scholarly journals The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 599
Author(s):  
Sayantan Choudhury
Keyword(s):  
Canonical Quantization ◽  
Computational Method ◽  
Cosmological Perturbation ◽  
New Formalism ◽  
Random Events ◽  
Dynamical Time ◽  
Limiting Behaviour ◽  
Cosmological Scalar ◽  
Random Fluctuations ◽  
Non Equilibrium

The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by following the canonical quantization technique, we demonstrate a computational method to quantify the two different types of cosmological auto-correlated OTO functions during the epoch when the non-equilibrium features dominates in primordial cosmology. In this formulation, two distinct dynamical time scales are involved to define the quantum mechanical operators arising from the cosmological perturbation scenario. We have provided detailed explanation regarding the necessity of this new formalism to quantify any random events generated from quantum fluctuations in primordial cosmology. We have performed an elaborative computation for the two types of two-point and four-point auto-correlated OTO functions in terms of the cosmological perturbation field variables and its canonically conjugate momenta to quantify random auto-correlations in the non-equilibrium regime. For both of the cases, we found significantly distinguishable non-chaotic, but random, behaviour in the OTO auto-correlations, which was not pointed out before in this type of study. Finally, we have also demonstrated the classical limiting behaviour of the mentioned two types of auto-correlated OTOC functions from the thermally weighted phase-space averaged Poisson brackets, which we found to exactly match the large time limiting behaviour of the auto-correlations in the super-horizon regime of the cosmological scalar mode fluctuation.

scholarly journals The Cosmological OTOC: A New Proposal for Quantifying Auto-correlated Random Non-chaotic Primordial Fluctuations

2021 ◽  
Author(s):  
Sayantan Choudhury
Keyword(s):  
Canonical Quantization ◽  
Computational Method ◽  
Cosmological Perturbation ◽  
New Formalism ◽  
Random Events ◽  
Dynamical Time ◽  
Limiting Behaviour ◽  
Cosmological Scalar ◽  
Random Fluctuations ◽  
Non Equilibrium

The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by following the canonical quantization technique we demonstrate a computational method to quantify the two different types of Cosmological auto-correlated OTO functions during the epoch when the non-equilibrium features dominates in Primordial Cosmology. In this formulation, two distinct dynamical time scales are involved to define the quantum mechanical operators arising from cosmological perturbation scenario. We have provided detailed explanation regarding the necessity of this new formalism to quantify any random events generated from quantum fluctuations in Primordial Cosmology. We have performed an elaborative computation for the two types of two-point and four-point auto-correlated OTO functions in terms of the cosmological perturbation field variables and its canonically conjugate momenta to quantify random auto-correlations in the non-equilibrium regime. For both the cases we found significantly distinguishable non-chaotic, but random behaviour in the OTO auto-correlations, which was not pointed before in this type of studies. Finally, we have also demonstrated the classical limiting behaviour of the mentioned two types of auto-correlated OTOC functions from the thermally weighted phase space averaged Poisson Brackets, which we found exactly matches with the large time limiting behaviour of the auto-correlations in the super-horizon regime of the cosmological scalar mode fluctuation.

scholarly journals The Cosmological OTOC: A New Proposal for Quantifying Auto-correlated Random Non-chaotic Primordial Fluctuations

2021 ◽  
Author(s):  
Sayantan Choudhury
Keyword(s):  
Canonical Quantization ◽  
Computational Method ◽  
Cosmological Perturbation ◽  
New Formalism ◽  
Random Events ◽  
Dynamical Time ◽  
Limiting Behaviour ◽  
Cosmological Scalar ◽  
Random Fluctuations ◽  
Non Equilibrium

The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by following the canonical quantization technique we demonstrate a computational method to quantify the two different types of Cosmological auto-correlated OTO functions during the epoch when the non-equilibrium features dominates in Primordial Cosmology. In this formulation, two distinct dynamical time scales are involved to define the quantum mechanical operators arising from cosmological perturbation scenario. We have provided detailed explanation regarding the necessity of this new formalism to quantify any random events generated from quantum fluctuations in Primordial Cosmology. We have performed an elaborative computation for the two types of two-point and four-point auto-correlated OTO functions in terms of the cosmological perturbation field variables and its canonically conjugate momenta to quantify random auto-correlations in the non-equilibrium regime. For both the cases we found significantly distinguishable non-chaotic, but random behaviour in the OTO auto-correlations, which was not pointed before in this type of studies. Finally, we have also demonstrated the classical limiting behaviour of the mentioned two types of auto-correlated OTOC functions from the thermally weighted phase space averaged Poisson Brackets, which we found exactly matches with the large time limiting behaviour of the auto-correlations in the super-horizon regime of the cosmological scalar mode fluctuation.

