scholarly journals Path integral contour deformations for noisy observables

2020 ◽  
Vol 102 (1) ◽  
Author(s):  
William Detmold ◽  
Gurtej Kanwar ◽  
Michael L. Wagman ◽  
Neill C. Warrington
Keyword(s):  
Path Integral ◽  
Integral Contour

scholarly journals Path integral contour deformations for observables in SU(N) gauge theory

2021 ◽  
Vol 103 (9) ◽  
Author(s):  
William Detmold ◽  
Gurtej Kanwar ◽  
Henry Lamm ◽  
Michael L. Wagman ◽  
Neill C. Warrington
Keyword(s):  
Gauge Theory ◽  
Path Integral ◽  
Integral Contour

scholarly journals Eigenbranes in Jackiw-Teitelboim gravity

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Andreas Blommaert ◽  
Thomas G. Mertens ◽  
Henri Verschelde
Keyword(s):  
Finite Volume ◽  
Chaotic System ◽  
Path Integral ◽  
Hermitian Matrices ◽  
The Matrix ◽  
Integral Contour

Abstract It was proven recently that JT gravity can be defined as an ensemble of L × L Hermitian matrices. We point out that the eigenvalues of the matrix correspond in JT gravity to FZZT-type boundaries on which spacetimes can end. We then investigate an ensemble of matrices with 1 ≪ N ≪ L eigenvalues held fixed. This corresponds to a version of JT gravity which includes N FZZT type boundaries in the path integral contour and which is found to emulate a discrete quantum chaotic system. In particular this version of JT gravity can capture the behavior of finite-volume holographic correlators at late times, including erratic oscillations.

scholarly journals Classification of out-of-time-order correlators

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Felix Haehl ◽  
R. Loganayagam ◽  
Prithvi Narayan ◽  
Mukund Rangamani
Keyword(s):  
Correlation Function ◽  
Path Integral ◽  
Correlation Functions ◽  
General Structure ◽  
Natural Generalization ◽  
Functional Integrals ◽  
Time Order ◽  
Integral Contour ◽  
Point Correlation

The space of n-point correlation functions, for all possible time-orderings of operators, can be computed by a non-trivial path integral contour, which depends on how many time-ordering violations are present in the correlator. These contours, which have come to be known as timefolds, or out-of-time-order (OTO) contours, are a natural generalization of the Schwinger-Keldysh contour (which computes singly out-of-time-ordered correlation functions). We provide a detailed discussion of such higher OTO functional integrals, explaining their general structure, and the myriad ways in which a particular correlation function may be encoded in such contours. Our discussion may be seen as a natural generalization of the Schwinger-Keldysh formalism to higher OTO correlation functions. We provide explicit illustration for low point correlators (n\leq 4n≤4) to exemplify the general statements.

Vapour Pressure Isotope Effect on Evaporation from Pure Organic Phases - a PIMD Approach

2020 ◽  
Author(s):  
Luis Vasquez ◽  
Agnieszka Dybala-Defratyka
Keyword(s):  
Path Integral ◽  
Vapour Pressure ◽  
Density Functional ◽  
Isotope Effects ◽  
Tight Binding ◽  
Decomposition Analysis ◽  
Energy Decomposition Analysis ◽  
Special Importance ◽  
Non Covalent Interactions ◽  
Covalent Interactions

<p></p><p>Very often in order to understand physical and chemical processes taking place among several phases fractionation of naturally abundant isotopes is monitored. Its measurement can be accompanied by theoretical determination to provide a more insightful interpretation of observed phenomena. Predictions are challenging due to the complexity of the effects involved in fractionation such as solvent effects and non-covalent interactions governing the behavior of the system which results in the necessity of using large models of those systems. This is sometimes a bottleneck and limits the theoretical description to only a few methods.<br> In this work vapour pressure isotope effects on evaporation from various organic solvents (ethanol, bromobenzene, dibromomethane, and trichloromethane) in the pure phase are estimated by combining force field or self-consistent charge density-functional tight-binding (SCC-DFTB) atomistic simulations with path integral principle. Furthermore, the recently developed Suzuki-Chin path integral is tested. In general, isotope effects are predicted qualitatively for most of the cases, however, the distinction between position-specific isotope effects observed for ethanol was only reproduced by SCC-DFTB, which indicates the importance of using non-harmonic bond approximations.<br> Energy decomposition analysis performed using the symmetry-adapted perturbation theory (SAPT) revealed sometimes quite substantial differences in interaction energy depending on whether the studied system was treated classically or quantum mechanically. Those observed differences might be the source of different magnitudes of isotope effects predicted using these two different levels of theory which is of special importance for the systems governed by non-covalent interactions.</p><br><p></p>

Path integral for gauge theories with fermions

1980 ◽  
Vol 21 (10) ◽  
pp. 2848-2858 ◽  
Author(s):  
Kazuo Fujikawa
Keyword(s):  
Path Integral ◽  
Gauge Theories
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