atoms can be characterized by a single number $a$ called the S-wave scattering length. This property is known as begin{it}universalityend{it}. Increasingly accurate measurements will show deviations from universality. These effects are due to sensitivity to aspects of the interatomic interactions other than the scattering length. These effects are known as begin{it}nonuniversalend{it} effects. Intensive theoretical investigations into the homogeneous Bose gas revealed that properties could be calculated using a low-density expansion in powers of $sqrt{na^3}$, where $n$ is the number density. For example the energy density has the expansion begin{equation} frac{E}{N} = frac{2 pi na {hbar}^2}{m} Bigg( 1 + frac{128}{15sqrt{pi}}sqrt{na^3} + frac{8(4pi-3sqrt{3})}{3}na^3 (ln(na^3)+c) + ... Bigg) label{en} end{equation} The first term in this expansion is the mean-field approximation and was calculated by Bogoliubov cite{Bog}. The corrections to the mean-field approximation can be calculated using perturbation theory. The coefficient of the $(na^3)^{3/2}$ term was calculated by Lee, Huang, and Yang cite{LHY} and the last term was first calculated by Wu cite{wu}. Hugenholtz and Pines cite{hp} have shown that the constant $c_1$ and the higher-order terms in the expansion are all nonuniversal. Giorgini, Boronat, and Casulleras cite{GBC} have studied the ground state of a homogeneous Bose gas by exactly solving the N-bodied Schr"odinger (to within statistical error) using a diffusion Monte Carlo method.   Ã‚  Ã‚  Ã‚  Ã‚  In section II of this paper, theoretical background relevant to this problem is presented. Section III is a brief summary of the numerical data from Giorgini, Boronat, and Casulleras.

Non-violent Methods are Better Way of Training Children

As we know, physical punishment has always been an effective way for training animals. Once they become wild, flinging the whip is what we do to make them being well-behaved. However, does it work for training children? Are their behaviors all get better and better after that? In my point of view, I strongly object parents who admire that physical punishment is the best way to teach and train their own children. Although the pain of body is easy to make people learn the lesson, on the other hand, it may also be easy to leave the scars on body and heart, cause family problems and losing the opportunities for children to judge the right and wrong by themselves own.First of all, even the pain of punishment will disappear, the scars on body and heart somehow will remain for the entire life. With no doubt, teaching children not to spill the milk on the floor by simply slapping on their bottoms would be a rapid way to warn them not to make the same mistake again. However, I think your chil dren would remember how bad you treat them more than the lesson they’ve learned and reflect this rage on their children in the future by teaching them in same way. In addition, some researches even have shown the causes of some criminal’s psychological problems can be traced back to their parents’ serious physical punishment or even abuse. The former dictator of Iraq Saddam Hussein would be a good example.Second, without violence in the house, I believe children will have a happier childhood and get along with their parents better when they grow up. If we observe the relationship between parents and children more carefully, it is not hard to find out the happiness existing in the house is not only connected to children’s behavior but also parents’. After all, simply punish them physically can’t make them easier to understand what exact the mistake they make because they only know it’s wrong but don’t know why it is wrong. Howev er, although it takes more time, if you explain to them why they do is wrong and what bad results they may cause instead of punish them, then it would be easier to make them understand this mistake can not be done again without making an awkward atmosphere in the family.Finally, to let the children know what is right and what is wrong, I think the best way for them is to experience and judge by themselves. Like I mentioned above, the most important principle is let them know why it’s wrong. Once they find out, then their brain will naturally tell them not to do it before they get hurt (no matter by themselves or parents). For instance, even you strongly warned your children don’t get too close to the fire, they still want to touch and feel it what it is. But once they suffer from the pain of burning, I assure you they don’t dare to do it again on purpose.To make a conclusion, I think physical punishment is not the best way to train children. Although it is fast and effective sometimes, you will never know what consequences it may bring in the future. After all, compared to the bad relationship and many problems it may cause, the long time it takes to teach a child in a liberal and gentle way seems very worthy.

The Myth of Race - Free Essay Example

Sample details Pages: 2 Words: 649 Downloads: 6 Date added: 2019/02/05 Category Society Essay Level High school Tags: Racism Essay Did you like this example? Eric A. Watts and Robert Wald Sussman are successful authors and known for their passages. They both write an article that explores how racism being used and the origin of racism. Don’t waste time! Our writers will create an original "The Myth of Race" essay for you Create order The Color of Success is an article written by Eric A. Watts, and The Myth of Race written by Robert Wald both articles explore the history and the modern day of racism. Eric A. Watts explores how the black community destroying themselves by calling success, study or wants to progress in schools and having jobs considering as acting white. In addition, Wald Sussman explores how science shows the fact that racism is not in human nature it’s a learning behavior. In the article Watts express how The black community victimizing themselves. He uses examples from his childhood education when many of his black peers would call him out for acting white. Anytime he in a group of black speaking proper English and want to study or want to succeed in school and speak properly, they would consider him as â€Å" acting white†. Wald explores the fact how people been thaught and how to interpret and understand racism. For the past 500 years â€Å" we have been told that there are very specific things that relate to race, such as intelligence, sexual behaviors, birth rates, infants care, work ethics and abilities, personal restraint, lifespan, law-cohesion, and even brain size.† In Wald Susman article he demonstrates everything Watts friend think of him been to them by society the moment there was born to this day. We learned that some races are better than others because we are born into a racist society and our life ordered by this struc ture. Watts experience racism from his own race and confused by it. Furthermore, One of Watts friends stated that Justified dropping out of school and failing to look for a job on that basis of one factor: the cold, heartless, white power structure. These statements about his friend are used to show his reader that many Blacks exaggerate the racism that discriminates against them and uses it as an excuse to act victimized. Black people creating racism among themselves because going to school, looking for a job, is considered as ‘Acting White’. Society makes them believe success in life is white people thing, not black. Robert Sussman explores how race emerged as a social construct from early biblical justifications to the pseudoscientific studies of today. Racial prejudice and intolerance based on the myth of race remain deeply ingrained in this world. His friend believes just because the white man looking them down so, therefore, it gave him an excuse to not try and find a job at all. With these kinds of mindset, black people would ne ver be able to elevate. If you can not be successful unless you believe that you can be. In the article, Watts also share a story of how his friend thought crack was the only options he got in life because they didnt believe in any other options. Based on Sussman article, Biological races do not exist and never have. â€Å" I am not going to dwell upon all of the scientific information that has been gathered by the anthropologists, biologists, geneticists, and other scientists concerning the fact that there are no such things as human biological races.† Sussman attempts to prove that ‘race’ is a biological reality and racism is a cultural invention. Eric Watts confronted the idea of people of his race being preposterous. He shed a light on how people can be stereotypical and prejudice. When mentioning studying to someone he knew, Eric was derided as acting white. Watts finds his friends view of him as ‘acting white’ is offensive, and how people state of mind sounds ignorant and seemed so poor. His friends were acting stereotypically toward him because they felt that his valued- hard work, initiative, articulateness did not fit an African American student.