scholarly journals :THE COSMOLOGICAL OTOC: Formulating New Cosmological Micro-Canonical Correlation Functions for Random Chaotic Fluctuations in Out-Of-Equilibrium Quantum Statistical Field Theory

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1527 ◽  
Author(s):  
Sayantan Choudhury
Keyword(s):  
Field Theory ◽  
Time Scale ◽  
Quantum Correlation ◽  
The Other ◽  
Late Time ◽  
Cosmological Perturbation ◽  
Conjugate Momentum ◽  
Dynamical Time ◽  
Definition Of ◽  
Canonically Conjugate Momentum

The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, using for the first time the slogan “Cosmology meets Condensed Matter Physics”, we demonstrate a formalism to compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following the canonical quantization technique. In this computation, two dynamical time scales are involved—out of them, at one time scale, the cosmological perturbation variable, and for the other, the canonically conjugate momentum, is defined, which is the strict requirement to define the time scale-separated quantum operators for OTOC and is perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism, not only one can study the quantum correlation during stochastic inflation and reheating, but can also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism, we study the phenomenon of quantum chaos by computing the expression for the Lyapunov spectrum. Furthermore, using the well known Maldacena Shenker Stanford (MSS) bound on the Lyapunov exponent, λ≤2π/β, we propose a lower bound on the equilibrium temperature, T=1/β, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the perturbation variable is associated, we find decreasing, but not exponentially decaying, behaviour, which quantifies the random quantum correlation function out-of-equilibrium. We have also studied the classical limit of the OTOC and checked the consistency with the large time limiting behaviour of the correlation. Finally, we prove that the normalized version of OTOC is completely independent of the choice of the preferred definition of the cosmological perturbation variable.

scholarly journals The Cosmological OTOC: Formulating New Cosmological Micro-Canonical Correlation Functions for Random Chaotic Fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory

2020 ◽  
Author(s):  
Sayantan Choudhury
Keyword(s):  
Field Theory ◽  
Time Scale ◽  
Quantum Correlation ◽  
The Other ◽  
General Definition ◽  
Late Time ◽  
Conjugate Momentum ◽  
Statistical Field ◽  
Dynamical Time ◽  
Canonically Conjugate Momentum

The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, with the slogan "Cosmology meets Condensed Matter Physics" we demonstrate a formalism using which for the first time we compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following canonical quantization technique. In this computation, two dynamical time scales are involved, out of them at one time scale the cosmological perturbation variable and for the other the canonically conjugate momentum is defined, which is the strict requirement to define time scale separated quantum operators for OTOC and perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism not only one can study the quantum correlation during stochastic inflation and reheating, but also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism we study the phenomena of quantum chaos by computing the expression for {\it Lyapunov spectrum}. Further, using the well known Maldacena Shenker Stanford (MSS) bound, on Lyapunov exponent, λ≤2π/β, we propose a lower bound on the equilibrium temperature, T=1/β, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the perturbation variable is associated, we find decreasing but not exponentially decaying behaviour, which quantifies the random correlation at out-of-equilibrium. Finally, we have studied the classical limit of the OTOC to check the consistency with the large time limiting behaviour.

scholarly journals TIME AND TACHYON

2003 ◽  
Vol 18 (26) ◽  
pp. 4869-4888 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Canonical Quantization ◽  
Recent Analysis ◽  
Late Time ◽  
Classical Dynamics ◽  
One To One ◽  
Definition Of

Recent analysis suggests that the classical dynamics of a tachyon on an unstable D-brane is described by a scalar Born–Infeld type action with a runaway potential. The classical configurations in this theory at late time are in one to one correspondence with the configuration of a system of noninteracting (incoherent), nonrotating dust. We discuss some aspects of canonical quantization of this field theory coupled to gravity, and explore, following an earlier work on this subject, the possibility of using the scalar field (tachyon) as the definition of time in quantum cosmology. At late "time" we can identify a subsector in which the scalar field decouples from gravity and we recover the usual Wheeler–de Witt equation of quantum gravity.

