scholarly journals Thermodynamic formalism for quantum channels: Entropy, pressure, Gibbs channels and generic properties

2021 ◽  
Author(s):  
Jader E. Brasil ◽  
Josué Knorst ◽  
Artur O. Lopes
Keyword(s):  
Density Operator ◽  
A Priori ◽  
Thermodynamic Formalism ◽  
Quantum Channels ◽  
Generic Properties ◽  
Ruelle Operator ◽  
Density Operators ◽  
Starting Point ◽  
Generic Set ◽  
Related Process

Denote [Formula: see text] the set of complex [Formula: see text] by [Formula: see text] matrices. We will analyze here quantum channels [Formula: see text] of the following kind: given a measurable function [Formula: see text] and the measure [Formula: see text] on [Formula: see text] we define the linear operator [Formula: see text], via the expression [Formula: see text]. A recent paper by T. Benoist, M. Fraas, Y. Pautrat, and C. Pellegrini is our starting point. They considered the case where [Formula: see text] was the identity. Under some mild assumptions on the quantum channel [Formula: see text] we analyze the eigenvalue property for [Formula: see text] and we define entropy for such channel. For a fixed [Formula: see text] (the a priori measure) and for a given a Hamiltonian [Formula: see text] we present a version of the Ruelle Theorem: a variational principle of pressure (associated to such [Formula: see text]) related to an eigenvalue problem for the Ruelle operator. We introduce the concept of Gibbs channel. We also show that for a fixed [Formula: see text] (with more than one point in the support) the set of [Formula: see text] such that it is [Formula: see text]-Erg (also irreducible) for [Formula: see text] is a generic set. We describe a related process [Formula: see text], [Formula: see text], taking values on the projective space [Formula: see text] and analyze the question of the existence of invariant probabilities. We also consider an associated process [Formula: see text], [Formula: see text], with values on [Formula: see text] ([Formula: see text] is the set of density operators). Via the barycenter, we associate the invariant probability mentioned above with the density operator fixed for [Formula: see text].

scholarly journals Entropy and variational principle for one-dimensional lattice systems with a generala prioriprobability: positive and zero temperature

2014 ◽  
Vol 35 (6) ◽  
pp. 1925-1961 ◽  
Author(s):  
A. O. LOPES ◽  
J. K. MENGUE ◽  
J. MOHR ◽  
R. R. SOUZA
Keyword(s):  
Infinite Product ◽  
A Priori ◽  
Transfer Operator ◽  
Thermodynamic Formalism ◽  
General Setting ◽  
Lattice Systems ◽  
Ruelle Operator ◽  
Finite Set ◽  
Zero Entropy ◽  
Infinite Set

We generalize several results of the classical theory of thermodynamic formalism by considering a compact metric space$M$as the state space. We analyze the shift acting on$M^{\mathbb{N}}$and consider a generala prioriprobability for defining the transfer (Ruelle) operator. We study potentials$A$which can depend on the infinite set of coordinates in$M^{\mathbb{N}}$. We define entropy and by its very nature it is always a non-positive number. The concepts of entropy and transfer operator are linked. If$M$is not a finite set there exist Gibbs states with arbitrary negative value of entropy. Invariant probabilities with support in a fixed point will have entropy equal to minus infinity. In the case$M=S^{1}$, and thea priorimeasure is Lebesgue$dx$, the infinite product of$dx$on$(S^{1})^{\mathbb{N}}$will have zero entropy. We analyze the Pressure problem for a Hölder potential$A$and its relation with eigenfunctions and eigenprobabilities of the Ruelle operator. Among other things we analyze the case where temperature goes to zero and we show some selection results. Our general setting can be adapted in order to analyze the thermodynamic formalism for the Bernoulli space with countable infinite symbols. Moreover, the so-called$XY$model also fits under our setting. In this last case$M$is the unitary circle$S^{1}$. We explore the differentiable structure of$(S^{1})^{\mathbb{N}}$by considering a certain class of smooth potentials and we show some properties of the corresponding main eigenfunctions.

