UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
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Item Classical and quantum dynamics of Bose-Einstein condensates(2017) Mathew, Ranchu; Tiesinga, Eite; Sau, Jay D; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)After the first experimental realization of a Bose-Einstein condensate (BEC) in 1995, BECs have become a subject of intense experimental and theoretical study. In this dissertation, I present our results on the classical and quantum dynamics of BECs at zero temperature under different scenarios. First, I consider the analog of slow light in the collision of two BECs near a Feshbach resonance. The scattering length then becomes a function of the collision energy. I derive a generalization of the Gross-Pitaevskii equation for incorporating this energy dependence. In certain parameter regimes, the group velocity of a BEC traveling through another BEC decreases. I also study the feasibility of an experimental realization of this phenomena. Second, I analyze an experiment in which a BEC in a ring-shaped trap is stirred by a rotating barrier. The phase drop across and current flow through the barrier is measured from spiral-shaped density profiles created by interfering the BEC in the ring-shaped trap and a concentric reference BEC after release from all trapping potentials. I show that a free-particle expansion is sufficient to explain the origin of the spiral pattern and relate the phase drop to the geometry of a spiral. I also bound the expansion times for which the phase drop can be accurately determined and study the effect of inter-atomic interactions on the expansion time scales. Third, I study the dynamics of few-mode BECs when they become dynamically unstable after preparing an initial state at a saddle point of the Hamiltonian. I study the dynamics within the truncated Wigner approximation (TWA) and find that, due to phase-space mixing, the expectation value of an observable relaxes to a steady-state value. Using the action-angle formalism, we derive analytical expressions for the steady-state value and the time evolution towards this value. I apply these general results to two systems: a condensate in a double-well potential and a spin-1 (spinor) condensate. Finally, I study quantum corrections beyond the TWA in the semiclassical limit. I derive general expressions for the dynamics of an observable by using the van Vleck-Gutzwiller propagator and find that the interference of classical paths leads to non-perturbative corrections. As a case study, I consider a single-mode nonlinear oscillator; this system displays collapse and revival of observables. I find that the interference of classical paths, which is absent in the TWA, leads to revivals.Item Dynamics of wave packets in the quantum Lorentz gas(2005-06-30) Goussev, Arseni; Dorfman, J. Robert; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation addresses the dynamics of a quantum particle moving in an array of fixed scatterers. The system is known as the Lorentz gas. The scatterers are taken to be two- or three-dimensional hard-spheres. The quantum Lorentz gas is analyzed in two dynamical regimes: (i) semiclassical regime, and (ii) high-energy diffraction regime. In both regimes the dynamics of the quantum particle is found to be determined by properties characterizing chaotic dynamics of the counterpart classical Lorentz gas. Thus, this dissertation provides an attempt to more deeply understand the role that classical chaos plays in quantum mechanics of nonintegrable systems. In the semiclassical regime, the quantum particle is represented by a small Gaussian wave packet immersed in the array of scatterers. The de Broglie wavelength of the particle is considered to be much smaller than both the scatterer size and the typical separation between scatterers. It is found that for times, during which the wave packet size remains smaller than the scatterer size, the spreading of the quantum wave packet is exponential in time, and the spreading rate is determined by the sum of positive Lyapunov exponents of the corresponding classical system. The high-energy diffraction approximation allows one to analytically describe the dynamics of large wave packets in dilute scattering systems for times far beyond the Ehrenfest time. The latter is defined as the time during which the evolution of the wave packet is predominantly classical-like. The following two conditions are satisfied by the system in the high-energy diffraction regime: (i) the ratio of the particle s de Broglie wavelength to the scatterer size is much smaller than unity, and (ii) this ratio is much larger than the ratio of the scatterer size to the typical separation between scatterers. The time-dependent autocorrelation function is calculated for wave packets in hard-disk and hard-sphere geometrically open billiard systems. The envelope of the autocorrelation function is shown to decay exponentially with time, with the decay rate determined by the mean Lyapunov exponents and the Kolmogorov-Sinai entropy of the counterpart classical system.