{"id":{"repo_id":"freiburg-diss","oai_identifier":"oai:freidok.uni-freiburg.de:1328"},"canonical_url":"https://search.dev.ndltd.org/etd/freiburg-diss/oai:freidok.uni-freiburg.de:1328","repository":{"repo_id":"freiburg-diss","name":"University of Freiburg","base_url":"https://freidok.uni-freiburg.de/oai/oai2.php"},"display":{"title":"Conductance of single-electron devices from imaginary-time path integrals","abstract":"In this thesis we study two nanoscopic systems -- the metallic
single electron transistor and semiconductor quantum dots -- which
are important models for research on molecular electronics and
quantum computing. Our theoretical description is based on a
path-integral expression for the current autocorrelation function
which can be related to the conductance using linear response
theory. To circumvent the dynamical sign problem in the numerical
determination of real-time correlation functions, we calculated
the current autocorrelator for imaginary times and employed a
scheme for the analytical continuation of the numerical data.
For the metallic single electron transistor we used quantum Monte
Carlo methods for the evaluation of the path integrals. The
numerical data for the imaginary-time correlation function was
analytically continued to the real-time spectral function using
methods for the solution of inverse problems (SVD, MaxEnt). The
comparison of the results with recent experimental studies showed
excellent agreement between theory and experiment over the whole
range of system parameters.
In the description of semiconductor quantum dots we have used a
microscopic model to address the shortcomings of the (frequently
used) constant interaction model. As in the case of the metallic
single electron transistor, the current correlation function could
be expressed as a path-integral, although the resulting equations
are too complicated for an evaluation by Monte Carlo methods. The
application of the stationary phase approximation, on the other
hand, leads to a formulation in terms of a selfconsistent solution
of the Poisson equation and the Hartree equations for the single
particle states which have been applied successfully to the
theoretical description of transport in semiconductor quantum
dots.","abstract_html":"In this thesis we study two nanoscopic systems -- the metallic <br>single electron transistor and semiconductor quantum dots -- which <br>are important models for research on molecular electronics and <br>quantum computing. Our theoretical description is based on a <br>path-integral expression for the current autocorrelation function <br>which can be related to the conductance using linear response <br>theory. To circumvent the dynamical sign problem in the numerical <br>determination of real-time correlation functions, we calculated <br>the current autocorrelator for imaginary times and employed a <br>scheme for the analytical continuation of the numerical data. <br> <br>For the metallic single electron transistor we used quantum Monte <br>Carlo methods for the evaluation of the path integrals. The <br>numerical data for the imaginary-time correlation function was <br>analytically continued to the real-time spectral function using <br>methods for the solution of inverse problems (SVD, MaxEnt). The <br>comparison of the results with recent experimental studies showed <br>excellent agreement between theory and experiment over the whole <br>range of system parameters. <br> <br>In the description of semiconductor quantum dots we have used a <br>microscopic model to address the shortcomings of the (frequently <br>used) constant interaction model. As in the case of the metallic <br>single electron transistor, the current correlation function could <br>be expressed as a path-integral, although the resulting equations <br>are too complicated for an evaluation by Monte Carlo methods. The <br>application of the stationary phase approximation, on the other <br>hand, leads to a formulation in terms of a selfconsistent solution <br>of the Poisson equation and the Hartree equations for the single <br>particle states which have been applied successfully to the <br>theoretical description of transport in semiconductor quantum <br>dots.","abstract_has_math":false,"creators":["Theis, Christoph"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Grabert, Hermann"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T02:22:10Z","subjects":["Pfadintegral-Monte Carlo","Coherent State Pfadintegral","Coulomb Blockade","SET-Transistor","Path Integral Monte Carlo","Inverse Problem","Quantum Dots"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://freidok.uni-freiburg.de/data/1328","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Grabert, Hermann"]},{"key":"dc:creator","label":"Author","values":["Theis, Christoph"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["DoctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Pfadintegral-Monte Carlo","Coherent State Pfadintegral","Coulomb Blockade","SET-Transistor","Path Integral Monte Carlo","Inverse Problem","Quantum Dots"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we study two nanoscopic systems -- the metallic
single electron transistor and semiconductor quantum dots -- which
are important models for research on molecular electronics and
quantum computing. Our theoretical description is based on a
path-integral expression for the current autocorrelation function
which can be related to the conductance using linear response
theory. To circumvent the dynamical sign problem in the numerical
determination of real-time correlation functions, we calculated
the current autocorrelator for imaginary times and employed a
scheme for the analytical continuation of the numerical data.
