scholarly journals Conformal boundary conditions, loop gravity and the continuum

2018 ◽  
Vol 2018 (10) ◽  
Author(s):  
Wolfgang Wieland
Keyword(s):  
Boundary Conditions ◽  
Conformal Boundary ◽  
Loop Gravity ◽  
The Continuum

scholarly journals Bootstrapping boundary-localized interactions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Connor Behan ◽  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Balt C. van Rees
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Parameter Space ◽  
Three Dimensional ◽  
Conformal Boundary ◽  
Dimensional Boundary ◽  
Dirichlet And Neumann Conditions ◽  
Boundary Fields ◽  
Boundary Dynamics

Abstract We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a ‘shadow pair’ of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a ‘kink’ in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

scholarly journals BOUNDARY CONDITIONS IN THE DIRAC APPROACH TO GRAPHENE DEVICES

2012 ◽  
Vol 14 ◽  
pp. 240-249 ◽  
Author(s):  
C.G. BENEVENTANO ◽  
E.M. SANTANGELO
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Continuum Limit ◽  
Casimir Energy ◽  
Local Boundary ◽  
Graphene Devices ◽  
The Continuum

We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the ones which are in closest agreement with available experiments. For nanotubes of arbitrary chirality satisfying these last boundary conditions, we evaluate the Casimir energy via zeta function regularization, in such a way that the limit of nanoribbons is clearly determined.

scholarly journals Thermal Simulations, Open Boundary Conditions and Switches

2018 ◽  
Vol 175 ◽  
pp. 07004 ◽  
Author(s):  
Yannis Burnier ◽  
Adrien Florio ◽  
Olaf Kaczmarek ◽  
Lukas Mazur
Keyword(s):  
Boundary Conditions ◽  
Topological Charge ◽  
Finite Size ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Finite Size Effects ◽  
Compact Spaces ◽  
Integral Current ◽  
Thermal Simulations ◽  
The Continuum

SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.

scholarly journals EXCLUSION PROCESSES AND BOUNDARY CONDITIONS

2004 ◽  
Vol 18 (01) ◽  
pp. 1-9 ◽  
Author(s):  
FARINAZ ROSHANI ◽  
MOHAMMAD KHORRAMI
Keyword(s):  
Boundary Conditions ◽  
Exclusion Process ◽  
Conditional Probabilities ◽  
Exclusion Processes ◽  
Simple Exclusion Process ◽  
The Family ◽  
Simple Exclusion ◽  
The One ◽  
Push Model ◽  
The Continuum

A family of boundary conditions corresponding to exclusion processes is introduced. This family is a generalization of the boundary conditions corresponding to the simple exclusion process, the drop-push model, and the one-parameter solvable family of pushing processes with certain rates on the continuum.1–3 The conditional probabilities are calculated using the Bethe ansatz, and it is shown that at large times they behave like the corresponding conditional probabilities of the family of diffusion-pushing processes introduced in Refs. 1–3.

Study on the Mechanics State of Concrete under Penetration and the Deceleration of Projectile

2011 ◽  
Vol 413 ◽  
pp. 1-6
Author(s):  
Tao Deng ◽  
Tao Ge
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Wave Front ◽  
Mass Conservation ◽  
Conservation Of Mass ◽  
Conservation Of Momentum ◽  
Coulomb Criterion ◽  
The Continuum

The concrete under penetration has a restricted deform and is in intrinsic friction state. By used conservation of mass, conservation of momentum and velocity expression on wave front, the velocity field of the pulverized zone near penetration is obtained. The boundary conditions and the continuum conditions were also considered for the obtained velocity field. The pulverized concrete near the penetration is described by Mohr-Coulomb criterion. Based on the conclusions above, cavity expand theory and the expand equation of inconsistent deform, the resistance of projectile is gained in intrinsic friction state. In according to movement differential equation, the deceleration model is built which can describe different phases for penetration and perforation. The decelerations of different size projectiles with different velocity were calculated and were contrasted with experimental data.

scholarly journals Conformal boundary conditions from cutoff AdS3

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Evan Coleman ◽  
Vasudev Shyam
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
State Energy ◽  
Growth Characteristic ◽  
Temperature Limit ◽  
Flow Equation ◽  
Legendre Transform ◽  
Conformal Boundary ◽  
Deformation Parameters ◽  
Metric Fluctuations

Abstract We construct a particular flow in the space of 2D Euclidean QFTs on a torus, which we argue is dual to a class of solutions in 3D Euclidean gravity with conformal boundary conditions. This new flow comes from a Legendre transform of the kernel which implements the T$$ \overline{T} $$ T ¯ deformation, and is motivated by the need for boundary conditions in Euclidean gravity to be elliptic, i.e. that they have well-defined propagators for metric fluctuations. We demonstrate equivalence between our flow equation and variants of the Wheeler de-Witt equation for a torus universe in the so-called Constant Mean Curvature (CMC) slicing. We derive a kernel for the flow, and we compute the corresponding ground state energy in the low-temperature limit. Once deformation parameters are fixed, the existence of the ground state is independent of the initial data, provided the seed theory is a CFT. The high-temperature density of states has Cardy-like behavior, rather than the Hagedorn growth characteristic of T$$ \overline{T} $$ T ¯ -deformed theories.

scholarly journals Properties of RG interfaces for 2D boundary flows

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Anatoly Konechny
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Variational Method ◽  
Boundary Conditions ◽  
The Other ◽  
Two Dimensional ◽  
Conformal Boundary ◽  
First Approximation ◽  
Local Operators

Abstract We consider RG interfaces for boundary RG flows in two-dimensional QFTs. Such interfaces are particular boundary condition changing operators linking the UV and IR conformal boundary conditions. We refer to them as RG operators. In this paper we study their general properties putting forward a number of conjectures. We conjecture that an RG operator is always a conformal primary such that the OPE of this operator with its conjugate must contain the perturbing UV operator when taken in one order and the leading irrelevant operator (when it exists) along which the flow enters the IR fixed point, when taken in the other order. We support our conjectures by perturbative calculations for flows between nearby fixed points, by a non-perturbative variational method inspired by the variational method proposed by J. Cardy for massive RG flows, and by numerical results obtained using boundary TCSA. The variational method has a merit of its own as it can be used as a first approximation in charting the global structure of the space of boundary RG flows. We also discuss the role of the RG operators in the transport of states and local operators. Some of our considerations can be generalised to two-dimensional bulk flows, clarifying some conceptual issues related to the RG interface put forward by D. Gaiotto for bulk 𝜙1,3 flows.

Sign in / Sign up

Export Citation Format

Share Document