Transport and real-time dynamics in one-dimensional quantum magnets and ultra-cold atomic gases

The goal of this thesis is to study the transport properties and real-time dynamics of quantum magnets and ultra-cold 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 time-dependent density profiles we use the adaptive time-dependent density matrix renormalization group (DMRG). This numerical method allows for the simulation of time-dependent wave functions close to as well as far from equilibrium in a controlled manner. The studies of one-dimensional 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 current-current correlation functions. As first application we discuss the spin transport in the spin-$1/2$ Heisenberg chain with anisotropic exchange interactions (XXZ-chain). The second application of exact diagonalization, here in combination with time-dependent DMRG, is a discussion of the transverse components of the current-current 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 current-current correlation function exhibits coherent oscillations. In addition a second non-trivial frequency, different from the one expected from the usual Larmor precession, emerges and is studied varying temperature and field. Finally we calculate the frequency-dependent 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 low-temperature region of the observed phase diagram. As a main result, the spin and heat conductivity obtained from linear response theory are enhanced in the field-induced gapless phase. The last application in the field of one-dimensional quantum magnets is the simulation of time-dependent energy-density wave-packets close to as well as far from equilibrium using the time-dependent density renormalization group. The main results are ballistic energy dynamics independently of how far out-of-equilibrium the initial state is and a detailed understanding of the average expansion velocity. The applications in the field of ultra-cold 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 two-dimensional and the three-dimensional Fermi-Hubbard model. Here we investigate the sudden expansion of three different setups: For the expansion of a spin-balanced 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 Mott-insulating 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 time-dependent momentum distribution functions indicate a dynamical quasi-condensation. The last example is the sudden expansion of a spin-polarized gas of fermions in the presence of attractive interactions. This study is motivated by current effort to experimentally detect the Fulde-Ferrell-Larkin-Ovchinnikov state. Our results for the time-dependent momentum distribution functions and the wave-function 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

Light scattering and dissipative dynamics of many fermionic atoms in an optical lattice

We investigate the many-body dissipative dynamics of fermionic atoms in an optical lattice in the presence of incoherent light scattering. Deriving and solving a master equation to describe this process microscopically for many particles, we observe contrasting behaviour in terms of the robustness against this type of heating for different many-body states. In particular, we find that the magnetic correlations exhibited by a two-component gas in the Mott insulating phase should be particularly robust against decoherence from light scattering, because the decoherence in the lowest band is suppressed by a larger factor than the timescales for effective superexchange interactions that drive coherent dynamics. Furthermore, the derived formalism naturally generalizes to analogous states with SU(N) symmetry. In contrast, for typical atomic and laser parameters, two-particle correlation functions describing bound dimers for strong attractive interactions exhibit superradiant effects due to the indistinguishability of off-resonant photons scattered by atoms in different internal states. This leads to rapid decay of correlations describing off-diagonal long-range order for these states. Our predictions should be directly measurable in ongoing experiments, providing a basis for characterising and controlling heating processes in quantum simulation with fermions.Comment: 18 pages, 7 figure

Coherent spin-current oscillations in transverse magnetic fields

We address the coherence of the dynamics of spin-currents with components transverse to an external magnetic field for the spin-1/2 Heisenberg chain. We study current autocorrelations at finite temperatures and the real-time dynamics of currents at zero temperature. Besides a coherent Larmor oscillation, we find an additional collective oscillation at higher frequencies, emerging as a coherent many-magnon effect at low temperatures. Using numerical and analytical methods, we analyze the oscillation frequency and decay time of this coherent current-mode versus temperature and magnetic field.Comment: 4 pages, 5 figures (and supplemental material: 4 pages, 6 figures

Rohstoffsicherung

Mineralische Rohstoffe sind eine wichtige Grundlage wirtschaftlicher Entwicklung. Im Unterschied zu anderen freiraumbezogenen Nutzungs- und Funktionsbereichen existiert keine Fachplanung zur Gewährleistung der Rohstoffversorgung, weswegen der Raumordnung eine hohe Bedeutung für die Rohstoffsicherung zukommt

The impact of lateral heat and water fluxes from thermokarst lakes on tundra landscape dynamics and permafrost degradation