On Lower and Semi-Lower Density Operators

2007 ◽  
Vol 14 (4) ◽  
pp. 661-671
Author(s):  
Jacek Hejduk ◽  
Anna Loranty
Keyword(s):  
Density Operator ◽  
Baire Property ◽  
Density Operators ◽  
Dense Sets ◽  
Meager Sets ◽  
Algebras Of Sets

Abstract This paper contains some results connected with topologies generated by lower and semi-lower density operators. We show that in some measurable spaces (𝑋, 𝑆, 𝐽) there exists a semi-lower density operator which does not generate a topology. We investigate some properties of nowhere dense sets, meager sets and σ-algebras of sets having the Baire property, associated with the topology generated by a semi-lower density operator.

scholarly journals An historical framework for psychiatric nosology

2009 ◽  
Vol 39 (12) ◽  
pp. 1935-1941 ◽  
Author(s):  
K. S. Kendler
Keyword(s):  
Psychiatric Illness ◽  
Theoretical Orientation ◽  
A Priori ◽  
Early History ◽  
Top Down ◽  
Species Definition ◽  
Psychiatric Nosology ◽  
Bottom Up ◽  
Starting Point ◽  
History Of

This essay, which seeks to provide an historical framework for our efforts to develop a scientific psychiatric nosology, begins by reviewing the classificatory approaches that arose in the early history of biological taxonomy. Initial attempts at species definition used top-down approaches advocated by experts and based on a few essential features of the organism chosena priori. This approach was subsequently rejected on both conceptual and practical grounds and replaced by bottom-up approaches making use of a much wider array of features. Multiple parallels exist between the beginnings of biological taxonomy and psychiatric nosology. Like biological taxonomy, psychiatric nosology largely began with ‘expert’ classifications, typically influenced by a few essential features, articulated by one or more great 19th-century diagnosticians. Like biology, psychiatry is struggling toward more soundly based bottom-up approaches using diverse illness characteristics. The underemphasized historically contingent nature of our current psychiatric classification is illustrated by recounting the history of how ‘Schneiderian’ symptoms of schizophrenia entered into DSM-III. Given these historical contingencies, it is vital that our psychiatric nosologic enterprise be cumulative. This can be best achieved through a process of epistemic iteration. If we can develop a stable consensus in our theoretical orientation toward psychiatric illness, we can apply this approach, which has one crucial virtue. Regardless of the starting point, if each iteration (or revision) improves the performance of the nosology, the eventual success of the nosologic process, to optimally reflect the complex reality of psychiatric illness, is assured.

scholarly journals Ecocriticism as Subversive Aesthetics

2019 ◽  
pp. 17
Author(s):  
Jelka Kernev Štrajn
Keyword(s):  
Media Studies ◽  
Animal Studies ◽  
Academic Discipline ◽  
A Priori ◽  
Minority Literature ◽  
Contemporary Theory ◽  
Female Authors ◽  
Starting Point ◽  
Literary Art ◽  
Level Of Consciousness

Art is subversive when it crosses the boundary of the generally acceptable, though over time such art can and does become mainstream. A much more complicated question is what is subversive in aesthetics? Ecocriticism has already become, along with ecofeminism and animal studies, an academic discipline. It can be defined as subversive if it is understood in terms of an attitude, which is not anthropocentric. And here is the catch: how can the human also encompass the alien? The question that emerges here is all but rhetorical: how can we decentre and amplify our human consciousness and perspective to include zoocentric, biocentric or geocentric positions? At this point the contemporary theory creates contrasting opinions, which cross the boundaries of aesthetics, poetics and ecocriticism since they reach out to the fields of metaphysics and antimetaphysics. Within the phenomenon of perception the other always appears, as Deleuze said in his Logic of Sense, as “a priori Other”. We have to deal, henceforth, with a kind of pre-reflexive level of consciousness and amplified sensory perception, which, as we know, is the basic condition of artistic creation. Thus, this paper – because it seeks to penetrate into the node of these questions – takes literary art as its starting point. In the spirit of the above-mentioned observations, I have attempted to investigate in ‘minority literature’ (female authors of contemporary Polish and Slovene literature) how this decentred attitude, which Jure Detela, a Slovene poet, poetically defined, corresponds to our thesis on a particular ecocritical stream, which can be defined as an ecofeminist aesthetics. The ‘minoritarian literature’ here is meant exclusively in the sense that was defined by Deleuze and Guattari’s books Kafka and A Thousand Plateaus. Article received: April 12, 2019; Article accepted: July 6, 2019; Published online: October 15, 2019; Original scholarly paperHow to cite this article: Kernev Štrajn, Jelka. "Ecocriticism as Subversive Aesthetics." AM Journal of Art and Media Studies 20 (2019): 17-25. doi: 10.25038/am.v0i20.321

scholarly journals An Optimal Estimation Method for Nonlinear Models of Mechanical Systems

