Quantum Transport Theory Group

Quantum Transport Theory Group at the University of Delaware pursues a broad spectrum of research problems where interplay of quantum coherence and disorder, strong electron correlations, spin and charge dynamics brings forth novel phenomena in nanostructured condensed matter systems. Currently we are working on: mesoscopic spintronics, molecular electronics, quantum information processing and entanglement in solids, quantum (wave) chaos in glasses and mesoscopic disordered conductors, strongly correlated systems far from equilibrium ... We are colaborating with experimentalists at UD on projects in magnetic tunel junctions and shot noise. Every day we employ combination of analytical and High Performance computational techniques on local Linux workstations, Beowulf clusters, and remote supercomputing facilities to move the boundaries of knowledge.

Our research interest explained for nonspecialist:

Research interest of QTT group falls into the broad area of theoretical and computational condensed matter physics which deals with a plethora of phenomena emerging as a collective effect of huge number of elementary particles, that is usually impossible to decipher from the microscopic laws governing individual particles. Specifically, we try to choose problems where quantum-mechanical effects show up in systems which live on mesoscales. The greek word mesos means "something in between", and the term "mesoscopic" was coined by the bard of theoretical physics N. Van Kampen to denote the realm in between the world of atoms and usual bulk materials. Over the past two decades, the exciting field of mesoscopic physics has been developed to account for phenomena where traditional statistical physics description of multiparticle systems in terms of average values obtained for material constants in the thermodynamic limit breaks down, and one has to worry about specific quantum features of each electron and full statistical distribution of physical quantities. This has become a multifaceted field of research exploring systems as diverse as: nanoscale metallic and semiconducting systems at extremely low temperatures (where phase relaxation time, determined by electron-electron collision rate at these temperatures, can be orders of magnitude longer than the momentum relaxation time), inhomogeneous structures composed of superconductors and ferromagnets brought into the contact with mesoscopic samples, and even large molecules belonging to the scope of organic chemistry and molecular biology. The complexity of condensed matter phenomena requires employment of almost all major physical concepts, such as mechanics, electromagnetism, thermodynamics, statistical mechanics, relativity, quantum mechanics, and quantum field theory, including a wide range of advanced mathematical and computational methods. Nevertheless, such research also relies heavily on intuition (including years of building the ``quantum intuition'') invoked when one tries to explain present experiments and predict new ones.

Generally speaking, we have been looking into quantum effects in two different types of systems, particularly focusing on their impact on transport:   I. Transport phenomena in mesoscopic systems where most of essential physics is captured by a picture of quantum propagation of noninteracting quasiparticles. Here we employ quantum transport methods [like Landauer-Buttiker scattering approach or mesoscopic Kubo formula] to study the conduction in disordered , ballistic and spintronic [where the spin of the electron matters and an envisaged manipulation of the spin by controlling spin-orbit couplings may allow new quantum technologies] nanometer-scale structures. Sometimes, we also use the Bloch-Boltzmann formalism and other semiclassical limits to get the reference results describing particles that propagate classically along straight lines between scattering events, thereeby neglecting quantum superpositions along all possible trajectories. These superpositions are the salient feature of quantum states, and are taken into account by the mesoscopic transport techniques making it possible to account for the experiments (brought about by technological advances in nanofabrication) exhibiting celebrated quantum interference effects and holistic nature of quantum mechanics (where whole sample, together with various leads and measuring apparatus, represents one indivisible system full of nonlocal surprises), such as: small corrections to semiclassical picture (weak localization, conductance and other mesoscopic fluctuations); or dramatic deviations from semiclassics like Anderson localization , conductance quantization in ballistic point contacts, and Aharonov-Bohm flux induced effects on the conductance and on the thermodynamic properties (persistent currents) of mesoscopic rings. When these systems are in equilibrium, one can investigate how chaotic behavior of their classical counterparts affects energy levels and eigenstates---a topic of quantum chaos, random matrix theory, and beyond. Moreover, the same paradigm is unveiled in numerous other fields of physics (and elsewhere, like in statistical finance ) which are now encompassed by ``wave chaology'': microwave cavities, light propagation in disordered media, wireless phone signal propagation in buildings, photonic crystals, mean-field dynamics of Bose-Einstein condensates, vibrations in glasses, etc. It has been conjectured that, generically, the quantum energy levels of individual, classically integrable systems (those which have as many conserved quantities as degrees of freedom) are distributed like independent random numbers, and that those of classically chaotic systems are distributed like the eigenvalues of random matrices. Likewise, the eigenfunctions of the Schrodinger equation have been conjectured to behave like Gaussian random functions in the semiclassical (short wavelength) limit. However, in mesoscopic disordered systems, which are metallic but with finite conductance, significant daparture from Random Matrix Theory picture can be observed, signaling the presence of long-range spatial correlations (caused by massless modes) which underlie mesoscopic fluctuations of global quantities (like conductance) and, thereby, the absence of self-averaging in mesoscopic systems.      II. Quantum many-body systems where interactions correlate the motion of electrons, often leading to new exotic states of matter (such as superconductivity). Strong correlations entail either the introduction of better (renormalized) quasiparticles, or a complete breakdown of single-particle picture. In the latter case we use a recently developed nonperturbative many-body approach: dynamical mean-field theory and its inhomogeneous derivative, that extend mean-field archetype from classical statistical  mechanics to quantum problems where one can understand fully quantum fluctuations in time, while ignoring their spatial properties (such local description becomes exact in large enough dimensions). Among other things, it allows us to tackle  problems in which strongly correlated materials are brought into the contact with a superconductor (proximity effect)  to form an unconventional Josephson junction , or to study quantum phase transitions (occurring at zero temperature when a non-thermal parameter, like preassure or composition, is tuned causing quantum fluctuations and often dramatic qualitative change in the lowest energy ground state of a quantum Hamiltonian) in disordered strongly correlated systems. Mesoscopic physics has led to an enormous deepening of our  knowledge about transport in condensed matter systems, and we are currently combining these techniques with dynamical mean-field theory to describe non-equilibrium phenomena in strongly correlated systems.

The beauty of research in these subjects is that one has to dwell into the  fundamental quantum-mechanical problems, while reshaping at the same time the future of technology by reachingthe realm of nanoelectronics. Other related fundamental problems (that we in spare time on weekends) encompass: decoherence in open systems which seeks to explain how the classical world arises from an underlying quantum one (through the destruction of linear superpositions and therefore all of the intriguing mesoscopic phenomena) at large length scales and/or high temperatures due to the coupling to an environment; the transition from quantum to classical physics in non-integrable systems; the dissipation in quantum systems (the second principal consequence of the coupling to the environment) and quantum limits to the second law of thermodynamics; and fashionable, but conceptually important, quantum information theory and computing.

 
 
 

Auspicious links for specialist:

Quantum Point Contacts
Classical Point Contacts
Transport theory of GMR
Random Matrix Theory of Quantum Transport
Mesoscopic Quantum Physics and Quantum Chaos [look for Altshuler's lectures] [also B.D. Simons' page ]
Superconductivity
Spintronics [by Prof. J. Fabian]
Mesoscopic Spintronics
Spintronics at Groningen