For the metallic single electron transistor we used quantum Monte
Carlo methods for the evaluation of the path integrals. The
numerical data for the imaginary-time correlation function was
analytically continued to the real-time spectral function using
methods for the solution of inverse problems (SVD, MaxEnt). The
comparison of the results with recent experimental studies showed
excellent agreement between theory and experiment over the whole
range of system parameters.
In the description of semiconductor quantum dots we have used a
microscopic model to address the shortcomings of the (frequently
used) constant interaction model. As in the case of the metallic
single electron transistor, the current correlation function could
be expressed as a path-integral, although the resulting equations
are too complicated for an evaluation by Monte Carlo methods. The
application of the stationary phase approximation, on the other
hand, leads to a formulation in terms of a selfconsistent solution
of the Poisson equation and the Hartree equations for the single
particle states which have been applied successfully to the
theoretical description of transport in semiconductor quantum
dots.","In dieser Arbeit untersuchen wir den elektronischen Transport in
zwei nanoskopisches Systemen -- dem metallischen
Einzelelektronen-Transistor und dem Halbleiter-Quantenpunkt --
welche wichtige Modelle in der Erforschung der molekularen
Elektronik und auf dem Weg zur Verwirklichung eines
Quanten-Computers darstellen. Die theoretische Beschreibung
basiert auf dem Pfadintegral-Ausdruck für die
Strom-Autokorrelationsfunktion, welche durch die lineare
Antworttheorie mit dem Leitwert verknüpft werden kann. Um das
dynamische Vorzeichen-Problem in der numerischen Berechnung von
Realzeit-Korrelationsfunktionen zu umgehen, berechnen wir den
Strom-Autokorrelator für imaginäre Zeit und verwenden Methoden zur
analytischen Fortsetzung der numerischen Daten.
Für den metallischen Einzelelektronen-Transistor benutzen wir
Quanten-Monte Carlo Simulationen zur Auswertung des Pfadintegrals.
Um die numerischen Daten für die Imaginärzeit-Korrelationsfunktion
zu Realzeit-Spektren fortzusetzten, werden Methoden zur Lösung
inverser Probleme verwendet (SVD, MaxEnt). Der Vergleich der
theoretischen Ergebnisse mit neueren experimentellen
Untersuchungen zeigt eine hervorragende Übereinstimmung zwischen
Theorie und Experiment für den gesamten experimentell zugänglichen
Bereich der Systemparameter.
Bei der Beschreibung von Halbleiter-Quantenpunkten benutzen wir
ein mikroskopisches Modell, um die Unzulänglichkeiten der (häufig
verwendeten) Beschreibung durch eine konstante Wechselwirkung zu
vermeiden. Wie im Fall des metallischen
Einzelelektronen-Transistors kann die Strom-Korrelationsfunktion
durch ein Pfadintegral ausgedrückt werden, welches allerdings zu
kompliziert für eine Auswertung durch Monte Carlo Methoden ist.
Andererseits führt die Approximation der stationären Phase auf
eine Beschreibung in Form einer selbstkonsistenten Lösung der
Poisson-Gleichung und der Hartree-Gleichung für die
Einteilchen-Zustände, welche erfolgreich zur theoretischen
Beschreibung des Transportes in Halbleiter-Quantenpunkten
verwendet wurde."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Conductance of single-electron devices from imaginary-time path integrals","Leitwertberechnungen für Einzelelektronen-Schaltungen mittels Imaginärzeit-Pfadintegralen"]}]}],"canonical_facts":{"dc:contributor":["Grabert, Hermann"],"dc:creator":["Theis, Christoph"],"dc:description.abstract":["In this thesis we study two nanoscopic systems -- the metallic
single electron transistor and semiconductor quantum dots -- which
are important models for research on molecular electronics and
quantum computing. Our theoretical description is based on a
path-integral expression for the current autocorrelation function
which can be related to the conductance using linear response
theory. To circumvent the dynamical sign problem in the numerical
determination of real-time correlation functions, we calculated
the current autocorrelator for imaginary times and employed a
scheme for the analytical continuation of the numerical data.
