Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes

• URL: http://arxiv.org/abs/2207.05287v2
• Date: Sat, 21 Jan 2023 14:51:18 GMT
• Title: Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• Authors: Farzad Omidi
• Abstract summary: We investigate volume-complexity $mathcalC_rm gen$ for a two-sided uncharged HV black brane in $d+2$ dimensions. We numerically calculate the growth rate of $mathcalC_rm gen$ for different values of the hyperscaling violation exponent $theta$ and dynamical exponent $z$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we investigate generalized volume-complexity $\mathcal{C}_{\rm gen}$ for a two-sided uncharged HV black brane in $d+2$ dimensions. This quantity which was recently introduced in [arXiv:2111.02429], is an extension of volume in the Complexity=Volume (CV) proposal, by adding higher curvature corrections with a coupling constant $\lambda$ to the volume functional. We numerically calculate the growth rate of $\mathcal{C}_{\rm gen}$ for different values of the hyperscaling violation exponent $\theta$ and dynamical exponent $z$. It is observed that $\mathcal{C}_{\rm gen}$ always grows linearly at late times provided that we choose $\lambda$ properly. Moreover, it approaches its late time value from below. For the case $\lambda=0$, we find an analytic expression for the late time growth rate for arbitrary values of $\theta$ and $z$. However, for $\lambda \neq 0$, the late time growth rate can only be calculated analytically for some specific values of $\theta$ and $z$. We also examine the dependence of the growth rate on $d$, $\theta$, $z$ and $\lambda$. Furthermore, we calculate the complexity of formation obtained from volume-complexity and show that it is not UV divergent. We also examine its dependence on the thermal entropy and temperature of the black brane. At the end, we also numerically calculate the growth rate of $\mathcal{C}_{\rm gen}$ for the case where the higher curvature corrections are a linear combination of the Ricci scalar, square of the Ricci tensor and square of the Riemann tensor. We show that for appropriate values of the coupling constants, the late time growth rate is again linear.

Related papers

• Chaos in hyperscaling violating Lifshitz theories [0.0]
  We holographically study quantum chaos in hyperscaling-violating Lifshitz (HVL) theories (with charge) We present a detailed computation of the out-of-time ordered correlator (OTOC) via the shockwave analysis in the bulk HVL geometry with a planar horizon topology. We also analyze in detail, the behavior of $v_B$ with respect to the dynamical critical exponent (z), hyperscaling-violating parameter ($theta$), charge (Q) and the horizon radius ($r_h$)
  arXiv  Detail & Related papers  (2024-11-14T18:37:28Z)
• Diffusive entanglement growth in a monitored harmonic chain [0.0]
  We find that entanglement grows diffusively ($S sim t1/2$) for a large class of initial Gaussian states. We propose a modified quasi-particle picture which accounts for all of these main features and agrees quantitatively well with our essentially exact numerical results.
  arXiv  Detail & Related papers  (2024-03-06T20:07:25Z)
• Efficient Sampling on Riemannian Manifolds via Langevin MCMC [51.825900634131486]
  We study the task efficiently sampling from a Gibbs distribution $d pi* = eh d vol_g$ over aian manifold $M$ via (geometric) Langevin MCMC. Our results apply to general settings where $pi*$ can be non exponential and $Mh$ can have negative Ricci curvature.
  arXiv  Detail & Related papers  (2024-02-15T22:59:14Z)
• On the $O(\frac{\sqrt{d}}{T^{1/4}})$ Convergence Rate of RMSProp and Its Momentum Extension Measured by $\ell_1$ Norm [59.65871549878937]
  This paper considers the RMSProp and its momentum extension and establishes the convergence rate of $frac1Tsum_k=1T. Our convergence rate matches the lower bound with respect to all the coefficients except the dimension $d$. Our convergence rate can be considered to be analogous to the $frac1Tsum_k=1T.
  arXiv  Detail & Related papers  (2024-02-01T07:21:32Z)
• Correlated volumes for extended wavefunctions on a random-regular graph [0.0]
  We analyze the ergodic properties of a metallic wavefunction for the Anderson model in a disordered random-regular graph with branching number $k=2. We extract their corresponding fractal dimensions $D_q$ in the thermodynamic limit together with correlated volumes $N_q$ that control finite-size effects.
  arXiv  Detail & Related papers  (2023-11-13T19:15:18Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• On parametric resonance in the laser action [91.3755431537592]
  We consider the selfconsistent semiclassical Maxwell--Schr"odinger system for the solid state laser. We introduce the corresponding Poincar'e map $P$ and consider the differential $DP(Y0)$ at suitable stationary state $Y0$.
  arXiv  Detail & Related papers  (2022-08-22T09:43:57Z)
• Entanglement scaling for $\lambda\phi_2^4$ [0.0]
  We show that the order parameter $phi$, the correlation length $xi$ and quantities like $phi3$ and the entanglement entropy exhibit useful double scaling properties. We find the value $alpha_c=11.09698(31)$ for the critical point, improving on previous results.
  arXiv  Detail & Related papers  (2021-04-21T14:43:12Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)
• On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness [10.482805367361818]
  We show that for potentials with Lipschitz gradient, i.e. $beta=1$, our rate rate recovers the best known rate rate of dependency. Our results are applicable to $nu_* = eff$ in target distribution $nu_*$ in KL-divergence.
  arXiv  Detail & Related papers  (2020-05-27T00:26:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.