The Formal Theory of Scattering

Gell‐Mann, Murray; Goldberger, M. L.

doi:10.1103/physrev.91.398

Cited by 709 publications

(301 citation statements)

References 10 publications

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“…In the non-interacting system the scattering states ψ † αkσ can be calculated explicitly [10], in the form of the Lippmann-Schwinger equation [13,14] …”

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confidence: 99%

Imaginary-Time Formulation of Steady-State Nonequilibrium: Application to Strongly Correlated Transport

2007

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We extend the imaginary-time formulation of the equilibrium quantum many-body theory to steady-state nonequilibrium with an application to strongly correlated transport. By introducing Matsubara voltage, we keep the finite chemical potential shifts in the Fermi-Dirac function, in agreement with the Keldysh formulation. The formulation is applied to strongly correlated transport in the Kondo regime using the quantum Monte Carlo method.PACS numbers: 73.63. Kv, 72.10.Bg, 72.10.Di A coherent formulation of equilibrium and nonequilibrium is one of the ultimate goals of statistical physics. In the last two decades, this has become a particularly pressing issue with the advances in nanoelectronics. Although it has long been considered such Gibbsian description may exist in the steady-state nonequilibrium [1], implementation of time-independent nonequilibrium quantum statistics has produced limited success [2] without widely applicable algorithms.In nanoelectronics, the strong interplay between manybody interactions and nonequilibrium demands nonperturbative treatments of the quantum many-body effects. Perturbative Green function techniques [3,4] have been successful, but are often plagued by complicated diagrammatic rules and are limited to simple models. In the last few years, important advances have been made in this field to complement the diagrammatic theory. Timedependent renormalization group [5,6] and densitymatrix renormalization group method [7] were applied to calculate the real-time convergence toward the steadystate. Real-time methods [5,6,7] calculate the process toward the steady-state and therefore have clear physical interpretations. Unfortunately they often suffer from long-time behaviors associated with low energy strongly correlated states and finite size effects. Direct construction of nonequilibrium ensembles through the scattering state formalism [2,8,9, 10] and field theoretic approach [11] have provided new perspectives to the problem.The main goal of this work is to provide a critical step toward the time-independent description of equilibrium and steady-state nonequilibrium quantum statistics. In addition to the resolution of this fundamental problem, we provide a strong application. The steadystate nonequilibrium can be solved within the same formal structure as equilibrium, and therefore the powerful equilibrium many-body tools, such as the quantum Monte Carlo (QMC) method, can be easily applied to complex transport systems with many competing interactions. We demonstrate this point by applying this formalism to strongly correlated transport in the Kondo regime by using QMC. In contrast to the real-time methods, this approach starts from the steady-state and simulates the effect of many-body interaction. However, numerical analytic continuation and low temperature calculation, especially with the QMC application, are technical difficulties.In the following, we first construct a time-independent statistical ensemble of steady-state nonequilibrium [2] in the non-interacting limit with the i...

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“…In the non-interacting system the scattering states ψ † αkσ can be calculated explicitly [10], in the form of the Lippmann-Schwinger equation [13,14] …”

mentioning

confidence: 99%

Imaginary-Time Formulation of Steady-State Nonequilibrium: Application to Strongly Correlated Transport

2007

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“…The filled circles marks the maxima of the amplitude (8), the open circles the maxima of the cross section according to (10) and the open squares the minima and maxima of the cross section according to (11).…”

Section: Figmentioning

confidence: 99%

“…A similar problem has been considered by Beregi et al who solved the problem with the help of the Faddeev technique [8,9,10]. We will adopt here a simpler approach which is possible due to the Gell-Mann and Goldberger formulation [11]. Due to the different occurring interactions, we define two channels, the one-particle scattering channel V 1 = V a +V b and the corresponding two-particle one, V 2 = V ab .…”

Section: Introductionmentioning

confidence: 99%

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Correlated two-particle scattering on finite cavities

Morawetz

Schreiber²,

Schmidt³

et al. 2005

Phys. Rev. B

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The correlated two-particle problem is solved analytically in the presence of a finite cavity. The method is demonstrated here in terms of exactly solvable models for both the cavity as well as the two-particle correlation where the two-particle potential is chosen in separable form. The twoparticle phase shift is calculated and compared to the single-particle one. The two-particle bound state behavior is discussed and the influence of the cavity on the binding properties is calculated.

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“…The collision ionizes the lithium atom from an initial eigenstate φ n to an ionic eigenstate φ −1 m and the corresponding transition amplitude is [25,26,50,51] …”

Section: A Electron Momentum Spectroscopymentioning

confidence: 99%

Time-resolved electron(e,2e)momentum spectroscopy: Application to laser-driven electron population transfer in atoms

Shao

Starace

2018

Phys. Rev. A

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Owing to its ability to provide unique information on electron dynamics, time-resolved electron momentum spectroscopy (EMS) is used to study theoretically a laser-driven electronic motion in atoms. Specifically, a chirped laser pulse is used to adiabatically transfer the populations of lithium atoms from the ground state to the first excited state. During this process, impact ionization near the Bethe ridge by time-delayed ultrashort, high-energy electron pulses is used to image the instantaneous momentum density of this electronic population transfer. Simulations with 100 fs and 1 fs pulse durations demonstrate the capability of EMS to image the time-varying momentum density, including its change of symmetry as the population transfer progresses. Moreover, the spectra corresponding to different pulse durations reveal different kinds of electronic motion. We discuss how to properly interpret these time-resolved EMS spectra, which represent a generalization of time-independent EMS.

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The Formal Theory of Scattering

Cited by 709 publications

References 10 publications

Imaginary-Time Formulation of Steady-State Nonequilibrium: Application to Strongly Correlated Transport

Imaginary-Time Formulation of Steady-State Nonequilibrium: Application to Strongly Correlated Transport

Correlated two-particle scattering on finite cavities

Time-resolved electron(e,2e)momentum spectroscopy: Application to laser-driven electron population transfer in atoms

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