scholarly journals Thermalization in large-N CFTs

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Robin Karlsson ◽  
Andrei Parnachev ◽  
Petar Tadić
Keyword(s):  
Stress Tensor ◽  
Finite Temperature ◽  
Degrees Of Freedom ◽  
Expectation Values ◽  
Universal Behavior ◽  
Bootstrap Argument ◽  
Stress Tensors ◽  
Large N ◽  
Thermal Light ◽  
Tensor Operators

AbstractIn d-dimensional CFTs with a large number of degrees of freedom an important set of operators consists of the stress tensor and its products, multi stress tensors. Thermalization of such operators, the equality between their expectation values in heavy states and at finite temperature, is equivalent to a universal behavior of their OPE coefficients with a pair of identical heavy operators. We verify this behavior in a number of examples which include holographic and free CFTs and provide a bootstrap argument for the general case. In a free CFT we check the thermalization of multi stress tensor operators directly and also confirm the equality between the contributions of multi stress tensors to heavy-heavy-light-light correlators and to the corresponding thermal light-light two-point functions by disentangling the contributions of other light operators. Unlike multi stress tensors, these light operators violate the Eigenstate Thermalization Hypothesis and do not thermalize.

scholarly journals Quantum information probes of charge fractionalization in large-N gauge theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Brandon S. DiNunno ◽  
Niko Jokela ◽  
Juan F. Pedraza ◽  
Arttu Pönni
Keyword(s):  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
Strongly Coupled ◽  
Information Theoretic ◽  
Large N ◽  
Wide Range ◽  
Charge Fractionalization ◽  
Electric Flux

Abstract We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of large-N gauge theories. For concreteness, we focus on a simple holographic (2 + 1)-dimensional strongly coupled electron fluid whose charged states organize themselves into fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To address this deficiency, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a U(1) gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic c-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.

A NUCLEAR MANY-BODY THEORY AT FINITE TEMPERATURE APPLIED TO A PROTONEUTRON STAR

2002 ◽  
Vol 11 (02) ◽  
pp. 83-104 ◽  
Author(s):  
GUILHERME F. MARRANGHELLO ◽  
CESAR A. Z. VASCONCELLOS ◽  
MANFRED DILLIG ◽  
J. A. DE FREITAS PACHECO
Keyword(s):  
Phase Transition ◽  
Nuclear Matter ◽  
Finite Temperature ◽  
Degrees Of Freedom ◽  
Many Body ◽  
Many Body Theory ◽  
The Masses ◽  
Protoneutron Stars ◽  
Protoneutron Star

Thermodynamical properties of nuclear matter are studied in the framework of an effective many-body field theory at finite temperature, considering the Sommerfeld approximation. We perform the calculations by using the nonlinear Boguta and Bodmer model, extended by the inclusion of the fundamental baryon octet and leptonic degrees of freedom. Trapped neutrinos are also included in order to describe protoneutron star properties through the integration of the Tolman–Oppenheimer–Volkoff equations, from which we obtain, beyond the standard relations for the masses and radii of protoneutron stars as functions of the central density, new results of these quantities as functions of temperature. Our predictions include: the determination of an absolute value for the limiting mass of protoneutron stars; new structural aspects on the nuclear matter phase transition via the behavior of the specific heat and, through the inclusion of quark degrees of freedom, the properties of a hadron-quark phase transition and hybrid protoneutron stars

Education Committee Best Paper of 1995 Award: Methods of Classical Mechanics Applied to Turbulence Stresses in a Tip Leakage Vortex

1996 ◽  
Vol 118 (4) ◽  
pp. 622-629 ◽  
Author(s):  
J. G. Moore ◽  
S. A. Schorn ◽  
J. Moore
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Surface Model ◽  
Reynolds Stresses ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Stress Tensors ◽  
Principal Directions

Moore et al. measured the six Reynolds stresses in a tip leakage vortex in a linear turbine cascade. Stress tensor analysis, as used in classical mechanics, has been applied to the measured turbulence stress tensors. Principal directions and principal normal stresses are found. A solid surface model, or three-dimensional glyph, for the Reynolds stress tensor is proposed and used to view the stresses throughout the tip leakage vortex. Modeled Reynolds stresses using the Boussinesq approximation are obtained from the measured mean velocity strain rate tensor. The comparison of the principal directions and the three-dimensional graphic representations of the strain and Reynolds stress tensors aids in the understanding of the turbulence and what is required to model it.

scholarly journals Semi-classical approximations based on Bohmian mechanics

2020 ◽  
Vol 35 (14) ◽  
pp. 2050070 ◽  
Author(s):  
Ward Struyve
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Quantum Electrodynamics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Expectation Values ◽  
Usual Approach ◽  
Classical Approximation

Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which evolves according to some Schrödinger equation with a Hamiltonian that depends on the classical degrees of freedom. The classical degrees of freedom satisfy classical equations that depend on the expectation values of quantum operators. In this paper, we study an alternative approach based on Bohmian mechanics. In Bohmian mechanics the quantum system is not only described by the wave function, but also with additional variables such as particle positions or fields. By letting the classical equations of motion depend on these variables, rather than the quantum expectation values, a semi-classical approximation is obtained that is closer to the exact quantum results than the usual approach. We discuss the Bohmian semi-classical approximation in various contexts, such as nonrelativistic quantum mechanics, quantum electrodynamics and quantum gravity. The main motivation comes from quantum gravity. The quest for a quantum theory for gravity is still going on. Therefore a semi-classical approach where gravity is treated classically may be an approximation that already captures some quantum gravitational aspects. The Bohmian semi-classical theories will be derived from the full Bohmian theories. In the case there are gauge symmetries, like in quantum electrodynamics or quantum gravity, special care is required. In order to derive a consistent semi-classical theory it will be necessary to isolate gauge-independent dependent degrees of freedom from gauge degrees of freedom and consider the approximation where some of the former are considered classical.

