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Extracting Information from Non Adiabatic Dynamics: Excited Symmetric States of the Bose-Hubbard Model

100%
Łącki M., Delande D., Zakrzewski J.
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EN
Using Fourier transform on a time series generated by unitary evolution, we extract many-body eigenstates of the Bose-Hubbard model corresponding to low energy excitations, which are generated when the insulator-superfluid phase transition is realised in a typical experiment. The analysis is conducted in a symmetric external potential both without and with a disorder. A simple classification of excitations in the absence disorder is provided. The evolution is performed assuming the presence of the parity symmetry in the system rendering many-body quantum states either symmetric or antisymmetric. Using symmetry-breaking technique, those states are decomposed into elementary one-particle processes.
2
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Quantum Bright Soliton in a Disorder Potential

100%
Sacha K., Delande D., Zakrzewski J.
Acta Physica Polonica A
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2009
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vol. 116
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issue 5
772-778
EN
At very low temperature, a quasi-one-dimensional ensemble of atoms with attractive interactions tend to form a bright soliton. When exposed to a sufficiently weak external potential, the shape of the soliton is not modified, but its external motion is affected. We develop in detail the Bogoliubov approach for the problem, treating, in a non-perturbative way, the motion of the center of mass of the soliton. Quantization of this motion allows us to discuss its long time properties. In particular, in the presence of a disordered potential, the quantum motion of the center of mass of a bright soliton may exhibit Anderson localization, on a localization length which may be much larger than the soliton size and could be observed experimentally.
3
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Many-Body Localization for Randomly Interacting Bosons

100%
Sierant P., Delande D., Zakrzewski J.
Acta Physica Polonica A
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2017
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vol. 132
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issue 6
1707-1712
EN
We study many-body localization in a one dimensional optical lattice filled with bosons. The interaction between bosons is assumed to be random, which can be realized for atoms close to a microchip exposed to a spatially fluctuating magnetic field. Close to a Feshbach resonance, such controlled fluctuations can be transfered to the interaction strength. We show that the system reveals an inverted mobility edge, with mobile particles at the lower edge of the spectrum. A statistical analysis of level spacings allows us to characterize the transition between localized and excited states. The existence of the mobility edge is confirmed in large systems, by time dependent numerical simulations using tDMRG. A simple analytical model predicts the long time behavior of the system.
4
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Chaos Assisted Tunneling and Nonspreading Wave Packets

100%
Zakrzewski J., Delande D., Buchleitner A.
Acta Physica Polonica A
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1998
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vol. 93
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issue 1
179-186
EN
Consider an initial state lying on a primary resonance island. The state may tunnel into the chaotic sea surrounding it and further escape to infinity via chaotic diffusion. Properties of transport in such a situation are studied on an exemplary system - the hydrogen atom driven by microwaves. We show that the combination of tunneling followed by chaotic diffusion leads to peculiar large scale fluctuations of the AC Stark shift and ionization rates. An appropriate random matrix model describes accurately these statistical properties.
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