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From integrability to conductance, impurity systems

Castro-Alvaredo, O A, Fring, A

Published May 8, 2002• 26 citations
OpenAlex

Abstract

We compute the DC conductance with two different methods, which both exploit the integrability of the theories under consideration. On one hand we determine the conductance through a defect by means of the thermodynamic Bethe ansatz and standard relativistic potential scattering theory based on a Landauer transport theory picture. On the other hand, we propose a Kubo formula for a defect system and evaluate the current-current two-point correlation function it involves with the help of a form factor expansion. For a variety of defects in a fermionic system we find excellent agreement between the two different theoretical descriptions.

Related papers

Conductance from Non-perturbative Methods I

Olalla A. Castro-Alvaredo, Andreas Fring

We investigate different methods to compute the DC conductance in a quantum wire doped with some impuritied by exploiting the integrability of the theories under consideration. As an essential ingredient in all methods we evaluate the reflection and transmission amplitudes ofthe impurities for a variety of defects. When the impurities inthe wire are coupled to an external three dimensional laser field, we predict the generation of harmonic emission spectra. We propose a modified version of the well-known Kubo formula, which incorporates the impurities of the system and evaluate the current-current two-point correlation function it involves with the help of a form factor expansion. A comparison with the corresponding quantities computed in a Landauer transport theory picture is carried out in part II.

arXiv:cond-mat/0210599•Oct 28, 2002•0 citations

Conductance from Non-perturbative Methods II

Olalla A. Castro-Alvaredo, Andreas Fring

This talk provides a natural continuation of the talk presented by Andreas Fring in this conference.Part I was focused on explaining how the DC conductance for a free Fermion theory in the presence of different kinds of defects can be computed by evaluating the Kubo formula.In this talk I will focus on an alternative method for the computation of the same quantity, that is the evaluation of Landauer formula.Once again, the integrability of the theories under consideration will be exploited, since a thermodynamic Bethe ansatz analysis provides all the input needed in that case, apart from the corresponding reflection and transmition amplitudes of the defect.The basic conclusion of our analysis will be the perfect agreement between the two different theoretical descriptions mentioned.The results I will talk about are contained on a series of papers [1,2,3,4,5,6], with emphasis on the first two, resulting mainly from a collaboration with Andreas Fring, who presented the first part of the work.

arXiv:cond-mat/0210592•Workshop on Integrable Theories, Solitons and Duality•Dec 1, 2002•0 citations

Conductance from Non-perturbative Methods I

Andreas Fring, Olalla A. Castro-Alvaredo

We investigate different methods to compute the DC conductance in a quantum wire doped with some impuritied by exploiting the integrability of the theories under consideration.As an essential ingredient in all methods we evaluate the reflection and transmission amplitudes of the impurities for a variety of defects.When the impurities in the wire are coupled to an external three dimensional laser field, we predict the generation of harmonic emission spectra.We propose a modified version of the well-known Kubo formula, which incorporates the impurities of the system and evaluate the current-current two-point correlation function it involves with the help of a form factor expansion.A comparison with the corresponding quantities computed in a Landauer transport theory picture is carried out in part II.The work I want to report about is based on a series of papers [1,2,3,4,5,6] with an emphasis on the first two.Olalla Castro-Alvaredo will present the second part of this talk.

Workshop on Integrable Theories, Solitons and Duality•Dec 1, 2002•0 citations

Unstable particles versus resonances in impurity systems, conductance in quantum wires

Olalla A. Castro-Alvaredo, Andreas Fring

We compute the DC conductance for a homogeneous sine-Gordon model and an impurity system of Luttinger liquid type by means of the thermodynamic Bethe ansatz and standard potential scattering theory. We demonstrate that unstable particles and resonances in impurity systems lead to a sharp increase of the conductance as a function of the temperature, which is characterized by the Breit-Wigner formula.

arXiv:cond-mat/0112199•Dec 11, 2001•0 citations

Unstable particles versus resonances in impurity systems; conductance in quantum wires

Olalla A. Castro-Alvaredo, Andreas Fring

We compute the DC conductance for a homogeneous sine–Gordon model and an impurity system, which in the conformal limit can be reduced to a Luttinger liquid, by means of the thermodynamic Bethe ansatz and standard potential scattering theory. We demonstrate that unstable particles and resonances in impurity systems lead to a sharp increase of the conductance as a function of the temperature, which is characterized by the Breit–Wigner formula.

