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 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

Euclidean path integrals and quantum mechanics (QM)

2021 ◽  
pp. 18-41
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Correlation Functions ◽  
Path Integrals ◽  
Continuous Phase ◽  
Functional Integral ◽  
Smooth Transition ◽  
Path Integral Representation ◽  
The Matrix ◽  
Functional Measure

Functional integrals are basic tools to study first quantum mechanics (QM), and quantum field theory (QFT). The path integral formulation of QM is well suited to the study of systems with an arbitrary number of degrees of freedom. It makes a smooth transition between nonrelativistic QM and QFT possible. The Euclidean functional integral also emphasizes the deep connection between QFT and the statistical physics of systems with short-range interactions near a continuous phase transition. The path integral representation of the matrix elements of the quantum statistical operator e-β H for Hamiltonians of the simple separable form p2/2m +V(q) is derived. To the path integral corresponds a functional measure and expectation values called correlation functions, which are generalized moments, and related to quantum observables, after an analytic continuation in time. The path integral corresponding to the Euclidean action of a harmonic oscillator, to which is added a time-dependent external force, is calculated explicitly. The result is used to generate Gaussian correlation functions and also to reduce the evaluation of path integrals to perturbation theory. The path integral also provides a convenient tool to derive semi-classical approximations.

scholarly journals THE AREA LAW IN MATRIX MODELS FOR LARGE N QCD STRINGS

2002 ◽  
Vol 13 (04) ◽  
pp. 555-563 ◽  
Author(s):  
K. N. ANAGNOSTOPOULOS ◽  
W. BIETENHOLZ ◽  
J. NISHIMURA
Keyword(s):  
Numerical Simulations ◽  
Matrix Models ◽  
Matrix Model ◽  
Hermitian Matrices ◽  
Yang Mills ◽  
Loop Area ◽  
Large N ◽  
Volume Limit ◽  
The Matrix ◽  
Area Law

We study the question whether matrix models obtained in the zero volume limit of 4d Yang–Mills theories can describe large N QCD strings. The matrix model we use is a variant of the Eguchi–Kawai model in terms of Hermitian matrices, but without any twists or quenching. This model was originally proposed as a toy model of the IIB matrix model. In contrast to common expectations, we do observe the area law for Wilson loops in a significant range of scale of the loop area. Numerical simulations show that this range is stable as N increases up to 768, which strongly suggests that it persists in the large N limit. Hence the equivalence to QCD strings may hold for length scales inside a finite regime.

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 Honeycombs from Hermitian Matrix Pairs

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Glenn Appleby ◽  
Tamsen Whitehead
Keyword(s):  
Crystal Structure ◽  
Representation Theory ◽  
Linear Algebra ◽  
Hermitian Matrix ◽  
Hermitian Matrices ◽  
Orthonormal Bases ◽  
Crystal Graphs ◽  
The Matrix ◽  
International Audience ◽  
Matrix Pair

International audience Knutson and Tao's work on the Horn conjectures used combinatorial invariants called hives and honeycombs to relate spectra of sums of Hermitian matrices to Littlewood-Richardson coefficients and problems in representation theory, but these relationships remained implicit. Here, let $M$ and $N$ be two $n ×n$ Hermitian matrices. We will show how to determine a hive $\mathcal{H}(M, N)={H_ijk}$ using linear algebra constructions from this matrix pair. With this construction, one may also define an explicit Littlewood-Richardson filling (enumerated by the Littlewood-Richardson coefficient $c_μν ^λ$ associated to the matrix pair). We then relate rotations of orthonormal bases of eigenvectors of $M$ and $N$ to deformations of honeycombs (and hives), which we interpret in terms of the structure of crystal graphs and Littelmann's path operators. We find that the crystal structure is determined \emphmore simply from the perspective of rotations than that of path operators.

