Natural Justice and Conscience of the Judges in Case Ridge V. Baldwin

Shytov, Alexander

doi:10.1007/978-94-015-9745-6_9

Cited by 4 publications

(7 citation statements)

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“…In fact, the Landau-Zener theory is not directly applicable to the present situation in which the phase is not an external parameter swept at a constant rate, but is instead a dynamical variable undergoing a driven diffusive motion. A rigorous theory of this dissipative nonadiabatic mechanism, valid for arbitrary transmission, remains to be developed for our system, along the lines of [20] or [21], for example.…”

Section: Supercurrent In Atomic Point Contacts and Andreev Statesmentioning

confidence: 99%

Supercurrent in Atomic Point Contacts and Andreev States

et al. 2000

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We have measured the supercurrent in aluminum atomic point contacts containing a small number of well characterized conduction channels. For most contacts, the measured supercurrent is adequately described by the opposite contributions of two thermally populated Andreev bound states per conduction channel. However, for contacts containing an almost perfectly transmitted channel 0.9 # t # 1 the measured supercurrent is higher than expected, a fact that we attribute to nonadiabatic transitions between bound states. PACS numbers: 73.40.Jn, 73.20.Dx, 74.50. + r In 1962, Josephson predicted that a surprisingly large supercurrent could flow between two weakly coupled superconducting electrodes when a phase difference d is applied across the whole structure. This phasedriven supercurrent I͑d͒ has subsequently been observed in a variety of weak coupling configurations such as thin insulating barriers, narrow diffusive wires, and ballistic point contacts between large electrodes. However, a theoretical framework powerful enough to predict the current-phase relation I͑d͒ in all configurations has emerged only during the last decade [1]. It applies in the mesoscopic regime, when electron transport between the electrodes is a quantum coherent process. Such transport is described by a set of N transmission coefficients ͕t i ͖ corresponding to N independent conduction channels. In the normal state, the conductance is given by G 0 P N i1 t i where G 0 2e 2 ͞h is the conductance quantum. In the superconducting state, electrons (holes) transmitted in one channel are Andreev reflected at the electrodes into holes (electrons) in the same channel. After a cycle involving two reflections at the electrodes, they acquire at the Fermi energy an overall phase factor p 1 d (Fig. 1). In a "short" coupling structure, these cycles give rise to two electron-hole resonances per channel, called Andreev bound states (AS) [2] with energies E 6 ͑d, t i ͒ 6D͓1 2 t i sin 2 ͑d͞2͔͒ 1͞2 (D is the energy gap in the electrodes). These two AS carry current in opposite directions, I 6 ͑d, t͒ w 21 0 dE 6 ͑d, t i ͒͞dd (where w 0 h͞2e), and the net supercurrent results from the imbalance of their populations. A quantitative comparison of the predictions of this "mesoscopic superconductivity" picture of the Josephson effect with experimental results is usually hindered by the fact that in most devices the current flows through a very large number of channels with unknown t i . However, an atomic-size constriction between two electrodes, referred to hereafter simply as an atomic contact [3], is an extreme type of weak coupling structure which accommodates just a few channels. Because their set ͕t i ͖ is amenable to a complete experimental determination and because it can be controlled in a certain range [4], atomic contacts are ideal systems on which to test quantitatively the concepts of mesoscopic physics. The knowledge of ͕t i ͖ allows in principle the calculation of all transport quantities. In particular, the phase-driven supercurrent is given bywhere n...

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Section: Supercurrent In Atomic Point Contacts and Andreev Statesmentioning

confidence: 99%

Supercurrent in Atomic Point Contacts and Andreev States

et al. 2000

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“…It is not surprising that the attempts to find the exactly solvable multistate analogues of the Landau-Zener model have attracted considerable attention in the literature (see, for instance, [9][10][11][12][13][14][15][16][17][18][19][20] and bibliography therein). The present study continues this direction of research.…”

Section: Introductionmentioning

confidence: 99%

Exact results for survival probability in the multistate Landau–Zener model

Volkov

Ostrovsky

2004

J. Phys. B: At. Mol. Opt. Phys.

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An exact formula is derived for survival probability in the multistate Landau–Zener model in the special case where the initially populated state corresponds to the extremal (maximum or minimum) slope of a linear diabatic potential curve. The formula was originally guessed by S Brundobler and V Elzer (1993 J. Phys. A: Math. Gen. 26 1211) based on numerical calculations. It is a simple generalization of the expression for the probability of diabatic passage in the famous two-state Landau–Zener model. Our result is obtained via analysis and summation of the entire perturbation theory series.

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“…4 The intermediate situation of soft (algebraic) phase decay leads to the wellknown non-Fermi liquid features of a LL. [5][6][7] In all these situations, great complexity arises due to the coupling of the bosonic mode to static disorder or dynamical defects, such as discrete Andreev levels 8,9 in superconducting weak links 10 ) or magnetic Kondo impurities in metallic junctions 11,12 and interacting unidimensional wires. 13,14 Focusing the discussion on the case of impurity effects in LL, but keeping this more general framework in mind, many technical and physical questions are still open to date, both in the original fermionic formulation and in the bosonic version of the problem.…”

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confidence: 99%

“…This development could allow to address many currently open issues, such as nonequilibrium transport with strong correlations (using a mapping onto equilibrium q-oscillator models 32 ), Kondo physics in Luttinger liquids, [12][13][14] and ohmic dissipation in Andreev level qubits. [8][9][10]…”

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Numerical Renormalization Group at Marginal Spectral Density: Application to Tunneling in Luttinger Liquids

Freyn

Florens

2011

Phys. Rev. Lett.

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Many quantum mechanical problems (such as dissipative phase fluctuations in metallic and superconducting nanocircuits or impurity scattering in Luttinger liquids) involve a continuum of bosonic modes with a marginal spectral density diverging as the inverse of energy. We construct a numerical renormalization group in this singular case, with a manageable violation of scale separation at high energy, capturing reliably the low energy physics. The method is demonstrated by a nonperturbative solution over several energy decades for the dynamical conductance of a Luttinger liquid with a single static defect.

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Natural Justice and Conscience of the Judges in Case Ridge V. Baldwin

Cited by 4 publications

References 1 publication

Supercurrent in Atomic Point Contacts and Andreev States

Supercurrent in Atomic Point Contacts and Andreev States

Exact results for survival probability in the multistate Landau–Zener model

Numerical Renormalization Group at Marginal Spectral Density: Application to Tunneling in Luttinger Liquids

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