scholarly journals Large distance expansion of mutual information for disjoint disks in a free scalar theory

2016 ◽  
Vol 2016 (11) ◽  
Author(s):  
Cesar A. Agón ◽  
Isaac Cohen-Abbo ◽  
Howard J. Schnitzer
Keyword(s):  
Mutual Information ◽  
Large Distance ◽  
Scalar Theory ◽  
Free Scalar

scholarly journals Dynamics of logarithmic negativity and mutual information in smooth quenches

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
Hiroyuki Fujita ◽  
Mitsuhiro Nishida ◽  
Masahiro Nozaki ◽  
Yuji Sugimoto
Keyword(s):  
Mutual Information ◽  
Time Evolution ◽  
Qualitative Difference ◽  
Time Dependent ◽  
Late Time ◽  
Finite Mass ◽  
Scalar Theory ◽  
Quasi Particle ◽  
Logarithmic Negativity ◽  
Free Scalar

Abstract We study the time evolution of mutual information (MI) and logarithmic negativity (LN) in two-dimensional free scalar theory with two kinds of time-dependent masses: one time evolves continuously from non-zero mass to zero; the other time evolves continuously from finite mass to finite mass, but becomes massless once during the time evolution. We call the former protocol ECP, and the latter protocol CCP. Through numerical computation, we find that the time evolution of MI and LN in ECP follows a quasi-particle picture except for their late-time evolution, whereas that in CCP oscillates. Moreover, we find a qualitative difference between MI and LN which has not been known so far: MI in ECP depends on the slowly moving modes, but LN does not.

scholarly journals Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yan Song ◽  
Tong-Tong Hu ◽  
Yong-Qiang Wang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Cosmic Censorship ◽  
Mass Ratio ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Free Scalar ◽  
The One ◽  
Nonzero Scalar ◽  
Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

scholarly journals COVARIANT FORMULATION OF NOETHER'S THEOREM FOR κ-MINKOWSKI TRANSLATIONS

2009 ◽  
Vol 24 (07) ◽  
pp. 1333-1358 ◽  
Author(s):  
ALESSANDRA AGOSTINI
Keyword(s):  
Plane Waves ◽  
Equation Of Motion ◽  
Space Time ◽  
Noncommutative Space ◽  
Covariant Formulation ◽  
Scalar Theory ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Free Scalar ◽  
Conserved Currents

The problem of finding a formulation of Noether's theorem in noncommutative geometry is very important in order to obtain conserved currents and charges for particles in noncommutative space–times. In this paper, we formulate Noether's theorem for translations of κ-Minkowski noncommutative space–time on the basis of the five-dimensional κ-Poincaré covariant differential calculus. We focus our analysis on the simple case of free scalar theory. We obtain five conserved Noether currents, which give rise to five energy–momentum charges. By applying our result to plane waves it follows that the energy–momentum charges satisfy a special-relativity dispersion relation with a generalized mass given by the fifth charge. In this paper, we provide also a rigorous derivation of the equation of motion from Hamilton's principle in noncommutative space–time, which is necessary for the Noether analysis.

scholarly journals Reflected entropy for free scalars

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Pablo Bueno ◽  
Horacio Casini
Keyword(s):  
Mutual Information ◽  
Scalar Fields ◽  
Monotonicity Property ◽  
Cross Ratio ◽  
Free Fermion ◽  
Length Scales ◽  
General Inequality ◽  
Fermionic Case ◽  
Free Scalar ◽  
Arbitrary Dimensions

Abstract We continue our study of reflected entropy, R(A, B), for Gaussian systems. In this paper we provide general formulas valid for free scalar fields in arbitrary dimensions. Similarly to the fermionic case, the resulting expressions are fully determined in terms of correlators of the fields, making them amenable to lattice calculations. We apply this to the case of a (1 + 1)-dimensional chiral scalar, whose reflected entropy we compute for two intervals as a function of the cross-ratio, comparing it with previous holographic and free-fermion results. For both types of free theories we find that reflected entropy satisfies the conjectural monotonicity property R(A, BC) ≥ R(A, B). Then, we move to (2 + 1) dimensions and evaluate it for square regions for free scalars, fermions and holography, determining the very-far and very-close regimes and comparing them with their mutual information counterparts. In all cases considered, both for (1 + 1)- and (2 + 1)-dimensional theories, we verify that the general inequality relating both quantities, R(A, B) ≥ I (A, B), is satisfied. Our results suggest that for general regions characterized by length-scales LA ∼ LB ∼ L and separated a distance ℓ, the reflected entropy in the large-separation regime (x ≡ L/ℓ ≪ 1) behaves as R(x) ∼ −I(x) log x for general CFTs in arbitrary dimensions.

scholarly journals Direct calculation of mutual information of distant regions

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Noburo Shiba
Keyword(s):  
Scalar Field ◽  
Mutual Information ◽  
Numerical Computation ◽  
Direct Calculation ◽  
Vacuum State ◽  
Analytical Continuation ◽  
Free Scalar

Abstract We consider the (Rényi) mutual information, $$ {I}^{(n)}\left(A,B\right)={S}_A^{(n)}+{S}_B^{(n)}-{S}_{A\cup B}^{(n)} $$ I n A B = S A n + S B n − S A ∪ B n , of distant compact spatial regions A and B in the vacuum state of a free scalar field. The distance r between A and B is much greater than their sizes RA,B. It is known that $$ {I}^{(n)}\left(A,B\right)\sim {C}_{AB}^{(n)}{\left\langle 0\left|\phi (r)\phi (0)0\right|\right\rangle}^2 $$ I n A B ∼ C AB n 0 ϕ r ϕ 0 0 2 . We obtain the direct expression of $$ {C}_{AB}^{(n)} $$ C AB n for arbitrary regions A and B. We perform the analytical continuation of n and obtain the mutual information. The direct expression is useful for the numerical computation. By using the direct expression, we can compute directly I(A, B) without computing SA, SB and SA∪B respectively, so it reduces significantly the amount of computation.

scholarly journals Superradiance in a ghost-free scalar theory

2018 ◽  
Vol 98 (8) ◽  
Author(s):  
Valeri P. Frolov ◽  
Andrei Zelnikov
Keyword(s):  
Scalar Theory ◽  
Free Scalar

scholarly journals Radiation from an emitter in the ghost free scalar theory

2016 ◽  
Vol 93 (10) ◽  
Author(s):  
Valeri P. Frolov ◽  
Andrei Zelnikov
Keyword(s):  
Scalar Theory ◽  
Free Scalar

scholarly journals Free energy and defect C-theorem in free scalar theory

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Tatsuma Nishioka ◽  
Yoshiki Sato
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Flat Space ◽  
Neumann Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Scalar Theory ◽  
Free Scalar ◽  
The Difference ◽  
Recent Classification

Abstract We describe conformal defects of p dimensions in a free scalar theory on a d-dimensional flat space as boundary conditions on the conformally flat space ℍp+1× 𝕊d−p−1. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace ℍp+1 which correspond to the types of conformal defects in the free scalar theory. We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions. Our results match with a recent classification of the non-monodromy defects, showing Neumann boundary conditions are associated with non-trivial defects. We check this observation by calculating the difference of the free energies on ℍp+1× 𝕊d−p−1 between Dirichlet and Neumann boundary conditions. We also examine the defect RG flows from Neumann to Dirichlet boundary conditions and provide more support for a conjectured C-theorem in defect CFTs.

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