Lehmann-Symanzik-Zimmermann Formalism in the Lee Model (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>V</mml:mi><mml:mo>−</mml:mo><mml:mi>θ</mml:mi></mml:math>Sector)

Maxon, M. Stephen

doi:10.1103/physrev.149.1273

Cited by 23 publications

(7 citation statements)

References 17 publications

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“…In fact, it is turn out that the multi-particle scattering problems (such as N -θθ scattering) in the Anderson and Lee models were both successfully studied by the LSZ reduction approach 29,30,33,34 . In the following, we start with the model (2) to investigate the S-matrix of scattering photon in the hybrid CRA systems.…”

Section: Relation To Lee Modelmentioning

confidence: 99%

Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

2009

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We present a quantum field theoretical approach based on the Lehmann-Symanzik-Zimmermann reduction for the multi-photon scattering process in a nano-architecture consisting of the coupledresonator arrays (CRA), which are also coupled to some artificial atoms as a controlling quantum node. By making use of this approach, we find the bound states of single photon for an elementary unit, the T-type CRA, and explicitly obtain its multi-photon scattering S-matrix in various situations. We also use this method to calculate the multi-photon S-matrices for the more complex quantum network constructed with main T-type CRA's, such as a H-type CRA waveguide.

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Section: Relation To Lee Modelmentioning

confidence: 99%

Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

2009

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“…Now that we have analyzed one-photon scattering, we will move into the two-photon domain. Following [59] we define 7 the matrix elements in the two-photon sector as…”

Section: Two-photon Scatteringmentioning

confidence: 99%

Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides

Kocabaş

2016

Phys. Rev. A

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We study one-and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atom-photon bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the Lippmann-Schwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed form formulas that successfully predict the trapping rate of a photon in the atom-photon bound state. We verify our formalism through Krylov-subspace based numerical studies with pulsed excitations. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.

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“…(30) we have extended the r --ir to complex z, and extended the lower limit of the integral to q 1 by using the relation (7c). If we set, singular MUSKHELISHIVlLI-type of integral equation can be obtained by a similar procedure that has been used by MAxoN [5] and SCARFONE [7], The solution is given by …”

Section: -K(x Xo) [ X -Z X O + D(~o)c+(~ -X0) (~(X -Z) I~+(~ -~O))]mentioning

confidence: 99%

“…The LEHMAN~--SYMANZIK--ZIMMERMANN (LSZ) technique [1] has been widely used in the L~~ model [2] to calculate the scattering amplitudes in different sectors [3,4,5,6,7]. Previously the dispersion theoretical teehnique based on LSZ formalista was applied to evaluate the scattering amplitudes for a particular process in a sector.…”

Section: Introductionmentioning

confidence: 99%

“…In lower sectors, the MATTHEws--SALAM equations ate coupled in a considerably simpler way which makes the determination of the ~-functions comparatively easier, although in these processes we may be confronted with some singular integral equations. MAXON [5] showed that such techniques can easily be used to determine scattering and production amplitudes in the VO-sector. SCARFONE, on the other hand, applied the technique to the VN- [6] and later on the VV-sectors [7].…”

Section: Introductionmentioning

confidence: 99%

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Multichannel processes inVN- andVV-sectors in an extended lee model

Choudhury

1974

Acta Physica

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The LEHMANN--SYMANZIK--ZIMMERMANN (LSZ) formalism is used in an extended LEE model to calculate the multichannel scattering and production amplitudes in VN-and VV-sectors. The extended model is comprised of two heavy recoiiless particles V and N; and n O particles. The interactions ate in such a way that only processes V ~_ NOI, i = 1,2 .... , n, are allowed. In this multi-O LEE model, the z-functions are evaluated by solving the MAT-THEWS--SALAM equations in the VN-and VV-sectors. Finally the multichannel scattering and production amplitudes are obtained by using standard techniques.

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Lehmann-Symanzik-Zimmermann Formalism in the Lee Model (V−θSector)

Cited by 23 publications

References 17 publications

Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides

Multichannel processes inVN- andVV-sectors in an extended lee model

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