Langer, Stephan Markus (2012): Transport and realtime dynamics in onedimensional quantum magnets and ultracold atomic gases. Dissertation, LMU München: Faculty of Physics 

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Abstract
The goal of this thesis is to study the transport properties and realtime dynamics of quantum magnets and ultracold atomic gases in one spatial dimension using numerical methods. The focus will be on the discussion of diffusive versus ballistic dynamics along with a detailed analysis of characteristic velocities in ballistic regimes. For the simulation of timedependent density profiles we use the adaptive timedependent density matrix renormalization group (DMRG). This numerical method allows for the simulation of timedependent wave functions close to as well as far from equilibrium in a controlled manner. The studies of onedimensional quantum magnets are partially motivated by the experimental evidence for a highly anisotropic and for insulators comparably high thermal conductivity of certain cuprates. We use linear response theory to study transport coefficients at arbitrary temperatures by diagonalizing small systems exactly and then calculating the currentcurrent correlation functions. As first application we discuss the spin transport in the spin$1/2$ Heisenberg chain with anisotropic exchange interactions (XXZchain). The second application of exact diagonalization, here in combination with timedependent DMRG, is a discussion of the transverse components of the currentcurrent correlation function. While usually only a Zeeman field is considered in the theory of transport coefficients, we here investigate the dynamic induced by an additional transverse magnetic field. We find that in this scenario the currentcurrent correlation function exhibits coherent oscillations. In addition a second nontrivial frequency, different from the one expected from the usual Larmor precession, emerges and is studied varying temperature and field. Finally we calculate the frequencydependent spin and heat conductivity of dimerized spin chains in a magnetic field. Motivated by the recent experimental studies of the phase diagram of C$_5$H$_{12}$N$_2$CuBr$_4$ we take the dimerized chain as a minimal model that exhibits features of the lowtemperature region of the observed phase diagram. As a main result, the spin and heat conductivity obtained from linear response theory are enhanced in the fieldinduced gapless phase. The last application in the field of onedimensional quantum magnets is the simulation of timedependent energydensity wavepackets close to as well as far from equilibrium using the timedependent density renormalization group. The main results are ballistic energy dynamics independently of how far outofequilibrium the initial state is and a detailed understanding of the average expansion velocity. The applications in the field of ultracold atomic gases focus on the sudden expansion of an initially trapped gas into an empty optical lattice. This setup was recently realized in an experiment performed by U. Schneider {\it et al.} and discussed in the context of electronic transport in the twodimensional and the threedimensional FermiHubbard model. Here we investigate the sudden expansion of three different setups: For the expansion of a spinbalanced cloud of fermions, we identify the ballistic regime, and therein investigate the average expansion velocity of the cloud. As a main result the expansion velocity is determined by a small subset of the initial condition over a wide range of parameters. For instance, the Mottinsulating phase of the Hubbard model is characterized by a constant expansion velocity independently of the strength of the interaction. In the case of spinless bosons, we study the expansion from initial states that have a fixed particle number per lattice site and a certain concentration of defects. We study the expansion velocity as a function of interaction strength and investigate whether the timedependent momentum distribution functions indicate a dynamical quasicondensation. The last example is the sudden expansion of a spinpolarized gas of fermions in the presence of attractive interactions. This study is motivated by current effort to experimentally detect the FuldeFerrellLarkinOvchinnikov state. Our results for the timedependent momentum distribution functions and the wavefunction of the pair condensate suggest that the signatures of the FFLO state vanish quickly, yet a stationary form of the momentum distribution also emerges fast. The latter is shown to be determined by the initial conditions, which might eventually allow for an indirect detection of the FFLO phase.
Item Type:  Thesis (Dissertation, LMU Munich) 

Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  8. August 2012 
1. Referee:  Schollwöck, Ulrich 
Persistent Identifier (URN):  urn:nbn:de:bvb:19147217 
MD5 Checksum of the PDFfile:  8eb2cf6f06b20b6f879aac9d7c7a19af 
Signature of the printed copy:  0001/UMC 20555 
ID Code:  14721 
Deposited On:  16. Aug 2012 08:38 
Last Modified:  16. Oct 2012 09:04 