Excitons in Metals: Infinite Hole Mass

Mahan, G. D.

doi:10.1103/physrev.163.612

Cited by 847 publications

(364 citation statements)

References 21 publications

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“…The original problem 8,9 was formulated for conduction electrons with a small effective mass and valence electrons with a large effective mass, bombarded by x rays. The x rays knock one electron out of the valence band, leaving behind an essentially stationary hole.…”

Section: Fermi-edge Singularitymentioning

confidence: 99%

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Keldysh action of a multiterminal time-dependent scatterer

Snyman

Nazarov

2008

Phys. Rev. B

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We present a derivation of the Keldysh action of a general multichannel time-dependent scatterer in the context of the Landauer-Büttiker approach. The action is a convenient building block in the theory of quantum transport. This action is shown to take a compact form that only involves the scattering matrix and reservoir Green's functions. We derive two special cases of the general result, one valid when reservoirs are characterized by well-defined filling factors, the other when the scatterer connects two reservoirs. We illustrate its use by considering full counting statistics and the Fermi-edge singularity.

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Section: Fermi-edge Singularitymentioning

confidence: 99%

“…In the language of the original diagrammatic treatment of the FES problem, 8,9 it represents the total closed loop contribution. We may also write this closed loop contribution as…”

Section: Fermi-edge Singularitymentioning

confidence: 99%

Keldysh action of a multiterminal time-dependent scatterer

Snyman

Nazarov

2008

Phys. Rev. B

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“…A prominent example is optical absorption, [3][4][5][6][14][15][16] for which AO leaves its imprint in the shape of the absorption spectrum, by reducing the probability for absorption. This is familiar from the x-ray edge problem.…”

Section: Ao and Post-quench Time Evolutionmentioning

confidence: 99%

“…[3][4][5][6] For the case of the X-ray edge singularity, Hopfield 5 gave a simple argument to explain the relation between ∆ AO and η. We frame Hopfield's argument in a more general setting and numerically illustrate the validity of the resulting generalized Hopfield rule (Eq.…”

Section: Introductionmentioning

confidence: 99%

Anderson orthogonality in the dynamics after a local quantum quench

et al. 2012

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We present a systematic study of the role of Anderson orthogonality for the dynamics after a quantum quench in quantum impurity models, using the numerical renormalization group. As shown by Anderson in 1967, the scattering phase shifts of the single-particle wave functions constituting the Fermi sea have to adjust in response to the sudden change in the local parameters of the Hamiltonian, causing the initial and final ground states to be orthogonal. This so-called Anderson orthogonality catastrophe also influences dynamical properties, such as spectral functions. Their low-frequency behaviour shows non-trivial power laws, with exponents that can be understood using a generalization of simple arguments introduced by Hopfield and others for the X-ray edge singularity problem. The goal of this work is to formulate these generalized rules, as well as to numerically illustrate them for quantum quenches in impurity models involving local interactions. As a simple yet instructive example, we use the interacting resonant level model as testing ground for our generalized Hopfield rule. We then analyse a model exhibiting population switching between two dot levels as a function of gate voltage, probed by a local Coulomb interaction with an additional lead serving as charge sensor. We confirm a recent prediction that charge sensing can induce a quantum phase transition for this system, causing the population switch to become abrupt. We elucidate the role of Anderson orthogonality for this effect by explicitly calculating the relevant orthogonality exponents.

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“…For the equilibrium QPC, the problem can be mapped [12] onto the classic Fermi edge singularity (FES) problem [15][16][17]. In effect the authors of [12] computed A in equilibrium.…”

mentioning

confidence: 99%

Polarization of a Charge Qubit Strongly Coupled to a Voltage-Driven Quantum Point Contact

Snyman

Nazarov

2007

Phys. Rev. Lett.

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We study a charge qubit with level splitting ", coupled to a quantum point contact driven by voltage V. In the limit of weak coupling, the qubit polarization shows cusps at " eV. We show that, for stronger couplings, prominent peculiarities occur at fractions " eV=2. Further increase of the coupling leads to a polarization corresponding to a pseudo Boltzmann distribution with an effective temperature eV. DOI: 10.1103/PhysRevLett.99.096802 PACS numbers: 73.23.ÿb, 03.67.Lx, 73.40.Jn, 85.30.Hi The quantum point contact [1] has become a basic concept in the field of quantum transport owing to its simplicity. Its common experimental realization is a narrow constriction that connects two metallic reservoirs. An adequate theoretical description for this setup is a noninteracting one-dimensional electron gas interrupted by a potential barrier. The barrier is completely characterized by its scattering matrix. This enables the scattering approach to quantum transport [2].Despite the correctness of the noninteracting electron description, truly many-body quantum correlations in a QPC do exist and are observable. These manifest themselves in the full counting statistics (FCS) of electron transfers [3] and allow for detection of two-particle entanglement [4] through the measurement of nonlocal current correlations. This suggests that the observation of manybody effects in a QPC crucially relies on a proper detection scheme.In this Letter, we probe a QPC with a charge qubit. Such a device has already been realized using single and double quantum dots. Previously, the QPC has been used as a detector of the qubit state [5,6]. We propose a scheme in which these roles are reversed. Provided the qubit and QPC are coupled strongly, switching between the qubit states is accompanied by severe Fermi-Sea shake-up in the QPC. The ratio of switching rates determines the qubit polarization. The dc current in the QPC reads the qubit polarization. Thereby we obtain information about the Fermi-Sea shake-up in the QPC.For our results to apply, the qubit transition rate induced by the QPC should therefore dominate the rate due to coupling with other environmental modes. We estimate this requirement to be fulfilled already in the weak coupling regime.Before analyzing the system in detail, the following qualitative conclusions can be drawn. The qubit owes its detection capabilities to the following fact: In order to be excited it has to absorb a quantum " of energy from the QPC. Here " is the qubit level splitting, a parameter that can be tuned easily in an experiment by means of a gate voltage. The QPC supplies the energy by transferring charge from the high voltage reservoir to the low voltage reservoir. The transfer of charge q allows qubit transitions for level splittings " < qV, V being the bias-voltage applied. Thus, the creation of excitations in the QPC is correlated with qubit switching.We can assume that successive switchings of the qubit between its states j1i and j2i are rare and uncorrelated. The qubit dynamics are then characte...

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Excitons in Metals: Infinite Hole Mass

Cited by 847 publications

References 21 publications

Keldysh action of a multiterminal time-dependent scatterer

Keldysh action of a multiterminal time-dependent scatterer

Anderson orthogonality in the dynamics after a local quantum quench

Polarization of a Charge Qubit Strongly Coupled to a Voltage-Driven Quantum Point Contact

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