The Many-Lined Spectrum of Sodium Hydride

Johnson, E. H.

doi:10.1103/physrev.29.85

Cited by 55 publications

(14 citation statements)

References 9 publications

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“…This result was found experimentally by Johnson in 1927 [1] and explained theoretically by Nyquist in 1928 [2]. Such relation between equilibrium noise and conductance can be seen as a consequence of the fluctuationdissipation theorem.…”

Section: Introductionsupporting

confidence: 65%

Tunneling and quantum noise in one-dimensional Luttinger liquids

Chamon¹,

Freed²,

Wen³

1995

Phys. Rev. B

154

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We study non-equilibrium noise in the transmission current through barriers in 1-D Luttinger liquids and in the tunneling current between edges of fractional quantum Hall liquids. The distribution of tunneling events through narrow barriers can be described by a Coulomb gas lying in the time axis along a Keldysh (or non-equilibrium) contour. We show that the charges tend to reorganize as a dipole gas, which we use to describe the tunneling statistics. The dipole-gas picture allows us to have a unified description of the low frequency shot noise and the high frequency "Josephson" noise. The correlation between the charges within a dipole (intra-dipole) contributes to the high-frequency "Josephson" noise, which has an algebraic singularity at ω = e * V /h, whereas the correlations between dipoles (inter-dipole) are responsible for the lowfrequency noise. We show that an independent or non-interacting dipole approximation gives a Poisson distribution for the locations of the dipole centers of mass, which gives a flat noise spectrum at low-frequencies and corresponds to uncorrelated shot noise. Including inter-dipole interactions gives an additional 1/t 2 correlation between the tunneling events that results in a |ω| 1 singularity in the noise spectrum. We present a diagrammatic technique to calculate the correlations in perturbation theory, and show that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the |ω| singularity, but its form should remain ∼ |ω| to all orders in perturbation theory. A counting argument also suggests that the leading algebraic singularity at ω J should be ∝ |ω − ω J | 2g−1 to all orders in perturbation theory.

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Section: Introductionsupporting

confidence: 65%

Tunneling and quantum noise in one-dimensional Luttinger liquids

Chamon¹,

Freed²,

Wen³

1995

Phys. Rev. B

154

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“…Observed by J. B. Johnson in 1927 [96][97][98] and theoretically explained by H. Nyquist in 1928, [99] this thermal noise (also called "Johnson noise") appears in all resistors, and results from the random motion of charge carriers in equilibrium with a thermal bath. One finds for the mean square voltage noise: hV 2 i = 4 k B TRDf, where k B is the Boltzmann constant, T the temperature, R the resistance of the sample, and Df the frequency bandwidth of the measurement.…”

Section: Thermal Noisementioning

confidence: 98%

Fluctuation Spectroscopy: A New Approach for Studying Low‐Dimensional Molecular Metals

Müller

2011

ChemPhysChem

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Fluctuations (or noise) are often merely considered a nuisance, an unwanted disturbance limiting the accuracy of a scientific measurement. Electronic fluctuations, however, reveal hidden pieces of information not present in the mean quantity (the resistance) itself. Herein we describe resistance noise spectroscopy as a powerful new tool for investigating the low-frequency dynamics of electronic processes in low-dimensional organic conductors. Over the years, these molecular charge-transfer complexes have provided unprecedented model systems for exploring the physics of low-dimensional materials. The combination of low dimensionality with other parameters, specific to molecular conductors, sets the stage for Coulomb correlation effects to become relevant and, under certain circumstances, even to dominate the properties of the π-electron system. The combined effects of strong electron-electron and electron-phonon interactions give rise to the rich phenomenology of ground states encountered in these materials. To provide examples, we describe noise spectroscopy as a method to study the coupling of the correlated charge carriers to intramolecular modes of lattice vibrations and to investigate the inhomogeneous coexistence region of antiferromagnetic (Mott) insulating and superconducting phases.

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“…This is the reason that the fluctuation dissipation theorem breaks down as one goes out of equilibrium. Recall that the key relation which leads to the fluctuation dissipation theorem [21] …”

Section: ) =mentioning

confidence: 99%

Reformulation of steady state nonequilibrium quantum statistical mechanics

1993

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Starting from the usual formulation of nonequilibrium quantum statistical mechanics, the expectation value of an operator A in a steady state nonequilibrium quantum system is shown to have the form {A) ==: Tr{e ~f iiH~Y) A}/Tv{e~p (H~Y) }, where H is the Hamiltonian, p is the inverse of the temperature, and Y is an operator which depends on how the system is driven out of equilibrium. Because {A) is not expressed as a sum of correlation functions integrated over real time, one can now consider performing nonperturbative calculations in interacting nonequilibrium quantum problems.PACS numbers: 72.10. Bg, 05.60,+w Nonequilibrium problems have come under increasing study in condensed matter physics. On the one hand, there exists a growing number of classical systems which undergo a phase transition as one drives them out of equilibrium. On the other hand, with technological advances allowing one to make measurements on smaller samples, it becomes easier to drive systems out of equilibrium. This is particularly true in making resistance measurements on very small (mesoscopic) devices at low temperatures [1], which is an inherently quantum problem. Furthermore, while linear response measurements do probe some equilibrium correlation functions, much more information can be obtained from the nonlinear response, which probes the full nonequilibrium problem. For example, nonlinear current-voltage characteristics in metal-insulator-superconductor tunnel junctions have long been used to determine the superconducting gap and the phonon density of states. In mesoscopic systems similar kinds of information about the density of states can be obtained from nonlinear transport [2][3][4][5].In spite of the experimental importance of studying nonlinear response there are far fewer theoretical techniques available for studying nonequilibrium quantum systems than for studying equilibrium ones. Again using the example of mesoscopic systems, the noninteracting quantum problem may be solved exactly using the scattering states for electrons coming from reservoirs which are at different chemical potentials. This is the essence of the Landauer formula [6] and its subsequent generalizations [7,8]. For an interacting system the nonlinear current-voltage characteristic can be computed by doing perturbation theory in the part of the Hamiltonian which drives the system out of equilibrium, e.g., an electric field or the tunneling between two leads at different chemical potentials. This perturbation theory, which we will call nonequilibrium quantum statistical mechanics, involves summing a set of real time correlation functions for the linear, quadratic, cubic, etc., response to this interaction [9,10].While there are many problems for which a perturbation theory is perfectly satisfactory, there is a large class of problems of current interest for which a nonperturbative approach would be quite useful and perhaps even essential. In the case of mesoscopic systems it is now possible to tunnel through a one-dimensional wire [11], a small quantum...

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The Many-Lined Spectrum of Sodium Hydride

Cited by 55 publications

References 9 publications

Tunneling and quantum noise in one-dimensional Luttinger liquids

Tunneling and quantum noise in one-dimensional Luttinger liquids

Fluctuation Spectroscopy: A New Approach for Studying Low‐Dimensional Molecular Metals

Reformulation of steady state nonequilibrium quantum statistical mechanics

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