Reforming the Garden: The Experimentalist Eden and Paradise Lost

Dirac’s method for constraints: an application to quantum wires

“…We have found that the anomalous commutation rules are modified causing the conductance to be anomalous. Applying this theory to quantum wires, we show that our theory can explain the anomalous conductance observed by [14,[16][17][18] and is in agreement with the Monte-Carlo simulation reported in refs. [21,22].…”

“…We will apply the quantum mechanical method given in equation (9) to the Hamiltonian for the wire given in equation (18). Since the constraint must obey dQ 1 (x,t) dt |F >= 0, and the commutator [Q 1 (x), Q 2 (x ′ )] can be inverted, the Lagrange multipliers can be computed.…”

“…The physics of the Hubbard model at U → ∞ might be relevant for studies of the 0.7 conductance anomaly discovered in quantum wires [14][15][16][17]. Experiments suggest that the anomalous conductance is observed at low electronic densities [18] and short in wires [24].…”

A scaling approach for interacting quantum wires—a possible explanation for the 0.7 anomalous conductance

“…The anomalous conductance G ≈ 0.7 × (2e 2 /h) discovered by Pepper et al [1] and further investigated by [2,3,4,5,6] is one of the major unexplained effects in quantum wires.…”

“…In chapter 9, we consider the case K ef f. < 1 2 which at zero temperature gives rise to a Wigner crystal with a charge density wave gap ∆. In chapter 10, we present our numerical results using the experimental parameters given by [3]. In chapter 11, we examine the effect of the Zeeman interaction.…”