35 research outputs found
Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy
Time-resolved measurement techniques are opening a window on nonequilibrium
quantum phenomena that is radically different from the traditional picture in
the frequency domain. The simulation and interpretation of nonequilibrium
dynamics is a conspicuous challenge for theory. This paper presents a novel
approach to quantum many-body dynamics that is based on a Hamiltonian
formulation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of
equations of motion for reduced density matrices. These equations have an
underlying symplectic structure, and we write them in the form of the classical
Hamilton equations for canonically conjugate variables. Applying canonical
perturbation theory or the Krylov-Bogoliubov averaging method to the resulting
equations yields a systematic approximation scheme. The possibility of using
memory-dependent functional approximations to close the Hamilton equations at a
particular level of the hierarchy is discussed. The geometric structure of the
equations gives rise to reduced geometric phases that are observable even for
noncyclic evolutions of the many-body state. The formalism is applied to a
finite Hubbard chain which undergoes a quench in on-site interaction energy U.
Canonical perturbation theory, carried out to second order, fully captures the
nontrivial real-time dynamics of the model, including resonance phenomena and
the coupling of fast and slow variables.Comment: 17 pages, revise
Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding
The motion of massless Dirac-electrons in graphene mimics the propagation of
photons. This makes it possible to control the charge-carriers with components
based on geometrical-optics and has led to proposals for an all-graphene
electron-optics platform. An open question arising from the possibility of
reducing the component-size to the nanometer-scale is how to access and
understand the transition from optical-transport to quantum-confinement. Here
we report on the realization of a circular p-n junction that can be
continuously tuned from the nanometer-scale, where quantum effects are
dominant, to the micrometer scale where optical-guiding takes over. We find
that in the nanometer-scale junction electrons are trapped in states that
resemble atomic-collapse at a supercritical charge. As the junction-size
increases, the transition to optical-guiding is signaled by the emergence of
whispering-gallery modes and Fabry-Perot interference. The creation of tunable
junctions that straddle the crossover between quantum-confinement and
optical-guiding, paves the way to novel design-architectures for controlling
electronic transport.Comment: 16 pages, 4 figure
Some open questions in TDDFT: Clues from Lattice Models and Kadanoff-Baym Dynamics
Two aspects of TDDFT, the linear response approach and the adiabatic local
density approximation, are examined from the perspective of lattice models. To
this end, we review the DFT formulations on the lattice and give a concise
presentation of the time-dependent Kadanoff-Baym equations, used to asses the
limitations of the adiabatic approximation in TDDFT. We present results for the
density response function of the 3D homogeneous Hubbard model, and point out a
drawback of the linear response scheme based on the linearized Sham-Schl\"uter
equation. We then suggest a prescription on how to amend it. Finally, we
analyze the time evolution of the density in a small cubic cluster, and compare
exact, adiabatic-TDDFT and Kadanoff-Baym-Equations densities. Our results show
that non-perturbative (in the interaction) adiabatic potentials can perform
quite well for slow perturbations but that, for faster external fields, memory
effects, as already present in simple many-body approximations, are clearly
required.Comment: 15 pages, submitted to Chemical Physic
Recipes for spin-based quantum computing
Technological growth in the electronics industry has historically been
measured by the number of transistors that can be crammed onto a single
microchip. Unfortunately, all good things must come to an end; spectacular
growth in the number of transistors on a chip requires spectacular reduction of
the transistor size. For electrons in semiconductors, the laws of quantum
mechanics take over at the nanometre scale, and the conventional wisdom for
progress (transistor cramming) must be abandoned. This realization has
stimulated extensive research on ways to exploit the spin (in addition to the
orbital) degree of freedom of the electron, giving birth to the field of
spintronics. Perhaps the most ambitious goal of spintronics is to realize
complete control over the quantum mechanical nature of the relevant spins. This
prospect has motivated a race to design and build a spintronic device capable
of complete control over its quantum mechanical state, and ultimately,
performing computations: a quantum computer.
In this tutorial we summarize past and very recent developments which point
the way to spin-based quantum computing in the solid-state. After introducing a
set of basic requirements for any quantum computer proposal, we offer a brief
summary of some of the many theoretical proposals for solid-state quantum
computers. We then focus on the Loss-DiVincenzo proposal for quantum computing
with the spins of electrons confined to quantum dots. There are many obstacles
to building such a quantum device. We address these, and survey recent
theoretical, and then experimental progress in the field. To conclude the
tutorial, we list some as-yet unrealized experiments, which would be crucial
for the development of a quantum-dot quantum computer.Comment: 45 pages, 12 figures (low-res in preprint, high-res in journal)
tutorial review for Nanotechnology; v2: references added and updated, final
version to appear in journa
Metallic, magnetic and molecular nanocontacts
Scanning tunnelling microscopy and break-junction experiments realize metallic and molecular nanocontacts that act as ideal one-dimensional channels between macroscopic electrodes. Emergent nanoscale phenomena typical of these systems encompass structural, mechanical, electronic, transport, and magnetic properties. This Review focuses on the theoretical explanation of some of these properties obtained with the help of first-principles methods. By tracing parallel theoretical and experimental developments from the discovery of nanowire formation and conductance quantization in gold nanowires to recent observations of emergent magnetism and Kondo correlations, we exemplify the main concepts and ingredients needed to bring together ab initio calculations and physical observations. It can be anticipated that diode, sensor, spin-valve and spin-filter functionalities relevant for spintronics and molecular electronics applications will benefit from the physical understanding thus obtained
The 2021 room-temperature superconductivity roadmap.
Designing materials with advanced functionalities is the main focus of contemporary solid-state physics and chemistry. Research efforts worldwide are funneled into a few high-end goals, one of the oldest, and most fascinating of which is the search for an ambient temperature superconductor (A-SC). The reason is clear: superconductivity at ambient conditions implies being able to handle, measure and access a single, coherent, macroscopic quantum mechanical state without the limitations associated with cryogenics and pressurization. This would not only open exciting avenues for fundamental research, but also pave the road for a wide range of technological applications, affecting strategic areas such as energy conservation and climate change. In this roadmap we have collected contributions from many of the main actors working on superconductivity, and asked them to share their personal viewpoint on the field. The hope is that this article will serve not only as an instantaneous picture of the status of research, but also as a true roadmap defining the main long-term theoretical and experimental challenges that lie ahead. Interestingly, although the current research in superconductor design is dominated by conventional (phonon-mediated) superconductors, there seems to be a widespread consensus that achieving A-SC may require different pairing mechanisms.In memoriam, to Neil Ashcroft, who inspired us all
Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF
We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = Rc, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical Rc by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M-1 prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇Rχ(R) and ∇Rn(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation—an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n)
Ferromagnetic Kondo Effect in a Triple Quantum Dot System
We propose that a simple device of three laterally-coupled quantum dots, the central one contacted by metal leads, can realize the ferromagnetic Kondo model, which is characterized by interesting properties like a non-analytic inverted zero-bias anomaly and an extreme sensitivity to a magnetic field. Furthermore, by tuning the gate voltages of the lateral dots, this device may allow to study the transition from ferromagnetic to antiferromagnetic Kondo effect, a simple case of a Berezinskii-Kosterlitz-Thouless transition. We model the device by three coupled Anderson impurities that we study by numerical renormalization group. We calculate the single-particle spectral function of the central dot, which at zero frequency is proportional to the zero-bias conductance, across the transition, both in the absence and in the presence of a magnetic field