Perturbations of the excited quantum oscillator: From number states to statistical distributions

Sunko, D. K.; Gumhalter, B.

doi:10.1119/1.1587703

Cited by 9 publications

(11 citation statements)

References 31 publications

(45 reference statements)

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“…This exactly solvable limit of the particle-boson Hamiltonian is known as the forced oscillator model [16,17,69,70]. If the correlations are nonvanishing but small, then the second order cumulant expansion provides a good approximation for the calculation of quasiparticle amplitudes (24) [23,32].…”

Section: Range Of Validity and Limitations Of The Second Order Cummentioning

confidence: 99%

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

et al. 2016

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PACS numbers: 71.15.Qe, 71.45.Gm Appendix A: Integral representation of cumulant seriesThe purpose of this appendix is to provide a rigorous mathematical foundation for the transformation (37) and its inverse (39) of the main text. We omit subscripts and superscripts and write simply ρ and C. Our goal is to define the mapping ρ(ν) → C(t), specify its domain and range, prove that it is one-to-one and onto, and describe its inverse map C(t) → ρ(ν). Moreover, at the end of the section we restrict our attention to a rather generic particular case that is sufficient for the application explained in the main part of this paper.Let M + (R) and M(R) respectively denote the space of finite positive measures and the space of finite signed measures on the real line (cf. Sections 1.2 and 4.1 in [1]). Indeed, an element of M(R) is simply a difference of two elements from M + (R). This space contains all absolutely integrable real-valued functions, but it also contains the "true" measures, such as absolutely summable linear combinations of Dirac delta-functions at certain points of R. For any finite signed measure ρ ∈ M(R) we interpret (37)of the main text asThis transformation is well-defined since the function (e −iνt − 1 + iνt)/ν 2 can be extended at ν = 0 in a way that it becomes a bounded continuous function on the whole real line and thus it can be integrated against the measure ρ. The basics of integration theory with respect to abstract measures can be found in the classical textbooks on measure theory, such as [1] and [2]. Let us remark that integration with respect to a general measure ρ is usually written with ρ(ν)dν replaced by dρ(ν) or ρ(dν) in mathematical literature in order to emphasize that ρ need not have a density (i.e. it could be a true measure). We will stick to the former notation, since it is also common to understand signed (or even complex) measures as particular cases of distributions (cf. Section 6.11 in [3]). * Corresponding author. Email: branko@ifs.hr Differentiation of (A1) is justified using the dominated convergence theorem (cf. Theorem 2.27(b) from [2]) and it yieldsĊ In the literature on probability theory (such as Chapter 3 of [7]), ρ is usually called the characteristic function of ρ, even though the normalization is slightly different there. Substituting t = 0 into (A1) and (A2) givesFrom (A3)-(A6) we see that an equivalent way of expressing C in terms of ρ iswith the usual convention thatIt is easy to see that C(t) is always two times continuously differentiable, but it is not true that every such function can be obtained from some ρ ∈ M(R), as we shall soon see.Now we claim that the transform defined by (A1) is a one-to-one map from M(R) to some collection of twice continuously differentiable functions, i.e. that different measures ρ map to different functions C. In order to verify that we assume ρ 1 → C and ρ 2 → C. From (A3) we get2 so the well-known fact that the Fourier-Stieltjes transform ρ → ρ is one-to-one (see Subsection VI. for any choice of points t 1 , . . . , t n ∈ R an...

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Section: Range Of Validity and Limitations Of The Second Order Cummentioning

confidence: 99%

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

et al. 2016

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“…The occupations are determined by the plasmon excitation dynamics and various distributions of excited plasmonic states can be constructed once their values or generating functions are known. [39] In the currently addressed problem obeying the temporal boundary conditions of photoemission induced by ultrashort pulses the cloud of excited plasmons reaches the form of a coherent…”

Section: B Plasmonically Induced Vector Potentialmentioning

confidence: 99%

“…Another limitation affecting expression (45), and thereby (41), may come from the form factor for higher order processes that result in large k (n) f and correspondingly small |ũ s (k 3). Adaptation of expressions (38) for description of experimental situation of n-plasmon assisted electron emission with K = 0 proceeds by combining expressions (39), (41), (42) and (45) to obtain the electron emission cur- rent J s (k…”

Section: Electron Emission From Surface Floquet Bandsmentioning

confidence: 99%

Electron emission from plasmonically induced Floquet bands at metal surfaces

Gumhalter,

Novko,

Petek

2022

Preprint

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We explore the possibility of existence of plasmonically generated electronic Floquet bands at metal surfaces by studying the gauge transformed electron-surface plasmon interaction in the prepumped plasmonic coherent state environment. These bands may promote non-Einsteinian electron emission from metal surfaces exposed to primary interactions with strong electromagnetic fields. Resonant behaviour and scaling of emission yield with the parent electronic structure and plasmonic state parameters are estimated for Ag(111) surface. Relative yield intensities from non-Einsteinian emission channels in photoelectron spectra offer the means to calibrate the mediating plasmonic fields and therefrom ensuing surface Floquet bands.

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“…Hence, in the complete absence of such correlations, as is the case with boson fields perturbed either by structureless or classical time dependent potentials, the cumulant series (25) reduces to a single term given by the second order cumulant (33) in which V k−q,k → V q and ǫ 0 k−q − ǫ 0 k → 0. This exactly solvable limit of the particle-boson Hamiltonian is known as the forced oscillator model [16,17,69,70]. If the correlations are nonvanishing but small, then the second order cumulant expansion provides a good approximation for the calculation of quasiparticle amplitudes (24) [23,32].…”

Section: Range Of Validity and Limitations Of The Second Order Cumula...mentioning

confidence: 99%

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

Gumhalter,

Kovač,

Caruso

et al. 2016

Preprint

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Since the earliest implementations of the various GW approximations and cumulant expansion in the calculations of quasiparticle propagators and spectra, several attempts have been made to combine the advantageous properties and results of these two theoretical approaches. While the GW plus cumulant approach has proven successful in interpreting photoemission spectroscopy data in solids, the formal connection between the two methods has not been investigated in detail. By introducing a general bijective integral representation of the cumulants, we can rigorously identify at which point these two approximations can be connected for the paradigmatic model of quasiparticle interaction with the dielectric response of the system that has been extensively exploited in recent interpretations of the satellite structures in photoelectron spectra. We establish a protocol for consistent practical implementation of the thus established GW+cumulant scheme, and illustrate it by comprehensive state-of-the-art first-principles calculations of intrinsic angle-resolved photoemission spectra from Si valence bands.

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Perturbations of the excited quantum oscillator: From number states to statistical distributions

Cited by 9 publications

References 31 publications

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

Electron emission from plasmonically induced Floquet bands at metal surfaces

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

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