Journal of Physics Condensed Matter•Nov 20, 2002•10 citations

Scattering Bethe Ansatz approach

Sung‐Po Chao

We derive the transport properties of a quantum impurity system, often realized as a quantum dot, subject to a source-drain bias voltage at zero temperature and magnetic field. Using the Scattering Bethe Anstaz(SBA), a generalization of the traditional Thermodynamic Bethe Ansatz(TBA) to open systems out of equilibrium, we derive some transport results for the small quantum dot, described by Anderson impurity Hamiltonian. Exact dot occupation out of equilibrium and the nonlinear conductance are obtained by introducing phenomenological spin- and charge-fluctuation distribution functions in the computation of the current. The current and dot occupation as a function of voltage are evaluated numerically. We also vary the gate voltage and study the transition from the mixed valence to the Kondo regime in the presence of a non-equilibrium current. For the larger quantum dot the Interacting Resonance Level Model is used to describe the strog correlation problem in this system. We show some current vs voltage results and compare with other theoretical results. We conclude with the difficulties we encountered by using this method and suggest some future extensions related to this SBA approach.

•Jan 1, 2010•0 citations
We compute the DC conductance with two different methods, which both exploit the integrability of the theories under consideration. On one hand we determine the conductance through a defect by means of the thermodynamic Bethe ansatz and standard relativistic potential scattering theory based on a Landauer transport theory picture. On the other hand, we propose a Kubo formula for a defect system and evaluate the current-current two-point correlation function it involves with the help of a form factor expansion. For a variety of defects in a fermionic system we find excellent agreement between the two different theoretical descriptions.
We investigate different methods to compute the DC conductance in a quantum wire doped with some impuritied by exploiting the integrability of the theories under consideration. As an essential ingredient in all methods we evaluate the reflection and transmission amplitudes ofthe impurities for a variety of defects. When the impurities inthe wire are coupled to an external three dimensional laser field, we predict the generation of harmonic emission spectra. We propose a modified version of the well-known Kubo formula, which incorporates the impurities of the system and evaluate the current-current two-point correlation function it involves with the help of a form factor expansion. A comparison with the corresponding quantities computed in a Landauer transport theory picture is carried out in part II.
This talk provides a natural continuation of the talk presented by Andreas Fring in this conference.Part I was focused on explaining how the DC conductance for a free Fermion theory in the presence of different kinds of defects can be computed by evaluating the Kubo formula.In this talk I will focus on an alternative method for the computation of the same quantity, that is the evaluation of Landauer formula.Once again, the integrability of the theories under consideration will be exploited, since a thermodynamic Bethe ansatz analysis provides all the input needed in that case, apart from the corresponding reflection and transmition amplitudes of the defect.The basic conclusion of our analysis will be the perfect agreement between the two different theoretical descriptions mentioned.The results I will talk about are contained on a series of papers [1,2,3,4,5,6], with emphasis on the first two, resulting mainly from a collaboration with Andreas Fring, who presented the first part of the work.
We investigate different methods to compute the DC conductance in a quantum wire doped with some impuritied by exploiting the integrability of the theories under consideration.As an essential ingredient in all methods we evaluate the reflection and transmission amplitudes of the impurities for a variety of defects.When the impurities in the wire are coupled to an external three dimensional laser field, we predict the generation of harmonic emission spectra.We propose a modified version of the well-known Kubo formula, which incorporates the impurities of the system and evaluate the current-current two-point correlation function it involves with the help of a form factor expansion.A comparison with the corresponding quantities computed in a Landauer transport theory picture is carried out in part II.The work I want to report about is based on a series of papers [1,2,3,4,5,6] with an emphasis on the first two.Olalla Castro-Alvaredo will present the second part of this talk.
We derive the transport properties of a quantum impurity system, often realized as a quantum dot, subject to a source-drain bias voltage at zero temperature and magnetic field. Using the Scattering Bethe Anstaz(SBA), a generalization of the traditional Thermodynamic Bethe Ansatz(TBA) to open systems out of equilibrium, we derive some transport results for the small quantum dot, described by Anderson impurity Hamiltonian. Exact dot occupation out of equilibrium and the nonlinear conductance are obtained by introducing phenomenological spin- and charge-fluctuation distribution functions in the computation of the current. The current and dot occupation as a function of voltage are evaluated numerically. We also vary the gate voltage and study the transition from the mixed valence to the Kondo regime in the presence of a non-equilibrium current. For the larger quantum dot the Interacting Resonance Level Model is used to describe the strog correlation problem in this system. We show some current vs voltage results and compare with other theoretical results. We conclude with the difficulties we encountered by using this method and suggest some future extensions related to this SBA approach.