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Theoretical Developments for the Real-Time Description and Control of Nanoscale Systems

Hopjan, Miroslav LU (2018)
Abstract (Swedish)
In the age of miniaturization where the physical systems approach the nanoscale limit and
where more complex materials are created there is necessity for understanding in terms of
quantum mechanics. The understanding then opens and gives possibilities for manipulation
and engineering of such systems and thus practical applications.

Quantum mechanics states that the electron cannot be characterized as a classical particle
with a certain position and momentum. Instead the electron is described by the wave
function, which gives the probability for the electron to be at certain space. The wave
property of the electron then affects its behavior in nanoscale systems. In many electron
systems the wave function... (More)
In the age of miniaturization where the physical systems approach the nanoscale limit and
where more complex materials are created there is necessity for understanding in terms of
quantum mechanics. The understanding then opens and gives possibilities for manipulation
and engineering of such systems and thus practical applications.

Quantum mechanics states that the electron cannot be characterized as a classical particle
with a certain position and momentum. Instead the electron is described by the wave
function, which gives the probability for the electron to be at certain space. The wave
property of the electron then affects its behavior in nanoscale systems. In many electron
systems the wave function concept becomes even more important.

In modern experiments, in order to learn more about the system, the strong and time-
dependent external forces are often used to disturb the system out of its equilibrium state.
One example is a pump-probe experiment where the strong electromagnetic pulse is used
to transfer energy into the system and thus excite it into higher energy state. The second
electromagnetic pulse can be used to probe the excited system and study relaxation processes
taking place in the system.

Another experiment which can reveal the physical mechanism in a system is transport experiments
where a central region is connected to leads which are electrically biased and an
electric current is running through the central region. The leads are responsible for the
excitation of the central region to higher energies but at the same time for the dissipation
processes. Also, the magnetic field can be used to induce the nonequilibrium situation
which can be useful for understanding the underlying physical processes. Ultimately the
external time-dependent forces can also be used to manipulate with the system.

This bring us towards the main topic of the thesis. How to theoretically describe the influence
of the external forces on a many electron system which cannot be longer described
as a set of independent classical particles (in similar way as i.e. bouncing balls in classical
gases)? In these systems quantum mechanics requires to construct a many-body wave function
- an object which accounts for all possible effects of the interactions. The wave function
contains full information about the system from which one can access and possibly predict
reduced quantities which can be measured.

However, to obtain the full many-body wave function and its time evolution is a difficult
task, and the system size for which the wave function can be reached is limited. To by-
pass the computation of the full wave function alternative methods designed directly for
the reduced quantities can be developed; among them, popular ones are the formalism of
Green’s Function and Density Functional Theory. These methods in principle account exactly
for the many-body effects, however in practice the approximations are used. In addition,
correspondingly to the experiment, the methods need to be extended to account for the
nonequilibrium regime.

This thesis focus on improvements of the description of the electron-electron correlation
effects in nonequilibrium nanosystems. We mainly focus on developments of two nonequi-
librium methods, namely the formalism of Nonequilibrium Green’s Function and Time De-
pendent Density Functional Theory and we explore the possibility to improve existing ap-
proximations in these theories. A smaller part of the thesis is devoted to the Exact Diagon-
alization method which provides a numerically exact description of small systems.

The outcome of the thesis will contribute to better understanding, improved description
and consequently more efficient engineering of nanosystems where correlation effects are
important. In particular, we consider the effect of i) strong electron-electron correlation,
ii) electron-nuclear interactions, iii) disorder + interactions and iv) magnetic impurities. (Less)
Abstract
In this thesis we focus on improvements of the description of the electron-electron correlation effects in nonequilibrium nanosystems. We mainly focus on developments of two nonequilibrium methods, namely the formalism of Nonequilibrium Green’s Function and Time Dependent Density Functional Theory and we explore the possibility to improve existing approximations in these theories. A smaller part of the thesis is devoted to the Exact Diagonalization method which provides a numerically exact description of small systems.

Paper I: We review the current methods for description of correlated materials in nonequilibrium and their connection to pump-probe spectroscopy.

Paper II: We propose a hybrid method for the real time... (More)
In this thesis we focus on improvements of the description of the electron-electron correlation effects in nonequilibrium nanosystems. We mainly focus on developments of two nonequilibrium methods, namely the formalism of Nonequilibrium Green’s Function and Time Dependent Density Functional Theory and we explore the possibility to improve existing approximations in these theories. A smaller part of the thesis is devoted to the Exact Diagonalization method which provides a numerically exact description of small systems.

