Phase-Coherent Dynamics of Quantum Devices with Local Interactions
Abstract
:1. Introduction
2. Phase-Coherence in Quantum Devices with Local Interactions
3. What Are Local Fermi Liquids and Why Are They Important to Understand Quantum-Dot Devices?
3.1. The Local Fermi Liquid
3.2. The Role of the Friedel Sum Rule in Local Fermi Liquid Theories
3.3. Derivation of the LFL Theory in the Coulomb Blockade and Anderson Model
3.3.1. Coulomb Blockade Model
3.3.2. Anderson Impurity Model
4. The Mesoscopic Capacitor
- The total capacitance C is given by the static charge susceptibility of the cavity and does not generally correspond to a series of a geometric and quantum contribution, proportional to the density of states in the cavity. For instance, in Kondo regimes, the charge susceptibility of the cavity remains small, because of frozen charge fluctuations, while the density of states increases below the Kondo temperature [49]. This effect was directly probed in a recent experiment with a quantum dot device embedded in circuit-QED architecture [145];
- The LFL approach shows various non-trivial dissipative effects triggered by strong correlations. In particular, it predicts a mesoscopic crossover between two universal regimes in which [65] by increasing the dot size, also at charge degeneracy, in which the CBM maps on the Kondo model [101]. It also predicts giant dissipative regimes, described by giant universal peaks in , triggered by the destruction of the Kondo singlet by a magnetic field [67,147];
- In proper out-of-equilibrium regimes, interactions and inelastic effects become unavoidable and circuit analogies, such as Equation (31), do not capture the dynamic behavior of the mesoscopic capacitor [148]. We show here how previously published data [25] also show a previously overlooked signature of non-trivial many-body dynamics induced by interactions.
4.1. Hamiltonian Description of the Quantum RC Circuit: Differential Capacitance and Korringa–Shiba Relation
4.2. The Origin of the Differential Capacitance as a ‘Quantum’ Capacitance as far as Interactions are Neglected
4.3. The Physical Origin of the Universal Charge Relaxation Resistance
4.4. The Open-Dot Limit
4.5. The Tunneling Limit and the Quasi-Static Approximation
4.6. The LFL Theory of Large Quantum Dots: The Mesoscopic Crossover
4.7. The Multi-Channel Case and Universal Effects Triggered by Kondo Correlations
5. What about Out-Of-Equilibrium Regimes? A New Twist on Experiments
Experimental Signatures of the Effects of Interaction in Quantum Cavities Driven out of Equilibrium
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
QPC | quantum point contact |
LFL | local Fermi liquid |
CBM | Coulomb blockade model |
AIM | Anderson impurity model |
SW | Schrieffer–Wolff |
DC | direct current |
2DEG | two-dimensional electron gas |
KS | Korringa–Shiba |
AC | alternate current |
NRG | numerical renormalization group |
Appendix A. Scattering Theory, Phase-Shifts and the Friedel Sum Rule
Appendix A.1. General Definitions
Appendix A.2. The Friedel Sum Rule
Appendix A.3. Illustration on the Resonant Level Model
Appendix A.4. T-Matrix in the Potential Scattering Hamiltonian
Appendix B. Self-Consistent Description- of a 2DEG Quantum RC Circuit
Appendix B.1. Self-Consistent Theory
Appendix B.2. Hamiltonian Description of the Quantum RC Circuit with a Resonant Level Model
Multi-Level Case
Appendix C. Useful Results of Linear Response Theory
Appendix C.1. Parity of the Dynamical Charge Susceptibility
Appendix C.2. Energy Dissipation in the Linear Response Regime
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Filippone, M.; Marguerite, A.; Le Hur, K.; Fève, G.; Mora, C. Phase-Coherent Dynamics of Quantum Devices with Local Interactions. Entropy 2020, 22, 847. https://doi.org/10.3390/e22080847
Filippone M, Marguerite A, Le Hur K, Fève G, Mora C. Phase-Coherent Dynamics of Quantum Devices with Local Interactions. Entropy. 2020; 22(8):847. https://doi.org/10.3390/e22080847
Chicago/Turabian StyleFilippone, Michele, Arthur Marguerite, Karyn Le Hur, Gwendal Fève, and Christophe Mora. 2020. "Phase-Coherent Dynamics of Quantum Devices with Local Interactions" Entropy 22, no. 8: 847. https://doi.org/10.3390/e22080847
APA StyleFilippone, M., Marguerite, A., Le Hur, K., Fève, G., & Mora, C. (2020). Phase-Coherent Dynamics of Quantum Devices with Local Interactions. Entropy, 22(8), 847. https://doi.org/10.3390/e22080847