scholarly journals Normal modes in thermal AdS via the Selberg zeta function

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Victoria Martin ◽  
Andrew Svesko
Keyword(s):  
Zeta Function ◽  
Heat Kernel ◽  
Normal Mode ◽  
Kernel Method ◽  
Normal Modes ◽  
Quasinormal Mode ◽  
Partition Functions ◽  
Selberg Zeta Function ◽  
Exact Agreement ◽  
Spin Fields

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin ss fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z}ℍ3/ℤ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1}AdS2n+1 backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z}ℍ2n+1/ℤ. Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.

scholarly journals BTZ one-loop determinants via the Selberg zeta function for general spin

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Cynthia Keeler ◽  
Victoria L. Martin ◽  
Andrew Svesko
Keyword(s):  
Scalar Field ◽  
Partition Function ◽  
Zeta Function ◽  
Heat Kernel ◽  
Arbitrary Spin ◽  
Quasinormal Mode ◽  
Scattering Operator ◽  
Selberg Zeta Function ◽  
Zero Modes ◽  
Spin Fields

Abstract We relate the heat kernel and quasinormal mode methods of computing the 1-loop partition function of arbitrary spin fields on a rotating (Euclidean) BTZ background using the Selberg zeta function associated with ℍ3/ℤ, extending (arXiv:1811.08433) [1]. Previously, Perry and Williams [2] showed for a scalar field that the zeros of the Selberg zeta function coincide with the poles of the associated scattering operator upon a relabeling of integers. We extend the integer relabeling to the case of general spin, and discuss its relationship to the removal of non-square-integrable Euclidean zero modes.

scholarly journals Connecting quasinormal modes and heat kernels in 1-loop determinants

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Cynthia Keeler ◽  
Victoria Martin ◽  
Andrew Svesko
Keyword(s):  
Zeta Function ◽  
Heat Kernel ◽  
Kernel Method ◽  
Quasinormal Modes ◽  
Heat Kernels ◽  
Quasinormal Mode ◽  
Selberg Zeta Function ◽  
Hyperbolic Spacetime ◽  
Mode Method ◽  
Thermal Sum

We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes.

scholarly journals Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Victoria Martin ◽  
Andrew Svesko
Keyword(s):  
Kernel Methods ◽  
Normal Modes ◽  
De Sitter Space ◽  
Quasinormal Mode ◽  
Partition Functions ◽  
De Sitter ◽  
Wick Rotation ◽  
Conformal Dimension ◽  
Mode Method ◽  
Higher Spin

In this note we compute the 1-loop partition function of spin-ss fields on Euclidean de Sitter space S^{2n+1}S2n+1 using the quasinormal mode method. Instead of computing the quasinormal mode frequencies from scratch, we use the analytic continuation prescription L_{\text{AdS}}\to iL_{\text{dS}}LAdS→iLdS, appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal \text{AdS}_{2n+1}AdS2n+1 into the quasinormal mode frequencies of fields on de Sitter space. We compare the quasinormal mode and heat kernel methods of calculating 1-loop determinants, finding exact agreement, and furthermore explicitly relate these methods via a sum over the conformal dimension. We discuss how the Wick rotation of normal modes on thermal \text{AdS}_{2n+1}AdS2n+1 can be generalized to calculating 1-loop partition functions on the thermal spherical quotients S^{2n+1}/\mathbb{Z}_{p}S2n+1/ℤp. We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the analysis made for thermal AdS in [1-3] .

Acoustic Green's Function Approximations

1998 ◽  
Vol 06 (04) ◽  
pp. 435-452 ◽  
Author(s):  
Robert P. Gilbert ◽  
Zhongyan Lin ◽  
Klaus Hackl
Keyword(s):  
Inverse Problem ◽  
Normal Mode ◽  
Eigenvalue Problems ◽  
Normal Modes ◽  
Modal Parameters ◽  
Mindlin Plate ◽  
Ocean Bottom ◽  
Hankel Transformation ◽  
Poroelastic Materials ◽  
Function Approximations

Normal-mode expansions for Green's functions are derived for ocean–bottom systems. The bottom is modeled by Kirchhoff and Reissner–Mindlin plate theories for elastic and poroelastic materials. The resulting eigenvalue problems for the modal parameters are investigated. Normal modes are calculated by Hankel transformation of the underlying equations. Finally, the relation to the inverse problem is outlined.

Experimental Study for Extraction of Normal Modes

1995 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Normal Modes ◽  
Measurement Data ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Incomplete System ◽  
Coupled Structures

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.

scholarly journals Computational notes on the electronic properties of carboxylic acid

2020 ◽  
Vol 9 (2) ◽  
pp. 1079-1082
Keyword(s):  
Acetic Acid ◽  
Carboxylic Acid ◽  
Electronic Properties ◽  
Carboxylic Acids ◽  
Normal Mode ◽  
Normal Modes ◽  
Carboxyl Groups ◽  
Vibrational Characteristics ◽  
Vibrational Features ◽  
Acetic Acids

The present work describing the electronic properties and vibrational characteristics of carboxylic acids. Acetic acid is chosen as model molecules then optimized at B3LYP/6-31g(d,p) level of theory. The vibrational frequencies were calculated at the same level of theory. Band assignments which were calculated as 18 normal modes were assigned as one compare the normal mode coordinates with original one. Band assignments were described indicating the directions of normal modes in terms the vibrating atoms of the acetic acids. It could be concluded that DFT could be a useful tool for elucidation both the structural and vibrational features of carboxylic acids and then further utilized for assignment of the structures contains carboxyl groups which are known as most reactive structures in chemistry, biology and environment.

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