Note on the Path-Integral Variational Approach in Many-Body Theory

Devreese, Jozef T.

doi:10.1142/9789812811240_0026

Cited by 6 publications

(9 citation statements)

References 26 publications

(72 reference statements)

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“…A parabolic confinement potential characterized by the confinement energy Ω 0 and with a background charge is considered. Using a generalization of the Jensen-Feynman variational principle [98,100], the ground-state energy of a confined N-polaron system is analyzed as a function of N and of the electron-phonon coupling strength α [101,102].…”

Section: Many-polaron Systems In Quantum Dotsmentioning

confidence: 99%

Fröhlich polarons from 0D to 3D: concepts and recent developments

Devreese

2007

J. Phys.: Condens. Matter

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Section: Many-polaron Systems In Quantum Dotsmentioning

confidence: 99%

Fröhlich polarons from 0D to 3D: concepts and recent developments

Devreese

2007

J. Phys.: Condens. Matter

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“…A more detailed analysis of this variational principle for both local and retarded interactions can be found in Ref. [10]. It is required that the potentials are symmetric with respect to all permutations of the particle positions, and that both the exact propagator and the model propagator are antisymmetric (for fermions) with respect to permutations of any two electrons at any time.…”

Section: Theoretical Approachmentioning

confidence: 99%

“…In Refs. [6,7], the ground state and the optical response of a fixed number of identical interacting polarons are analyzed using the variational path-integral method for identical particles [8,9,10]. As far as we investigate a system with a fixed number of identical particles, it should be described using the canonical ensemble [10].…”

Section: Introductionmentioning

confidence: 99%

Characterization of shell filling of interacting polarons in a quantum dot through their optical absorption

Klimin

Fomin

Brosens

et al. 2004

Physica E: Low-dimensional Systems and Nanostructures

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The method for calculating the ground-state energy and the optical conductivity spectra is developed for a system of a finite number of interacting arbitrary-coupling polarons in a spherical quantum dot with a parabolic confinement potential. The path-integral formalism for identical particles is used in order to take into account the fermion statistics. Using a generalization of the Jensen-Feynman variational principle, the ground-state energy of a confined N -polaron system is analyzed as a function of N and of the electron-phonon coupling strength. The calculated optical conductivity spectra of the N -polaron system in a quantum dot manifest features related to ground-state transitions between states with different total spin.

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“…A more detailed analysis of this variational principle for both local and retarded interactions can be found in Ref. [4]. It is required that the potentials are symmetric with respect to all permutations of the particle positions, and that both the exact propagator and the model propagator are antisymmetric (for fermions) with respect to permutations of any two electrons at any point in time.…”

Section: Zp({no-}(3)=l (~Llp Jdx Fpxdx(t)e-sp[x(t)]mentioning

confidence: 99%

“…This means that those propagators must be defined on the same configuration space. Keeping in mind these requirements, the variational inequality for identical particles has the same form as the standard Jensen-Feynman variational principle: (4) where So is a model action with corresponding free energy Fo. So must fulfil the properties, which were mentioned above.…”

Section: Zp({no-}(3)=l (~Llp Jdx Fpxdx(t)e-sp[x(t)]mentioning

confidence: 99%

Polarons in Semiconductor Quantum Structures

Devreese

2004

Molecular Nanowires and Other Quantum Objects

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In this presentation three recent contributions to the theory of continuum (or "Frohlich"-) polarons are reviewed. (i) Using a generalization of the JensenFeynman variational principle within the path-integral formalism for identical particles, the ground-state energy of a confined N -polaron system is studied as a function of N and of the electron-phonon coupling strength.(ii) A theoretical investigation of the optical properties of stacked quantum dots is presented, which is based on the non-adiabatic approach. (iii) Cyclotron-resonance (CR) spectra of a gas of interacting polarons in a GaAs/AIAs quantum well are theoretically investigated taking into account the magnetoplasmon-phonon mixing and the band nonparabolicity. The theory explains that, for a high-density polaron gas, anticrossing of the CR spectra occurs near the GaAs TO-phonon frequency rather than near the GaAs LO-frequency in a good agreement with experimental data.Keywords: polaron, quantum dot, cyclotron resonance, optical absorption, luminescence Interacting poiarons in a quantum dotThermodynamic and optical properties of interacting polarons have attracted increasing attention because of their possible relevance to physical phenomena in high-Tc superconductors (see, e. g., Ref.[1] and references therein). In this section, a system of N electrons with mutual Coulomb repulsion and interacting with the lattice vibrations is considered. A parabolic confinement potential, characterised by the frequency parameter no, is assumed. The total number of electrons is N = 2:cr Ncr, where Ncr is the number of electrons with spin projection (J = ±1/2. A canonical ensemble is treated, where the numbers of electrons Ncr for each (J are fixed. The bulk phonons (characterized by wave vectors q and frequencies wq ) are described by complex coordinates. The full set of electron coordinates is denoted by x == {Xj,cr }.

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Note on the Path-Integral Variational Approach in Many-Body Theory

Cited by 6 publications

References 26 publications

Fröhlich polarons from 0D to 3D: concepts and recent developments

Fröhlich polarons from 0D to 3D: concepts and recent developments

Characterization of shell filling of interacting polarons in a quantum dot through their optical absorption

Polarons in Semiconductor Quantum Structures

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