fermi dirac bose einstein and boltzmann statistics

... A more comprehensive review of Bose- Einstein condensation can be found in 25 DIPOLE TRAPPING AND ALL-OPTICAL BOSE- EINSTEIN CONDENSATION the papers [12, 79, 80] and books [81, 82] Below a critical ... TRAPPING AND ALL-OPTICAL BOSE- EINSTEIN CONDENSATION ni = 1.1×1013 , and ρi = 2×10−5 These conditions are roughly what one would expect by loading the center region only from a compressed MOT and ... and efficient experimental methods are developed to cool and transport atoms These include the all-optical production of a Bose- Einstein condensate in a µm wavelength crossed beam dipole trap and...

Ngày tải lên: 09/09/2015, 10:18

... Alexander, Anders, Hanquan and Yang Li for providing me with useful comments and help in advancing my studies Finally, I would like to dedicate this thesis to my family, for the support and encouragement ... be predicted from the Bose- Einstein statistics for bosons At temperature T , a system of bosons distribute themselves among different energy levels according to the Bose- Einstein INTRODUCTION ... reasons, the idea of Bose- Einstein condensation was not paid much attention until superfluid He was discovered [72] and until the suggestion of superfluid He being a system of Bose- Einstein condensate...

Ngày tải lên: 10/09/2015, 15:51

... Summary Since 1995, Bose- Einstein condensates (BEC) of alkali atoms have been produced and studied extensively in experiments One central goal of experiments has been formation of Bose- Einstein condensates ... for his thoughtful kindness and priceless guidance He gave me great encouragement and help when I was in a maze and patiently led me to the right way in both research and life Furthermore, many ... scheme, and (ii) pseudospectral scheme In the former, Edwards and Burnetts [21] introduced a Runge-Kutta method to solve GPE for 1D ground state and 3D ground state with spherical symmetry; Bao and...

Ngày tải lên: 28/09/2015, 13:38

... PHUONG, LUU THI KIM THANH Substituting equation (6) and equation (7) into equation (5), we obtain the Fermi- Dirac distribution function q-deform Fermi Dirac as: ⟨ ⟩ eβ(ε−µ) − ˆ = n ¯ (ε) = N (8) e2β(ε−µ) ... APPLICATION OF Q-DEFORMED FERMI- DIRAC STATISTICS TO 141 In the q-deformed Fermions oscillator operators satisfying the relation contrast commutative ... perform transformations and when < q < we determine the total energy of free electron gas at temperature T : ] [ F (q)(kT )2 (17) E = E0 + µ20 APPLICATION OF Q-DEFORMED FERMI- DIRAC STATISTICS TO From...

Ngày tải lên: 30/10/2015, 20:47

... (2) Here TF is the Fermi temperature Now we consider aramagnetic susceptibility of metals in the theory of q-deformed FermiDirac statistiec In the q-deformed formalism, the Fermions oscillator ... 2600 [8] Landolt-B.rnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, II/16, Diamagnetic Susceptibilit Springer-Verlag, Heidelberg, (1986) [9] Landolt-B.rnstein, ... [10] Landolt-B.rnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, II/2, II/8, II/10, II/11 ,and II/12a, Coordination and Organometallic Transition Metal Compounds,...

Ngày tải lên: 31/10/2015, 10:41

... connection between the superfluidity of liquid He and Bose Einstein condensation [6] Superfluid liquid He is the prototype Bose Einstein condensate, and it has played a unique role in the development ... atoms, such atoms became attractive candidates for Bose Einstein condensation, and they were used in the first successful experiments to produce a gaseous Bose Einstein condensate Other atomic species, ... towards creating Bose Einstein condensates of excitons, which are bound states of an electron and a hole [20], and of biexcitons, molecules made up of two excitons [21] Bose Einstein condensation...

Ngày tải lên: 24/01/2014, 17:30

... “Mr and Mrs Smith”, “Mr And Mrs Smith”, and so on To deal with these aliasing forms, we transform all different forms into a standard form for the later ranking and identification The standard ... Yorker” and “紐約(pronounced as NiuYue)客(people, pronounced as Ke)” “橫濱” and “Yokohama”, “鈴木一朗” and “Ichiro Suzuki” “The Mask” and “ 摩 登 (modern) 大 (great) 聖 (saint)” “孫中山(Sun Zhong-Shan)” and “Sun ... retrieving candidates from returned snippets, combining both linguistic and statistical information to find the correct translation Our system can be split into three steps: candidate retrieving, candidate...

Ngày tải lên: 20/02/2014, 12:20

... maintenance of land in good agricultural and environmental condition) The utilised agricultural area (UAA) is the total arable land, permanent grassland, land used for permanent crops and kitchen ... Agriculture, fishery and forestry statistics  Introduction Introduction The pocketbook Agricultural Statistics presents selected tables and graphs providing an overview on developments and the situation ... data codes: ef_kvecsleg and ef_ov_kvaaesu and historical data) Agriculture, fishery and forestry statistics 13  Focus on the Common Agricultural Policy: 50 years in 2012 Land use Figure 1: Utilised...