Projected future warming of the Arctic will result in pronounced degradation of permafrost and thereby trigger large-scale landscape and ecosystem changes. In this context, the formation and expansion of thermokarst lakes play a key role as thermokarst dynamics represent a mechanism for abrupt degradation of permafrost soils. Using the process-based model CryoGrid-3 coupled to a model description of lake dynamics (FLake), we explore how the thermal and hydrological state of different permafrost landscapes is affected by an explicit consideration of the interaction between lakes and surrounding permafrost environments. Hereby we especially investigate the role of lateral fluxes in affecting the landscape heat and water budgets

Autonomic and circulatory alterations persist despite adequate resuscitation in a 5-day sepsis swine experiment.

Autonomic and vascular failures are common phenotypes of sepsis, typically characterized by tachycardia despite corrected hypotension/hypovolemia, vasopressor resistance, increased arterial stiffness and decreased peripheral vascular resistance. In a 5-day swine experiment of polymicrobial sepsis we aimed at characterizing arterial properties and autonomic mechanisms responsible for cardiovascular homeostasis regulation, with the final goal to verify whether the resuscitation therapy in agreement with standard guidelines was successful in restoring a physiological condition of hemodynamic profile, cardiovascular interactions and autonomic control. Twenty pigs were randomized to polymicrobial sepsis and protocol-based resuscitation or to prolonged mechanical ventilation and sedation without sepsis. The animals were studied at baseline, after sepsis development, and every 24 h during the 3-days resuscitation period. Beat-to-beat carotid blood pressure (BP), carotid blood flow, and central venous pressure were continuously recorded. The two-element Windkessel model was adopted to study carotid arterial compliance, systemic vascular resistance and characteristic time constant τ. Effective arterial elastance was calculated as a simple estimate of total arterial load. Cardiac baroreflex sensitivity (BRS) and low frequency (LF) spectral power of diastolic BP were computed to assess autonomic activity. Sepsis induced significant vascular and autonomic alterations, manifested as increased arterial stiffness, decreased vascular resistance and τ constant, reduced BRS and LF power, higher arterial afterload and elevated heart rate in septic pigs compared to sham animals. This compromised condition was persistent until the end of the experiment, despite achievement of recommended resuscitation goals by administered vasopressors and fluids. Vascular and autonomic alterations persist 3 days after goal-directed resuscitation in a clinically relevant sepsis model. We hypothesize that the addition of these variables to standard clinical markers may better profile patients' response to treatment and this could drive a more tailored therapy which could have a potential impact on long-term outcomes

Управління ресурсним потенціалом вугільних шахт

Викладено методичні підходи з удосконалення управління ресурсним потенціалом вугільних шахт на основі використання двокритерійної моделі градієнтного регулювання їх потужності. Запропоновано механізм оцінки параметрів стану шахт у процесі зміни їх потужності, який полягає у визначенні впливу градієнтної зміни ліміту наявного ресурсного потенціалу на рівень інвестиційної привабливості підприємства, що науково обґрунтовує їх віднесення до певних приватизаційних груп. Удосконалено процесний підхід до управління ресурсним потенціалом вугільних шахт в умовах невизначеності. Запропоновано організаційно-економічний механізм управління ресурсним потенціалом вугільних шахт в умовах нестійкого попиту на вугілля. Розрахована на фахівців з управління підприємствами вугільної промисловості та інженерно-технічних працівників, а також учених, викладачів вищих навчальних закладів

Real-time energy dynamics in spin-1/2 Heisenberg chains

We study the real-time dynamics of the local energy density in the spin-1/2 XXZ chain starting from initial states with an inhomogeneous profile of bond energies. Numerical simulations of the dynamics of the initial states are carried out using the adaptive time-dependent density matrix renormalization group method. We analyze the time dependence of the spatial variance associated with the local energy density to classify the dynamics as either ballistic or diffusive. Our results are consistent with ballistic behavior both in the massless and the massive phase. We also study the same problem within Luttinger Liquid theory and obtain that energy wave-packets propagate with the sound velocity. We recover this behavior in our numerical simulations in the limit of very weakly perturbed initial states.Comment: 15 pages, 21 figures, version as published, minor stylistic change