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

scholarly journals Language Family Engineering with Product Lines of Multi-level Models

2021 ◽  
Author(s):  
Juan de Lara ◽  
Esther Guerra
Keyword(s):  
Software Engineering ◽  
Arbitrary Number ◽  
Formal Theory ◽  
The Other ◽  
Language Family ◽  
Top Down ◽  
Product Lines ◽  
Modelling Languages ◽  
Multi Level ◽  
Definition Of

AbstractModelling is an essential activity in software engineering. It typically involves two meta-levels: one includes meta-models that describe modelling languages, and the other contains models built by instantiating those meta-models. Multi-level modelling generalizes this approach by allowing models to span an arbitrary number of meta-levels. A scenario that profits from multi-level modelling is the definition of language families that can be specialized (e.g., for different domains) by successive refinements at subsequent meta-levels, hence promoting language reuse. This enables an open set of variability options given by all possible specializations of the language family. However, multi-level modelling lacks the ability to express closed variability regarding the availability of language primitives or the possibility to opt between alternative primitive realizations. This limits the reuse opportunities of a language family. To improve this situation, we propose a novel combination of product lines with multi-level modelling to cover both open and closed variability. Our proposal is backed by a formal theory that guarantees correctness, enables top-down and bottom-up language variability design, and is implemented atop the MetaDepth multi-level modelling tool.

scholarly journals Smooth functorial field theories from B-fields and D-branes

2021 ◽  
Vol 16 (1) ◽  
pp. 75-153
Author(s):  
Severin Bunk ◽  
Konrad Waldorf
Keyword(s):  
Field Theory ◽  
Sigma Models ◽  
Lagrangian Approach ◽  
Field Theories ◽  
Open Strings ◽  
Homotopy Invariant ◽  
Target Manifold ◽  
Definition Of ◽  
Smooth Map

AbstractIn the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth open-closed functorial field theory (FFT) in the sense of Atiyah, Segal, and Stolz–Teichner. We give a detailed construction of this smooth FFT, based on the definition of a suitable smooth bordism category. In this bordism category, all manifolds are equipped with a smooth map to a spacetime target manifold. Further, the object manifolds are allowed to have boundaries; these are the endpoints of open strings stretched between D-branes. The values of our FFT are obtained from the B-field and its D-branes via transgression. Our construction generalises work of Bunke–Turner–Willerton to include open strings. At the same time, it generalises work of Moore–Segal about open-closed TQFTs to include target spaces. We provide a number of further features of our FFT: we show that it depends functorially on the B-field and the D-branes, we show that it is thin homotopy invariant, and we show that it comes equipped with a positive reflection structure in the sense of Freed–Hopkins. Finally, we describe how our construction is related to the classification of open-closed TQFTs obtained by Lauda–Pfeiffer.

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

Identity, Community and Belonging in gcc States

2018 ◽  
Vol 6 (4) ◽  
pp. 401-428
Author(s):  
Miriam R. Lowi
Keyword(s):  
Religious Affiliation ◽  
Protective Role ◽  
The Other ◽  
National Project ◽  
Scholarly Literature ◽  
National Community ◽  
The Difference ◽  
Definition Of

Studies of identity and belonging in Gulf monarchies tend to privilege tribal or religious affiliation, if not the protective role of the ruler as paterfamilias. I focus instead on the ubiquitous foreigner and explore ways in which s/he contributes to the definition of national community in contemporary gcc states. Building upon and moving beyond the scholarly literature on imported labor in the Gulf, I suggest that the different ‘categories’ of foreigners impact identity and the consolidation of a community of privilege, in keeping with the national project of ruling families. Furthermore, I argue that the ‘European,’ the non-gcc Arab, and the predominantly Asian (and increasingly African) laborer play similar, but also distinct roles in the delineation of national community: while they are differentially incorporated in ways that protect the ‘nation’ and appease the citizen-subject, varying degrees of marginality reflect Gulf society’s perceptions or aspirations of the difference between itself and ‘the other(s).’

scholarly journals Note on osmotic pressure

1914 ◽  
Vol 90 (615) ◽  
pp. 41-45
Keyword(s):  
Osmotic Pressure ◽  
Vapour Pressure ◽  
Numerical Data ◽  
The Other ◽  
Present Moment ◽  
Capillary Surface ◽  
Pure Solvent ◽  
Definition Of ◽  
Complete Account ◽  
Strict Definition

