By Hélène Bouchiat, Yuval Gefen, Sophie Guéron Engineering Diploma 1993D.E.A. de Physique des Solides 1994Ph.D. Université Paris VI 1997, Gilles Montambaux Ph.D. Thesis 1985, Jean Dalibard Ph.D.
The advancements of nanofabrication some time past years have enabled the layout of digital structures that show striking signatures of quantum coherence. Nanofabricated quantum wires and dots containing a small variety of electrons are excellent experimental playgrounds for probing electron-electron interactions and their interaction with ailment. happening to even smaller scales, molecules corresponding to carbon nanotubes, fullerenes or hydrogen molecules can now be inserted in nanocircuits. Measurements of shipping via a unmarried chain of atoms were played in addition. a lot growth has additionally been made within the layout and fabrication of superconducting and hybrid nanostructures, be they normal/superconductor or ferromagnetic/superconductor. Quantum coherence is then not that of person digital states, yet really that of a superconducting wavefunction of a macroscopic variety of Cooper pairs condensed within the similar quantum mechanical kingdom. past the examine of linear reaction regime, the physics of non-equilibrium shipping (including non-linear shipping, rectification of a excessive frequency electrical box in addition to shot noise) has obtained a lot awareness, with major experimental and theoretical insights. a lot of these amounts express very particular signatures of the quantum nature of shipping, which can't be received from uncomplicated conductance measurements.
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Extra resources for Nanophysics: Coherence and Transport
What we did not get quite right is that the velocities of both–spin- and charge-modes–are modified by the interactions. In fact, the exact solution shows that the velocity of the spin-mode remains equal to vF , whereas the velocity of the charge mode is modified. Obviously, there is no spin-charge separation for spinless electrons. Indeed, in this case diagram Fig. 8a does not have an additional factor of two as compared to Fig. 8c (but is still of opposite sign), so that the forward-scattering parts of these two diagrams cancel each other.
For a contact interaction, diagram b) is just -1/2 of a) (which can be seen by integrating over the fermionic momentum p first), so we will lump them together. Two given fermions interact via polarizing the medium consisting of other fermions. Hence, the effective interaction at the second order is just proportional to the polarization bubble, which shows how polarizable the medium is ImV R (ω, q) = −U 2 Im R (ω, q). Let’s focus on small angle-scattering first: q ≪ 2kF . 7) where νD = aD mkFD−2 is the DoS in D dimensions [a3 = (2π)−2 , a2 = (2π)−1 , a1 = 1/2π] and BD is a dimensionless function, whose main role is to impose a constraint ω ≤ vF q in 2D and 3D and ω = vF q in 1D.
Guéron, G. Montambaux and J. Dalibard, eds. V. All rights reserved 1 Contents 1. Introduction 2. 1. 2. 3. 1. 2. 2D 3. 1. 2. 3. 4. 5. 6. 7. 1. 2. Tunneling density of states 4. Renormalization group for interacting fermions 5. 1. 1. 2. 2. 3. 4. Comparison of bulk and edge tunneling exponents 6. 1. 1. 2. 3. 4. 5. 2. 1. Tunneling density of states 7. 1. 1. 2. 3. 4. 2. 3. L. 1. 2. 3. 4. 4. 5. Thermal conductance: Fabry-Perrot resonances of plasmons Appendix A. Polarization bubble for small q in arbitrary dimensionality Appendix B.
Nanophysics: Coherence and Transport by Hélène Bouchiat, Yuval Gefen, Sophie Guéron Engineering Diploma 1993D.E.A. de Physique des Solides 1994Ph.D. Université Paris VI 1997, Gilles Montambaux Ph.D. Thesis 1985, Jean Dalibard Ph.D.