This award supports theoretical research and education on dynamics of strongly correlated nanostructures out of equilibrium. The project will contribute to our understanding of how to describe interacting quantum systems carrying currents imposed by leads kept at different chemical potentials or temperatures, a subject of fundamental importance for theory and experiment with significant practical applications. The research combines several topical areas: the study of strongly correlated electron systems which seeks to understand new collective phenomena brought about by interactions; the study of nanostructures involving problems of transport and spectral properties analyzed in restricted geometries with emphasis on the interplay between disorder and interactions; nonequilibrium thermodynamics in many-body quantum systems. All these areas provide essential components in the study of the dynamics in nanoscale devices. Advances in fabrication have made nanodevices accessible to experiment. So, fundamental issues of nonequilibrium physics can be tested experimentally with a high degree of precision. This requires detailed theoretical predictions that the PI aims to provide.
The theoretical approach to be pursued is based on scattering theory with the scattering eigenstates constructed via the Bethe Ansatz. The eigenstates are defined on the open infinite line with boundary conditions set by the bias voltage or temperature drop imposed by the leads. One obtains explicit predictions for non-equilibrium properties, such as charge and heat currents, entropy production and dissipation, as well as for quantities central in mesoscopics such as decoherence times and relaxation rates. All of these quantities can be experimentally tested.
The PI will apply this approach to concrete models of nonequilibrium systems, including: the two leads Anderson model to model a quantum dot, the two leads Holstein model to model molecules in break junctions, and the two leads AB interferometer. The PI aims to develop precise predictions that can be compared with experiment and may lead to new insights about steady-state behaviors.
This project contributes to the education of postdocs and student researchers in learning advanced theoretical techniques and their application to concrete experimental systems. The PI is also currently writing a book on nonperturbative approaches to quantum impurity systems.
NONTECHNICAL SUMMARY
This award supports theoretical research and education on dynamics of electrons which interact strongly with each other in systems of atoms that are some ten to hundred times smaller than the diameter of a human hair. The PI will focus on situations where the electrons in these nanostructures are not in the balanced and tranquil state of equilibrium. Rather, the PI will investigate situations where the electrons are far from equilibrium as might happen when a voltage is applied across a nanostructure forcing the electrons to move. Systems far from equilibrium are not well understood. The correlated motion of electrons that results from their strong interaction provides additional complexity, but is an important ingredient to include in order to develop the theoretical and conceptual tools that enable the modeling and design of the necessarily quantum mechanical electronic devices that may be developed on the nanoscale.
Postdocs and student researchers will be involved in the research, which will contribute to their education in advanced theoretical techniques and the application of these techniques to materials and systems at the blurry interface of materials and devices on the nanoscale.
Non-equilibrium phenomena are ubiquitous in nature, yet are very poorly understood. They appear in great variety both in classical and in quantum physics. Examples from classical physics are: turbulence, fractures, rainfall, flow and overflow of rivers. Quantum mechanical examples are: time evolution of quantum states (quench dynamics), transport phenomena, scattering, periodically driven systems, heat flow across quantum impurities coupled to leads held at different temperatures and voltages. In contrast to equilibrium phenomena where a universal framework has been provided more than a century ago (by Boltzmann) no such framework exists when systems are out of equilibrium, no general minimization procedure or variational principle has been identified. Recent experiments, however, have started probing nonequilibrium dynamics under very controlled and precise conditions. Optically trapped ultra cold atomic cases, for example, can be thermally isolated from their environment and are therefore ideal for quench experiments where the unitray time evolution of a quantum state is followed and correlation encoded in it are monitored. Nano-structures provide ideal set ups where steady state nonequilibrium currents interplay and compete with strong correlations that develop on a quantum dot through which they flow. That is the background to the work of the PI. Together with his students he developed an approach that allows the calculation of the properties – typically encoded in terms of correlation functions – of a state evolving in time under the impact of a Hamiltonian. Much of the work concentrated on bosons moving on a line and interacting via short range potential. The corresponding Hamiltonian, the Lieb-Liniger Hamiltonian, is integrable and therefore possesses a large number of conserved charges that commute with it and influence the evolution of the quantum gas system. Questions of interest are whether the system equilibrates, namely, reaches a steady limit and whether this limit is thermal, described by a Gibbs ensemble or whether a generalized ensemble is reached. Several states were studies: starting from a Mott Insulator with the bosons arranged is a periodic array and then allowed to interact and propagate, starting from a BEC, a Bose-Einstein condensate, or starting with BEC packets that collide with each other. The approach developed was also applied to the Heisenberg chain, an array of spins on a lattice interacting via spin exchange. This is the basic model of magnetism with a wide range of experimental realizations and applications, one of which is in the field of quantum information with the spins playing the role of qubits. Again the basic questions touch on time evolution of the quantum states for which our formalism provides nice answers. Displayed are plots (Figures: Magnetization evolution) of the evolution of magnetization from initial states of flipped spins. The formation of bound states and their weight and velocity is clearly visible as a function of the spin anisotropy. A particularly interesting case of time evolution occurs when the system cannot reach equilibration. This occurs under a variety of interesting circumstances, for example when a quantum dot is attched to two leads or more held at different temperatures or voltages, or when the initial state in a magnet consists of a domain wall with half the spins being flipped up and halps flipped down and the size of the system is sent to infinity. The system may then reach a nonequilibrium steady state with constant currents flowing, energy and charge currents in the first example, spin current in the second. Nano-devices provide a practical setup of such dynamics with many interesting features. The PI considered a steady state heat current in a molecular device with the current driven across a single molecule coupled to electron baths at different temperatures and also to the a bosonic bath describing vibrational modes (Figure: Transistor). With his collaborators the PI obtained exact expression for the cases where the large molecules have small electron-phonon coupling. At low temperatures the heat current is found to have a power-law behaviorwith respect to the temperature difference with the power depending on the nature of the bosonic bath (Figure: Heat cuonductance). The device considered can also have interesting practical application allowing control of the current through it vibratinal coupling. The PI has carried out a number of studies of various systems out of equilibrium with theoretical and perhaps practical impact. The hope is the reach a deep and detailed understanding of the principles underlying nonequilbrium dynamics on the quantum level and gain a better control of quantum devices.