The vapour pressure theory regards osmotic pressure as the pressure required to produce equilibrium between the pure solvent and the solution. Pressure applied to a solution increases its internal vapour pressure. If the compressed solution be on one aide of a semi-permeable partition and the pure solvent on the other, there is osmotic equilibrium when the com-pression of the solution brings its vapour pressure to equality with that of the solvent. So long ago as 1894 Ramsay* found that with a partition of palladium, permeable to hydrogen but not to nitrogen, the hydrogen pressures on each side tended to equality, notwithstanding the presence of nitrogen under pressure on one side, which it might have been supposed would have resisted tin- transpiration of the hydrogen. The bearing of this experiment on the problem of osmotic pressure was recognised by van’t Hoff, who observes that "it is very instructive as regards the means by which osmotic pressure is produced." But it was not till 1908 that the vapour pressure theory of osmotic pressure was developed on a finu foundation by Calendar. He demonstrated, by the method of the "vapour sieve" piston, the proposition that “any two solutions in equilibrium through any kind of membrane or capillary surface must have the same vapour pressures in respect of each of their constituents which is capable of diffusing through their surface of separation"—a generalisation of great importance for the theory of solutions. Findlay, in his admirable monograph, gives a very complete account of the contending theories of osmotic pressure, a review of which leaves no doubt that at the present moment the vapour pressure theory stands without a serious rival Some confusion of ideas still arises from the want of adherence to a strict definition of osmotic pressure to which numerical data from experimental measurements should he reduced. Tire following definitions appear to be tire outcome of tire vapour pressure theory :— Definition I.—The vapour pressure of a solution is the pressure of the vapour with which it is in equilibrium when under pressure of its own vapour only.

Emerson's Atom and the Matter of Suffering

2009 ◽  
Vol 64 (1) ◽  
pp. 16-47
Author(s):  
Mark Noble
Keyword(s):  
Field Theory ◽  
Natural History ◽  
Classical Field Theory ◽  
Classical Field ◽  
The Other ◽  
History Of ◽  
The One ◽  
The Individual ◽  
Solid Bodies ◽  
Lines Of Force

This essay argues that Ralph Waldo Emerson's interest in the cutting-edge science of his generation helps to shape his understanding of persons as fluid expressions of power rather than solid bodies. In his 1872 "Natural History of Intellect," Emerson correlates the constitution of the individual mind with the tenets of Michael Faraday's classical field theory. For Faraday, experimenting with electromagnetism reveals that the atom is a node or point on a network, and that all matter is really the arrangement of energetic lines of force. This atomic model offers Emerson a technology for envisioning a materialized subjectivity that both unravels personal identity and grants access to impersonal power. On the one hand, adopting Faraday's field theory resonates with many of the affirmative philosophical and ethical claims central to Emerson's early essays. On the other hand, however, distributing the properties of Faraday's atoms onto the properties of the person also entails moments in which materialized subjects encounter their own partiality, limitation, and suffering. I suggest that Emerson represents these aspects of experience in terms that are deliberately discrepant from his conception of universal power. He presumes that if every experience boils down to the same lines of force, then the particular can be trivialized with respect to the general. As a consequence, Emerson must insulate his philosophical assertions from contamination by our most poignant experiences of limitation. The essay concludes by distinguishing Emersonian "Necessity" from Friedrich Nietzsche's similar conception of amor fati, which routes the affirmation of fate directly through suffering.

Two Commentaries on Euclid's Definition of Proportional Magnitudes

1994 ◽  
Vol 4 (1) ◽  
pp. 181-198 ◽  
Author(s):  
Bijan Vahabzadeh
Keyword(s):  
18Th Century ◽  
The Other ◽  
Identical Manner ◽  
Definition Of

Euclid's definition of proportional magnitudes in the Fifth Book of the Elements gave rise to many commentaries. We examine closely two of these commentaries, one by al-Jayyānī (11th century) and the other by Saunderson (18th century). Both al-Jayyānī and Saunderson attempted to defend Euclid's definition by making explicit what Euclid had only implied. We show that the two authors explain Euclid's position in a virtually identical manner.

Sign in / Sign up

Export Citation Format

Share Document