scholarly journals THE HAGEDORN TRANSITION AND THE MATRIX MODEL FOR STRINGS

1998 ◽  
Vol 13 (26) ◽  
pp. 2085-2094 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Matrix Model ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Low Energy ◽  
Matrix Formalism ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
The Continuum ◽  
String Worldsheet

We use the matrix formalism to investigate what happens to strings above the Hagedorn temperature. We show that is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of N D-0-branes arranged to form a string having N units of light-cone momentum. We find that at high temperatures the favored phase is one where the string worldsheet has disappeared and the low-energy degrees of freedom consists of N2 massless particles ("gluons"). The nature of the transition is very similar to the deconfinement transition in large-N Yang–Mills theories.

The Complementary Energy Theorem in Finite Elasticity

1965 ◽  
Vol 32 (4) ◽  
pp. 826-828 ◽  
Author(s):  
Mark Levinson
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Finite Elasticity ◽  
Strain Tensor ◽  
Complementary Energy ◽  
Elastic Continuum ◽  
Stress Tensors ◽  
Elastic Systems ◽  
Lagrange Strain ◽  
Castigliano’S Theorem

Other investigators have extended the complementary energy theorem (Castigliano’s theorem) to cover the finite deformation of elastic systems with a finite number of degrees of freedom (structures) and they then have indicated that the extension of the theorem to cover the finite deformation of an elastic continuum involved certain unstated difficulties. The present paper shows that when the strain tensor and Trefftz stress tensor, the usual choice of conjugate deformation and stress tensors, are chosen to characterize the finite deformation of an elastic continuum, one cannot establish a strict complementary energy theorem. It is then shown that a strict complementary energy theorem for the finite deformation of an elastic continuum can be established if what Fritz John calls the Lagrange strain and Lagrange stress tensors are used as the conjugate deformation and stress tensors characterizing the deformation.

scholarly journals Analytic Results in (2+1)-Dimensional Finite Temperature LGT

1997 ◽  
Vol 12 (32) ◽  
pp. 5753-5766 ◽  
Author(s):  
M. Billó ◽  
M. Caselle ◽  
A. D'Adda
Keyword(s):  
Monte Carlo ◽  
Effective Action ◽  
Finite Temperature ◽  
Mean Field ◽  
Polyakov Loop ◽  
Critical Coupling ◽  
Dimensional Theory ◽  
Field Techniques ◽  
Large N ◽  
Good Agreement

In a (2 + 1)-dimensional pure LGT at finite temperature the critical coupling for the deconfinement transition scales as βc(nt) = Jcnt + a1, where nt is the number of links in the "timelike" direction of the symmetric lattice. We study the effective action for the Polyakov loop obtained by neglecting the spacelike plaquettes, and we are able to compute analytically in this context the coefficient a1 for any SU(N) gauge group; the value of Jc is instead obtained from the effective action by means of (improved) mean field techniques. Both coefficients have already been calculated in the large N limit in a previous paper. The results are in very good agreement with the existing Monte Carlo simulations. This fact supports the conjecture that, in the (2 + 1)-dimensional theory, spacelike plaquettes have little influence on the dynamics of the Polyakov loops in the deconfined phase.

A MIXED NONCONFORMING FINITE ELEMENT FOR THE ELASTICITY AND STOKES PROBLEMS

1999 ◽  
Vol 09 (08) ◽  
pp. 1179-1199 ◽  
Author(s):  
M. FARHLOUL ◽  
M. FORTIN
Keyword(s):  
Finite Element ◽  
Stress Tensor ◽  
Degrees Of Freedom ◽  
Stokes Problem ◽  
Elasticity Problem ◽  
Optimal Error Estimates ◽  
Nonconforming Finite Element ◽  
Optimal Error ◽  
Stokes Problems ◽  
Symmetric Approximation

A mixed-hybrid formulation of the elasticity problem with a nonconforming symmetric approximation of the stress–tensor is considered. Based on such a formulation, a new finite element of low order with minimal number of degrees of freedom is constructed. Optimal error estimates are derived. Moreover all estimates are valid uniformly with respect to compressibility and apply for the Stokes problem. Finally, an equivalence between this finite element and the piecewise quadratic nonconforming approximation of the elasticity problem is established.

scholarly journals SPHALERONS AT FINITE TEMPERATURE

1993 ◽  
Vol 08 (31) ◽  
pp. 5563-5574 ◽  
Author(s):  
SYLVIE BRAIBANT ◽  
YVES BRIHAYE ◽  
JUTTA KUNZ
Keyword(s):  
Upper Bound ◽  
Finite Temperature ◽  
Higgs Mass ◽  
Higgs Field ◽  
Vacuum Expectation ◽  
Temperature Dependent ◽  
Expectation Values ◽  
Effective Potentials ◽  
Temperature Zero

We construct the sphaleron for several temperature-dependent effective potentials. We determine the sphaleron energy as a function of temperature and demonstrate that the sphaleron energy at a given temperature T is well approximated by the sphaleron energy at temperature zero scaled by the ratio of the vacuum expectation values of the Higgs field at temperatures T and zero. We address the cosmological upper bound on the Higgs mass.

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