Paper I: We review the current methods for description of correlated materials in nonequilibrium and their connection to pump-probe spectroscopy.

Paper II: We propose a hybrid method for the real time dynamics of strongly correlated materials which includes memory effects beyond the adiabatic local density approximation.

Paper III: We study the dynamics of desorption of a molecule from a surface with different levels of approximation for both the nuclear and the electronic part. We compare a full quantum mechanical treatment to the Ehrenfest
approximation for the molecule and perturbative approximations for the electrons.

Paper IV: We develop a theory of current-induced forces within Adiabatic Ehrenfest Dynamics which includes effects of electron-electron interactions. We study a dependence of the electronic friction on interaction strength.
We also benchmark it against nonadiabatic Ehrenfest dynamics.

Paper V: We study the competition of interaction and disorder in systems with steady state currents - in transport and ring geometries. We exactly define the exchange-correlation screening of the disorder by the interaction
effects via Kohn–Sham construction of DFT.

Paper VI: We study a competition between Kondo and RKKY interaction in small clusters of Periodic Anderson Model (ring geometries), we construct a nonequilibrium Doniach-phase like diagram. We then determine an
optimal pulse to induce transitions with the highest fidelity. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Bonitz, Michael, Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität Kiel, Germany
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Green’s Function, DFT, TDDFT, Hubbard Model, Many-Body Perturbation Theory, Strongly Correlated Systems, Quantum Transport, Disorder, Ehrenfest Dynamics, Electronic Friction, Exact Diagonalization, Periodic Anderson Model, Fysicumarkivet A:2018:Hopjan
pages
186 pages
publisher
Lund University, Faculty of Science, Department of Physics, Division of Mathematical Physics
defense location
Rydberg lecture hall, Department of Physics, Sölvegatan 14A, Lund
defense date
2018-02-23 13:15
ISBN
978-91-7753-500-3
978-91-7753-499-0
language
English
LU publication?
yes
id
62d34681-2351-4b16-9438-0ad93ad04526
date added to LUP
2018-01-28 18:16:59
date last changed
2018-05-29 09:20:54
@phdthesis{62d34681-2351-4b16-9438-0ad93ad04526,
  abstract     = {In this thesis we focus on improvements of the description of the electron-electron correlation effects in nonequilibrium nanosystems. We mainly focus on developments of two nonequilibrium methods, namely the formalism of Nonequilibrium Green’s Function and Time Dependent Density Functional Theory and we explore the possibility to improve existing approximations in these theories. A smaller part of the thesis is devoted to the Exact Diagonalization method which provides a numerically exact description of small systems.<br/><br/>Paper I: We review the current methods for description of correlated materials in nonequilibrium and their connection to pump-probe spectroscopy.<br/><br/>Paper II: We propose a hybrid method for the real time dynamics of strongly correlated materials which includes memory effects beyond the adiabatic local density approximation.<br/><br/>Paper III: We study the dynamics of desorption of a molecule from a surface with different levels of approximation for both the nuclear and the electronic part. We compare a full quantum mechanical treatment to the Ehrenfest<br/>approximation for the molecule and perturbative approximations for the electrons.<br/><br/>Paper IV: We develop a theory of current-induced forces within Adiabatic Ehrenfest Dynamics which includes effects of electron-electron interactions. We study a dependence of the electronic friction on interaction strength.<br/>We also benchmark it against nonadiabatic Ehrenfest dynamics.<br/><br/>Paper V: We study the competition of interaction and disorder in systems with steady state currents - in transport and ring geometries. We exactly define the exchange-correlation screening of the disorder by the interaction<br/>effects via Kohn–Sham construction of DFT.<br/><br/>Paper VI: We study a competition between Kondo and RKKY interaction in small clusters of Periodic Anderson Model (ring geometries), we construct a nonequilibrium Doniach-phase like diagram. We then determine an<br/>optimal pulse to induce transitions with the highest fidelity.},
  author       = {Hopjan, Miroslav},
  isbn         = {978-91-7753-500-3},
  keyword      = {Green’s Function,DFT,TDDFT,Hubbard Model,Many-Body Perturbation Theory,Strongly Correlated Systems,Quantum Transport,Disorder,Ehrenfest Dynamics,Electronic Friction,Exact Diagonalization,Periodic Anderson Model,Fysicumarkivet A:2018:Hopjan},
  language     = {eng},
  pages        = {186},
  publisher    = {Lund University, Faculty of Science, Department of Physics, Division of Mathematical Physics},
  school       = {Lund University},
  title        = {Theoretical Developments for the Real-Time Description and Control of Nanoscale Systems},
  year         = {2018},
}