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.

scholarly journals Secure and Efficient Image Compression-Encryption Scheme Using New Chaotic Structure and Compressive Sensing

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yongli Tang ◽  
Mingjie Zhao ◽  
Lixiang Li
Keyword(s):  
Image Compression ◽  
Information Transmission ◽  
Compressive Sensing ◽  
Chaotic System ◽  
Rapid Development ◽  
Chaotic Map ◽  
Performance Comparison ◽  
Encryption Scheme ◽  
The Matrix ◽  
Brute Force Attack

The rapid development of the Internet leads to a surge in the amount of information transmission and brings many security problems. For multimedia information transmission, especially digital images, it is necessary to compress and encrypt at the same time. The emergence of compressive sensing solves this problem. Compressive sensing can compress and encrypt at the same time, which can not only reduce the transmission bandwidth of the network but also improve the security of the system. However, when using compressive sensing encryption, the whole measurement matrix needs to be stored, and the compressive sensing can be combined with a chaotic system, so only the generation parameters of the matrix need to be stored, and the security of the system can be further improved by using the sensitivity of the chaotic system. This paper introduces a secure and efficient image compression-encryption scheme using a new chaotic structure and compressive sensing. The chaotic map used in the scheme is generated by our new and universal chaotic structure, which not only expands the chaotic range of the chaotic system but also improves the performance of the chaotic system. After analyzing the performance comparison of traditional one-dimensional chaotic maps and some existing methods, the image compression-encryption scheme based on a new chaotic structure and compressive sensing has a good encryption effect and large keyspace, which can resist brute force attack and statistical attack.

scholarly journals Towards leading isospin breaking effects in mesonic masses with O(a) improved Wilson fermions

2018 ◽  
Vol 175 ◽  
pp. 14019 ◽  
Author(s):  
Andreas Risch ◽  
Hartmut Wittig
Keyword(s):  
Finite Volume ◽  
Path Integral ◽  
Exploratory Study ◽  
Quark Mass ◽  
Electromagnetic Coupling ◽  
Light Quark ◽  
Isospin Symmetry ◽  
Isospin Breaking ◽  
Light Quark Mass ◽  
Wilson Fermions

We present an exploratory study of leading isospin breaking effects in mesonic masses using O(a) improved Wilson fermions. Isospin symmetry is explicitly broken by distinct masses and electric charges of the up and down quarks. In order to be able to make use of existing isosymmetric QCD gauge ensembles we apply reweighting techniques. The path integral describing QCD+QED is expanded perturbatively in powers of the light quark’ mass deviations and the electromagnetic coupling. We employ QEDL as a finite volume formulation of QED.

DEVELOPMENT OF A HIGHER-ORDER ACCURATE RECONSTRUCTION SCHEME WITH REDUCED LEAST SQUARE MATRIX FOR CONVECTIVE AND DIFFUSIVE FLUX EVALUATION

2009 ◽  
Vol 06 (03) ◽  
pp. 425-446 ◽  
Author(s):  
PRAVEEN NAIR ◽  
T. JAYACHANDRAN ◽  
BHAL CHANDRA PURANIK ◽  
V. UPENDRA BHANDARKAR
Keyword(s):  
Finite Volume ◽  
Higher Order ◽  
Least Square ◽  
Test Facility ◽  
Adaptive Grids ◽  
Computationally Efficient ◽  
Time Step ◽  
Reconstruction Scheme ◽  
The Matrix ◽  
Square Matrix

The development of a higher-order reconstruction scheme with reduced least square matrix is presented. The matrix used in conventional least square based reconstruction schemes for finite volume solvers contains bigger terms. For solution dependent schemes, this matrix has to be inverted for each time step, which is computationally costlier. To overcome this, certain mathematical principles applicable to finite volume formulation, have been used to eliminate a good number of terms appearing in the matrix. In addition, accurate and computationally efficient derivative plug-ins are incorporated to make the formulation generalized so that one can extend it to any order of accuracy. The presence of higher derivative terms in this scheme ensures uniformly higher-order accuracy throughout the flow domain. The reduced matrix can be used for data independent as well as solution dependent reconstruction schemes. Computationally efficient stencil searching algorithm, satisfying physical and topological requirements and capable of handling structured, unstructured, and adaptive grids has been coupled with the scheme. The scheme has been successfully used to simulate flow over blunt cone-flare, NASA B2 nozzle, and high altitude test facility. The solver has shown around 30% saving in least square matrix evaluation time.

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