A proposal to include damping effects in the spectral density approach

Campana, L. S.; D'Auria, A. Caramico; D'Ambrosio, M.; Cesare, L. De; Esposito, U.

doi:10.1088/0022-3719/16/17/001

Cited by 10 publications

(10 citation statements)

References 11 publications

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“…Notice that formally, as expected for internal consistency, the function C(ω) = βω or Q η (ω) = (1 + ηe −βDω )/D characterizes the classical or quantum nature of the problem under study, respectively. In analogy with the quantum case [45][46][47], we now introduce the time-dependent classical spectral density (CSD) for A and B [31,37,48,49]:…”

Section: A An Outline Of the Two-time Green's Function Framework In mentioning

confidence: 99%

Thermodynamics of the Classical Planar Ferromagnet Close to the Zero-Temperature Critical Point: A Many-Body Approach

Campana

Cavallo

Cesare

et al. 2012

Advances in Condensed Matter Physics

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We explore the low-temperature thermodynamic properties and crossovers of ad-dimensional classical planar Heisenberg ferromagnet in a longitudinal magnetic field close to its field-induced zero-temperature critical point by employing the two-time Green’s function formalism in classical statistical mechanics. By means of a classical Callen-like method for the magnetization and the Tyablikov-like decoupling procedure, we obtain, for anyd, a low-temperature critical scenario which is quite similar to the one found for the quantum counterpart. Remarkably, ford>2the discrimination between the two cases is found to be related to the different values of the shift exponent which governs the behavior of the critical line in the vicinity of the zero-temperature critical point. The observation of different values of the shift-exponent and of the related critical exponents along thermodynamic paths within the typical V-shaped region in the phase diagram may be interpreted as a signature of emerging quantum critical fluctuations.

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Section: A An Outline Of the Two-time Green's Function Framework In mentioning

confidence: 99%

Thermodynamics of the Classical Planar Ferromagnet Close to the Zero-Temperature Critical Point: A Many-Body Approach

Campana

Cavallo

Cesare

et al. 2012

Advances in Condensed Matter Physics

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“…In these cases, the basic idea of the SDM, related to the moment problem (73), remains still valid, but it is necessary to choose a more appropriate functional structure for the q SD which allows one to determine the modes of excitations in the system and their damping or life time. In the extensive context, a generalization of the SDM in this sense was first proposed by Nolting and Oles [47] for Fermi systems and by Campana et al [48] for Bose and classical systems whose SDs are not positive definite in the whole range of ω.…”

Section: Modified Gaussian Ansatzmentioning

confidence: 99%

“…Following their key idea, to assure the convergency of the q SD moments at any order and to preserve the intrinsic physical character of Λ qAB (ω), one can assume for the q SD the modified Gaussian ansatz [48] Λ qAB (ω) = 2π e βω q…”

Section: Modified Gaussian Ansatzmentioning

confidence: 99%

“…Clearly, with the functional representation (75) for Λ qAB (ω), the width of the peak in ω = 75) is only motivated by the fact that it makes direct contact with the notation used in the literature for extensive problems [47,48] and, in view of previous experiences, it is expected to simplify the algebra also in explicit calculations about q-induced nonextensivity effects.…”

Section: Modified Gaussian Ansatzmentioning

confidence: 99%

“…So, in order to solve self-consistently the finite set of q MEs, which arises from Eq. (73) using the ansatz (74) or (75), it is usually necessary to use some decoupling procedures and thus to introduce, in a systematic way, additional consistent approximations in the SDM as in the extensive case [7,9,47,48].…”

Section: Modified Gaussian Ansatzmentioning

confidence: 99%

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Two-time Green’s functions and spectral density method in nonextensive quantum statistical mechanics

2008

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We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multipliers representation, the q-spectral properties and the methods for a direct calculation of the two-time q-Green's functions and the related q-spectral density (q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q = 1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q-induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q-induced nonextensivity close to the extensive regime are explicitly calculated in the lowtemperature regime by overcoming the calculation of the q grand-partition function.

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Complete Analytical Solution for the Zero Bandwidth s—f Model

Nolting

Matlak

1984

Physica Status Solidi (b)

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The s-f model, which describes an interacting system of localized magnetic moments and itinerant conduction electrons (magnetic 4f-, 5f-systems), is exactly solved in the zero bandwidth limit without further restrictions. The s-f exchange leads to a splitting of the S-''bad'' into four quasiparticle sub"bands", the spectral weights of which are strongly temperature (T)and carrier concentration (n)-dependent. For special parameter constellations certain spectral weights disappear, so that corresponding excitations are forbidden. Besides the spectral weights some relevant correlation functions as the average spin-dependent occupation number (n,), the density correlation , die nichtekorrelation (nun -,), die ,,gemischte" Korrelation dt(0 = (S(*)c:t)ct(l)) & (Sznl(l)) und speziell die Spin-Polarisation P = ((nt) --(ni))/((nt> + (nl)) als sehr einfache Funktionen von T, n und dem Spinwert S formulieren. Es wird ein qualitativ vollig unterschiedliches Verhalten dieser Funktionen fur ferromagnetische s-f-Kopplung (4f-Systeme) und antiferromagnetische s-f-Kopplung (5f-Systeme) gefunden. the "mixed" correlation &) = (S(*)c;t)ey(l)) ') Domagkstr. 75, D-4400 Miinster, FRG. z, On leave from:

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A proposal to include damping effects in the spectral density approach

Cited by 10 publications

References 11 publications

Thermodynamics of the Classical Planar Ferromagnet Close to the Zero-Temperature Critical Point: A Many-Body Approach

Thermodynamics of the Classical Planar Ferromagnet Close to the Zero-Temperature Critical Point: A Many-Body Approach

Two-time Green’s functions and spectral density method in nonextensive quantum statistical mechanics

Complete Analytical Solution for the Zero Bandwidth s—f Model

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