Ngày tải lên: 08/03/2014, 23:20

... Continuous Random Variables 3.5 Review Exercises Moments of Random Variables and Chebychev Inequality 73 4.1 Moments of Random Variables 4.2 Expected Value of Random Variables 4.3 Variance of Random ... contradiction to the fact that A and B are possible events The possible events A and B exclusive implies A and B are not independent; and A and B independent implies A and B are not exclusive 2.2 ... Bivariate Random Variables 8.1 Covariance of Bivariate Random Variables 8.2 Independence of Random Variables 8.3 Variance of the Linear Combination of Random Variables 8.4 Correlation and Independence...

Ngày tải lên: 17/03/2014, 14:20

... estimate them statistically and how to carry out edge corrections On the other hand, spatial statistics uses Monte Carlo simulations and random fields as models in geology and biology, but without ... approaches and fundamental results by means of a tutorial review Basic definitions and notions were explained and discussed to clarify different notations and terms and thus overcome language barriers and ... in stochastic geometry and spatial statistics, generates random structures through overlapping random ‘grains’ (spheres, sticks) each with an arbitrary random location and orientation Wolfgang...

Ngày tải lên: 17/03/2014, 14:59

... tụ Bose – Einstein - Chương 2: Tính chất nhiệt động ngưng tụ Bose – Einstein khí Bose tương tác yếu NỘI DUNG CHƯƠNG TỔNG QUAN VỀ NGƯNG TỤ BOSE- EINSTEIN Trong chương giới thiệu ngưng tụ Bose- Einstein, ... Bose- Einstein, điều kiện để xuất ngưng tụ Bose- Einstein, làm lạnh nguyên tử để có ngưng tụ, ngưng tụ Bose - Einstein khí Bose lí tưởng 1.1 Giới thiệu Ngưng tụ Bose- Einstein tượng lượng tử kì lạ quan ... tụ Bose- Einstein (BEC), xảy hạt boson có tổng số spin nguyên Ngưng tụ Bose- Einstein trình ngưng tụ nó, dự đoán có nhiều thuộc tính kì lạ nhiều năm thí nghiệm cố gắng sản xuất ngưng tụ Bose- Einstein...

Ngày tải lên: 17/04/2014, 14:26

... Size, Mean, Standard Deviation, and Standard Error of the Mean 1.4 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean Objective: To find the sample size (n), mean, standard deviation ... find the sample size, mean, standard deviation, and standard error of the mean for these data Label your answers and round off the mean, standard deviation, and standard error of the mean to two ... teaching educational and psychological statistics And it focuses exclusively on this topic in order to render the subject matter applicable and practical – and, easy to comprehend and apply Unique...

Ngày tải lên: 21/06/2014, 15:20

... estimate them statistically and how to carry out edge corrections On the other hand, spatial statistics uses Monte Carlo simulations and random fields as models in geology and biology, but without ... approaches and fundamental results by means of a tutorial review Basic definitions and notions were explained and discussed to clarify different notations and terms and thus overcome language barriers and ... in stochastic geometry and spatial statistics, generates random structures through overlapping random ‘grains’ (spheres, sticks) each with an arbitrary random location and orientation Wolfgang...

Ngày tải lên: 29/06/2014, 06:20

... discrete and continuous variables, referred to as mixed random variables For a general discussion of random variables and corresponding properties we refer to Hogg and Tanis (2010, Chapters and 4) and ... to the standard normal random variable is required The standard normal random variable, denoted Z, is a normal random variable that takes mean and variance The pdf associated with the standard ... continuous, and mixed random variables and statistical distributions are discussed in Sections 1.2.1, 1.2.2, and 1.2.3 Expectations of random variables are introduced in Section 1.3, and moment...

Ngày tải lên: 04/07/2014, 07:58

... tụ Bose - Einstein Nội dung khóa luận đề cập đến là: - Giới thiệu ngưng tụ Bose - Einstein, điều kiện để xuất ngưng tụ Bose- Einstein, làm lạnh nguyên tử để có ngưng tụ Bose - Einstein khí Bose ... xuất ngưng tụ Bose - Einstein, làm lạnh nguyên tử để có ngưng tụ BoseEinstein khí boson lí tưởng trình thực nghiệm hình thành ngưng tụ Bose - Einstein 1.1 Hệ hạt đồng Ngưng tụ Bose - Einstein tượng ... ngưng tụ Bose - Einstein - Chương 2: Hình thức luận Bogoliubov ngưng tụ Bose - Eienstein NỘI DUNG CHƯƠNG 1: LÍ THUYẾT CHUNG VỀ NGƯNG TỤ BOSE - EINSTEIN Trong chương giới thiệu ngưng tụ Bose - Einstein, ...

Ngày tải lên: 11/09/2014, 12:40

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