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Thermodynamics of a Bose gas: Sound velocity from global variables and equivalence with other approaches

A. R. Fritsch

Published Mar 28, 2017• 4 citations
Publisher

Abstract

Without question, this is one of the hardest part of the thesis, and where we can commit a mistake forgetting people that helped in this thesis.Therefore, if this occurs, my sincere apologies.I would like to thank my family for their love.For believe me and wish me all the best, for the education and the support.Live far from the family is not easy, but the talks and a few visits help us, and also motivate me to return.A lovely person who helps me in everything, also makes it more easy, and is always on my side.This is my wife.Thank you Joyciane, for help me in everything, for your love, dedication, your patience, mainly in this days of writing the thesis and with the classes, our time together becomes short, but you supported me always.Also for her family, my second family, for their love, confidence, and to consider me as a son.My supervisor Emanuel, for the time dedicated to this thesis.For the patience in reading and correcting this thesis many times, and for teaching me during this period

DOI
10.11606/t.76.2017.tde-13032017-144758

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Without question, this is one of the hardest part of the thesis, and where we can commit a mistake forgetting people that helped in this thesis.Therefore, if this occurs, my sincere apologies.I would like to thank my family for their love.For believe me and wish me all the best, for the education and the support.Live far from the family is not easy, but the talks and a few visits help us, and also motivate me to return.A lovely person who helps me in everything, also makes it more easy, and is always on my side.This is my wife.Thank you Joyciane, for help me in everything, for your love, dedication, your patience, mainly in this days of writing the thesis and with the classes, our time together becomes short, but you supported me always.Also for her family, my second family, for their love, confidence, and to consider me as a son.My supervisor Emanuel, for the time dedicated to this thesis.For the patience in reading and correcting this thesis many times, and for teaching me during this period
com apoio da Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brasil.Processos nº 2022/01421-9 e nº 2022/14069-1.Eu agradeço muito pelo suporte financeiro, que me permitiu atender eventos importantes do meu campo de pesquisa e a fazer um intercâmbio inesquecível.iv I would first like to thank my advisor, Bárbara Amaral.Her guidance over these almost four years of undergraduate and master's studies has been essential to my development as a student and researcher.Thank you for all your patience, for giving me so many incredible opportunities, and for showing me that it is possible to do physics without giving up on other important aspects of life.Thank you for being an incredible person, in whom I draw inspiration.I hope to continue learning a lot from you and gossiping over coffee breaks at conferences and IFQIFs.To my parents, Maria de Fátima and Jones, who are my foundation and the loves of my life.I am immensely grateful for all the support you have given me.This work is largely the result of your efforts.Mom, thank you for being strong, loving and for teaching me to believe in myself.Dad, thank you for supporting me, making awful jokes (which I laugh at from time to time), and for teaching me that life is too short not to enjoy the people we love.So thank you very much, I love you.To my siblings, Gabriela and Matheus, for being my biggest inspirations, even though I try hard not to admit it in front of you.Gabi, thank you for being the sweetest person I know (and the fiercest too!).You have the gift of making me feel welcome and comfortable.Being with you is easy.Math, thanks for getting excited about me studying something remotely close to quantum computing and genuinely believing that I'm going to get rich from it.If that happens, although it's highly unlikely, I'll dedicate part of the fortune to you.But beyond that, thank you for showing me that someone so serious and responsible can be so playful and kind.And to my brother and sister-in-law, Luc and Malu, thank you for making Gabi and Math so happy.I love you all.And Malu, thanks for Sosô.To my grandparents, Eunice, Jurandir, Victória and Olize.Abuela, know that the most important part of who I am today comes from you.Thank you for teaching me to laugh on difficult days and to look at life through the eyes of a child.Grandpa, I didn't have the privilege of knowing you, but thank you for raising this family with grandma.Vivitória, you're not here anymore either, but I'll never forget talking to you by the wood-burning stove on cold mornings in Caçador.And Grandpa, "Life is bitter enough already, isn't it?Barbarity."So I'll try to write happier things next.
To my family, who are always there for me... Acknowledgements First and foremost, I wish to express my sincerest gratitude to my thesis supervisor Prof. Berge Englert, for giving me with an interesting and fascinating topic to explore, for providing me valuable insights at various stages of the project, such as extremely helpful advice on which promising ideas to pursue and which veritable methods to attempt, and most especially for his mild-mannered approach and utmost patience in dealing with my struggles in this entire endeavor. I would also like to express my heartfelt appreciation for all the support I have re-ceived from the Centre for Quantum Technologies, mostly in the form of facilities that definitely eased the burden of the many little chores of research like printing documents. I would also like to thank the NUS Department of Physics for a providing me with a wonderful opportunity to teach tutorial classes during the final stages of my thesis write-up, an experience that I feel will be valuable for many years to come.
Approved by Supervising Committee: For my parents. Thank you for your love and support. Acknowledgments First of all, I would like to thank my supervisor, Prof. Mark Raizen. Mark, you allowed me great freedom in my work and put a lot of trust in me. Nevertheless, you were always there with good advice and great ideas when I needed you. I am very proud that I was given the opportunity to work in your group. Thank you for supporting me during my time in Austin and beyond. I am equally thankful to my fellow group members and friends Adam Libson, Dr. Ed Narevicius and Christian Parthey. Everything we accomplished during the last one and a half years was a group effort and they are the main reason I am writing this thesis using the pronoun “we”. Adam, although you sometimes “unnerved ” us with your constant fear of leaks or fatal rotor destruction, I wouldn’t have wanted to work with anybody else than you on this project. You often foresaw problems we would have easily