Conditional interpretation of time in quantum gravity and a time operator in relativistic quantum mechanics

2020 ◽  
Vol 35 (21) ◽  
pp. 2050114
Author(s):  
M. Bauer ◽  
C. A. Aguillón ◽  
G. E. García
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Relativistic Quantum ◽  
Canonical Quantization ◽  
Time Operator ◽  
Relativistic Quantum Mechanics ◽  
Problem Of Time ◽  
Quantization Of Gravity ◽  
Dynamical Time ◽  
Spatial Coordinates

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.

Coupled Non-Equilibrium Green’s Function (NEGF) Electron-Phonon Interaction in Thermoelectric Materials

2011 ◽  
Author(s):  
T. D. Musho ◽  
D. G. Walker
Keyword(s):  
Thermoelectric Materials ◽  
Thermal Transport ◽  
Phonon Scattering ◽  
Computational Method ◽  
Direct Result ◽  
Inelastic Electron ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Scattering ◽  
Non Equilibrium

Over the last decade, nano-structured materials have shown a promising avenue for enhancement of the thermoelectric figure of merit. These performance enhancements in most cases have been a direct result of selectively modifying certain geometric attributes that alter the thermal or electrical transport in a desirable fashion. More often, models used to study the electrical and/or thermal transport are calculated independent of each other. However, studies have suggested electrical and thermal transport are intimately linked at the nanoscale. This provides an argument for a more rigorous treatment of the physics in an effort to capture the response of both electrons and phonons simultaneously. A simulation method has been formulated to capture the electron-phonon interaction of nanoscale electronics through a coupled non-equilibrium Greens function (NEGF) method. This approach is unique because the NEGF electron solution and NEGF phonon solution have only been solved independently and have never been coupled to capture a self-consistent inelastic electron-phonon scattering. One key aspect of this formalism is that the electron and phonon description is derived from a quantum point of view and no correction terms are necessary to account for the probabilistic nature of the transport. Additionally, because the complete phonon description is solved, scattering rates of individual phonon frequencies can be investigated to determine how electron-phonon scattering of particular frequencies influences the transport. This computational method is applied to the study of Si/Ge nanostructured superlattice thermoelectric materials.

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 HEAVY QUARK EFFECTIVE THEORY ON THE LIGHT FRONT

1996 ◽  
Vol 11 (18) ◽  
pp. 3297-3305 ◽  
Author(s):  
WEI-MIN ZHANG ◽  
CHI-YEE CHEUNG ◽  
GUEY-LIN LIN
Keyword(s):  
Heavy Quark ◽  
Bound States ◽  
Canonical Quantization ◽  
Light Front ◽  
Effective Theory ◽  
Heavy Quark Effective Theory ◽  
New Formalism ◽  
Heavy Hadron ◽  
Quark Spin ◽  
Simple Operator

The light front heavy quark effective theory is derived to all orders in 1/mQ. In the limit mQ→∞, the theory exhibits the familiar heavy quark spin-flavor symmetry. This new formalism permits a straightforward canonical quantization to all orders in 1/mQ; moreover, higher order terms have rather simple operator structures. The light front heavy quark effective theory can serve as a useful framework for the study of nonperturbative QCD dynamics of heavy hadron bound states.

Application of analytical electron microscopy to studies of equilibrium and non-equilibrium segregation in materials

1992 ◽  
Vol 50 (2) ◽  
pp. 1214-1215
Author(s):  
Edward A Kenik
Keyword(s):  
Electron Microscopy ◽  
Analytical Electron Microscopy ◽  
Extended Defects ◽  
Probe Diameter ◽  
Specimen Holder ◽  
Analytical Electron ◽  
Scanning Transmission ◽  
Solute Atoms ◽  
Equilibrium Segregation ◽  
Non Equilibrium

Segregation of solute atoms to grain boundaries, dislocations, and other extended defects can occur under thermal equilibrium or non-equilibrium conditions, such as quenching, irradiation, or precipitation. Generally, equilibrium segregation is narrow (near monolayer coverage at planar defects), whereas non-equilibrium segregation exhibits profiles of larger spatial extent, associated with diffusion of point defects or solute atoms. Analytical electron microscopy provides tools both to measure the segregation and to characterize the defect at which the segregation occurs. This is especially true of instruments that can achieve fine (<2 nm width), high current probes and as such, provide high spatial resolution analysis and characterization capability. Analysis was performed in a Philips EM400T/FEG operated in the scanning transmission mode with a probe diameter of <2 nm (FWTM). The instrument is equipped with EDAX 9100/70 energy dispersive X-ray spectrometry (EDXS) and Gatan 666 parallel detection electron energy loss spectrometry (PEELS) systems. A double-tilt, liquid-nitrogen-cooled specimen holder was employed for microanalysis in order to minimize contamination under the focussed spot.

Equilibrium and Non-Equilibrium Statistical Thermodynamics

2004 ◽  
Author(s):  
Michel Le Bellac ◽  
Fabrice Mortessagne ◽  
G. George Batrouni
Keyword(s):  
Statistical Thermodynamics ◽  
Non Equilibrium
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