Construction of statistical operators for nonequilibrium processes

Condensed Matter Physics

“…As it is seen from (5.15) and (5.16), retarded (advanced) and causal Green functions are defined via time correlation functions 1|p n (t)p m (t ′ )|̺ 0 , 1|p + n (t)p m (t ′ )|̺ 0 , which satisfy conditions (5.10). For completeness, let us write dispersion relations which connect the imaginary parts ℑm G r,a nm (ω), ℑm G c nm (ω) (5.13), (5.14) and the real parts ℜe G r,a nm (ω), ℜe G c nm (ω) of spectral functions of the corresponding Green functions [ 21,33]:…”

Description of isolated macroscopic systems inside quantum mechanics

“…Not only̺ t provides by construction the expectation values of the relevant observables through the expressions Tr (Â j (ξ)̺ t ) which are linked to the objective state parameter, but also provides probability distributions for measurements which can be performed on the system by the usual tools of quantum mechanics (in the most refined case instruments or operation valued measures). The result (4) is very close to the non-equilibrium statistical operator proposed by Zubarev [2]; the main difference is the choice T → −∞ in the formulation of Zubarev, linked to the fact that no clear distinction is introduced between preparation of the system and its spontaneous evolution. The limit T → −∞ presupposes a thermodynamic limit and introduces big difficulties for a non-equilibrium system.…”

“…Our approach points toward following developments: state parameters ζ(t) in more general situations than already well established hydrodynamics [2], should be considered: e.g., a generalized chemical potential µ(ξ) related to a kinetic description (as already pointed out in reference [9]); also the relevance of the state parameters related to the energy dispersion, first pointed out in other context [10] by Ingarden, should be further investigated. The way in which the parameters ζ(t) and the additional preparation parameters determine the statistical operator is the main point in this paper: one has the indication that the concrete feature of the preparation procedure can be represented inside the formalism; so we expect that the concept of suitable preparation procedure should be amenable to experimental text.…”

“…The relevance of densities of conserved quantities has been stressed in non-equilibrium statistical mechanics, e.g., by Zubarev [2]. They provide in most natural way slow enough quantities, if smeared with sufficiently homogeneous probe functions.…”

Nonequilibrium statistical Zubarev's operator and Green's functions for an inhomogeneous electron gas

“…They play a determining role in the processes of absorption, desorption, in catalytic reactions between atoms and molecules at the surfaces of transition metals [3][4][5], in carbon nanostructures [6,7], including the processes of excitation and ionization of gas atoms and molecules [8][9][10]. Nonequilibrium properties of many-electron systems were explored by means of various methods, in particular by the Green's functions method [11][12][13][14][15][16][17]. For further studies of the Green's function and for specific calculations, the time-dependent method of density functional [24][25][26][27][28][29][30] is developed [24][25][26][27][28][29][30] based on the Kohn-Sham ideas [18][19][20], with formulation based on the hydrodynamic approach [21,22] and Mori-like projection operators [23].…”