By Tim Langen
This paintings offers a chain of experiments with ultracold one-dimensional Bose gases, which identify stated gases as a terrific version procedure for exploring quite a lot of non-equilibrium phenomena. With assistance from newly constructed instruments, like complete distributions capabilities and part correlation features, the booklet unearths the emergence of thermal-like temporary states, the light-cone-like emergence of thermal correlations and the remark of generalized thermodynamic ensembles. This issues to a traditional emergence of classical statistical houses from the microscopic unitary quantum evolution, and lays the basis for a common framework of non-equilibrium physics. The thesis investigates a vital query that's hugely contested in quantum physics: how and to which quantity does an remoted quantum many-body procedure sit back? this query arises in lots of different parts of physics, and lots of of the open difficulties seem at tremendously various strength, time and size scales, starting from high-energy physics and cosmology to condensed subject and quantum details. A key problem in trying to solution this query is the shortage of quantum many-body platforms which are either good remoted from the surroundings and obtainable for experimental study.
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Additional resources for Non-equilibrium Dynamics of One-Dimensional Bose Gases
For lower atom numbers they become identical As the statistical properties of the phase fluctuations in a quasi-condensate are Gaussian, the spatial variation of the phase can be described by a Gaussian diffusion process d φ(z) = f (z). 53) dz The basic idea is to model the stochastic force f (z) in such a way that it reproduces the correct exponentially decaying correlation properties of Eq. 27. To this end we (s) define f (z) such that it fulfills f (z) f (z ) = 2δ(z − z )/λT and f (z) = 0. 54) 20 1 Introduction to One-Dimensional Bose Gases where N is a random number drawn from a Gaussian distribution with zero mean and unit standard deviation.
Stringari, Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463–512 (1999) 102. P. Gross, Structure of a quantized vortex in boson systems. Nuovo Cimento 20, 454–477 (1961) 103. P. Pitaevskii, Vortex lines in an imperfect Bose gas. Zh. Eksp. Teor. Fiz. 40, 646 (1961) 104. T. Langen, Addressing of ultracold atoms in optical lattices. Diplomarbeit (Johannes Gutenberg-Universität Mainz, 2008) 105. W. Bao, D. A. Markowich, Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation.
Further information about the system beyond the two-point correlation function can be obtained from the shot-to-shot fluctuations of the contrast. Such noise measurements have a long and rich history in the characterization of quantum systems . Examples range from the Hanbury Brown-Twiss effect in light [183, 184] and matter-waves [185, 186] to the study of current fluctuations in quantum-Hall systems  and the coherence properties of atomic systems [188–190]. 82) 0 where P(α)dα measures the probability to observe a contrast in the interval between α and α + dα.