1994 ◽  
Vol 116 (4) ◽  
pp. 805-810 ◽  
Author(s):  
M. J. G. van de Molengraft ◽  
F. E. Veldpaus ◽  
J. J. Kok
Keyword(s):  
Nonlinear Models ◽  
A Priori ◽  
Mechanical Systems ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Model Structure ◽  
Unknown Parameters ◽  
Starting Point ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical Systems

This paper presents an optimal estimation method for nonlinear mechanical systems. The a priori knowledge of the system in the form of a nonlinear model structure is taken as a starting point. The method determines estimates of the parameters and estimates of the positions, velocities, accelerations, and inputs of the system. The optimal estimation method is applied to an experimental mechanical system. The unknown parameters in this system relate to inertia, friction and elastic deformation. It is shown that the optimal estimation method on the basis of a relatively simple model structure can lead to a useful description of the system.

scholarly journals Mass balance inverse modelling of methane in the 1990s using a Chemistry Transport Model

2004 ◽  
Vol 4 (11/12) ◽  
pp. 2561-2580 ◽  
Author(s):  
T. M. Butler ◽  
I. Simmonds ◽  
P. J. Rayner
Keyword(s):  
Mass Balance ◽  
Transport Model ◽  
A Priori ◽  
Inverse Modelling ◽  
Chemical Transport Model ◽  
Methane Cycle ◽  
Surface Distribution ◽  
Inverse Results ◽  
Methane Budget ◽  
Starting Point

Abstract. A mass balance inverse modelling procedure is applied with a time-dependent methane concentration boundary condition and a chemical transport model to relate observed changes in the surface distribution of methane mixing ratios during the 1990s to changes in its surface sources. The model reproduces essential features of the global methane cycle, such as the latitudinal distribution and seasonal cycle of fluxes, without using a priori knowledge of methane fluxes. A detailed description of the temporal and spatial variability of the fluxes diagnosed by the inverse procedure is presented, and compared with previously hypothesised changes in the methane budget, and previous inverse modelling studies. The sensitivity of the inverse results to the forcing data supplied by surface measurements of methane from the NOAA CMDL cooperative air sampling network is also examined. This work serves as an important starting point for future inverse modelling work examining changes in both the source and sink terms in the methane budget together.

Projected evolution superoperators and the density operator: theory and applications to inelastic scattering

1982 ◽  
Vol 60 (10) ◽  
pp. 1371-1386 ◽  
Author(s):  
R. E. Turner ◽  
J. S. Dahler ◽  
R. F. Snider
Keyword(s):  
Inelastic Scattering ◽  
Density Operator ◽  
Operator Method ◽  
Time Dependent ◽  
Interaction Picture ◽  
Von Neumann ◽  
First Order ◽  
Density Operators ◽  
Projection Operator Method ◽  
Time Dependent Solution

The projection operator method of Zwanzig and Feshbach is used to construct the time dependent density operator associated with a binary scattering event. The formula developed to describe this time dependence involves time-ordered cosine and sine projected evolution (memory) superoperators. Both Sehrödinger and interaction picture results are presented. The former is used to demonstrate the equivalence of the time dependent solution of the von Neumann equation and the more familiar, frequency dependent Laplaee transform solution. For two particular classes of projection superoperators projected density operators arc shown to be equivalent to projected wave functions. Except for these two special eases, no projected wave function analogs of projected density operators exist. Along with the decoupled-motions approximation, projected interaction picture density operators arc applied to inelastic scattering events. Simple illustrations arc provided of how this formalism is related to previously established results for two-state processes, namely, the theory of resonant transfer events, the first order Magnus approximation, and the Landau–Zener theory.

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