For the metallic single electron transistor we used quantum Monte
Carlo methods for the evaluation of the path integrals. The
numerical data for the imaginary-time correlation function was
analytically continued to the real-time spectral function using
methods for the solution of inverse problems (SVD, MaxEnt). The
comparison of the results with recent experimental studies showed
excellent agreement between theory and experiment over the whole
range of system parameters.
In the description of semiconductor quantum dots we have used a
microscopic model to address the shortcomings of the (frequently
used) constant interaction model. As in the case of the metallic
single electron transistor, the current correlation function could
be expressed as a path-integral, although the resulting equations
are too complicated for an evaluation by Monte Carlo methods. The
application of the stationary phase approximation, on the other
hand, leads to a formulation in terms of a selfconsistent solution
of the Poisson equation and the Hartree equations for the single
particle states which have been applied successfully to the
theoretical description of transport in semiconductor quantum
dots.","In dieser Arbeit untersuchen wir den elektronischen Transport in
zwei nanoskopisches Systemen -- dem metallischen
Einzelelektronen-Transistor und dem Halbleiter-Quantenpunkt --
welche wichtige Modelle in der Erforschung der molekularen
Elektronik und auf dem Weg zur Verwirklichung eines
Quanten-Computers darstellen. Die theoretische Beschreibung
basiert auf dem Pfadintegral-Ausdruck für die
Strom-Autokorrelationsfunktion, welche durch die lineare
Antworttheorie mit dem Leitwert verknüpft werden kann. Um das
dynamische Vorzeichen-Problem in der numerischen Berechnung von
Realzeit-Korrelationsfunktionen zu umgehen, berechnen wir den
Strom-Autokorrelator für imaginäre Zeit und verwenden Methoden zur
analytischen Fortsetzung der numerischen Daten.
Für den metallischen Einzelelektronen-Transistor benutzen wir
Quanten-Monte Carlo Simulationen zur Auswertung des Pfadintegrals.
Um die numerischen Daten für die Imaginärzeit-Korrelationsfunktion
zu Realzeit-Spektren fortzusetzten, werden Methoden zur Lösung
inverser Probleme verwendet (SVD, MaxEnt). Der Vergleich der
theoretischen Ergebnisse mit neueren experimentellen
Untersuchungen zeigt eine hervorragende Übereinstimmung zwischen
Theorie und Experiment für den gesamten experimentell zugänglichen
Bereich der Systemparameter.
Bei der Beschreibung von Halbleiter-Quantenpunkten benutzen wir
ein mikroskopisches Modell, um die Unzulänglichkeiten der (häufig
verwendeten) Beschreibung durch eine konstante Wechselwirkung zu
vermeiden. Wie im Fall des metallischen
Einzelelektronen-Transistors kann die Strom-Korrelationsfunktion
durch ein Pfadintegral ausgedrückt werden, welches allerdings zu
kompliziert für eine Auswertung durch Monte Carlo Methoden ist.
Andererseits führt die Approximation der stationären Phase auf
eine Beschreibung in Form einer selbstkonsistenten Lösung der
Poisson-Gleichung und der Hartree-Gleichung für die
Einteilchen-Zustände, welche erfolgreich zur theoretischen
Beschreibung des Transportes in Halbleiter-Quantenpunkten
verwendet wurde."],"dc:format.medium":["application/pdf"],"dc:subject":["Pfadintegral-Monte Carlo","Coherent State Pfadintegral","Coulomb Blockade","SET-Transistor","Path Integral Monte Carlo","Inverse Problem","Quantum Dots"],"dc:title":["Conductance of single-electron devices from imaginary-time path integrals","Leitwertberechnungen für Einzelelektronen-Schaltungen mittels Imaginärzeit-Pfadintegralen"],"dc:type":["DoctoralThesis"]},"updated_at":"2026-07-24T02:22:10Z"}