Quantum reservoir computing (QRC) has emerged as a promising paradigm for harnessing near-term quantum devices to tackle temporal machine learning tasks. Yet, identifying the mechanisms that underlie enhanced performance remains challenging, particularly in many-body open systems where nonlinear interactions and dissipation intertwine complex ways. Here, we investigate minimal model of driven-dissipative described by two coupled Kerr-nonlinear oscillators, an experimentally realizable...

We obtain bounds for the minimum and maximum mass/radius ratio of a stable, charged, spherically symmetric compact object in $D$-dimensional space-time framework general relativity, presence dark energy. The total energy, including gravitational component, stability objects with is also investigated. energy condition leads to representation mass radius charged terms charge vacuum only. As applied electron four-dimensional case, this procedure allows one re-obtain classical from purely...

The existence of both a minimum mass and density in nature, the presence positive cosmological constant, is one most intriguing results classical general relativity. These follow rigorously from Buchdahl inequalities four-dimensional de Sitter space. In this work, we obtain generalized arbitrary space–time dimensions with $$\Lambda \ne 0$$ consider anti-de cases. dependence on D, number dimensions, maximum masses for stable spherical objects explicitly obtained. analysis then extended to...

We consider (2+1)-QFT at finite temperature on a product of time with static spatial geometry. The suitably defined difference thermal vacuum free energy for the QFT deformation flat space from its value is UV quantity, and reasonable fall-off conditions IR too. For perturbations we show this goes quadratically perturbation amplitude may be computed linear response stress tensor. As an illustration compute it holographic CFT finding that any temperature, perturbation, decreases. Similar...

A bstract We compare the behavior of vacuum free energy (i.e. Casimir energy) various (2 + 1)-dimensional CFTs on an ultrastatic spacetime as a function spatial geometry. The we consider are Dirac fermion, conformally-coupled scalar, and holographic CFT, take geometry to be axisymmetric deformation round sphere. energies fermion scalar computed numerically using heat kernel methods; CFT is from static, asymptotically AdS dual novel approach introduce here. find that two theories...

Quantum reservoir computing (QRC) has emerged as a promising paradigm for harnessing near-term quantum devices to tackle temporal machine learning tasks. Yet identifying the mechanisms that underlie enhanced performance remains challenging, particularly in many-body open systems where nonlinear interactions and dissipation intertwine complex ways. Here, we investigate minimal model of driven-dissipative described by two coupled Kerr-nonlinear oscillators, an experimentally realizable...

We consider the toroidally compactified planar AdS-Schwarzschild solution to 4-dimensional gravity with negative cosmological constant. This has a flat torus conformal boundary metric. show that if spatial part of metric is deformed, keeping it static and temperature area fixed, then assuming bulk exists, its energy less than solution. The proof non-perturbative in deformation. While we expect same holds for free black hole solutions are so far not able prove it. In context AdS-CFT this...

In this work, we derive an upper bound on energetic quantities, namely vacuum energy and free energy, for static solutions of Einstein-Scalar theory in four dimensional asymptotically locally Anti-de Sitter(AlAdS) spacetime with a nontrivial scalar potential where the field mass parameter($m^2$) is equal to 0 or -2. This system holographic dual strongly coupled conformal theory(CFT) three dimensions being deformed by relevant marginal operator dimension $Δ=1, 2, 3$. The derived from purely...

We compare the behavior of vacuum free energy (i.e. Casimir energy) various $(2+1)$-dimensional CFTs on an ultrastatic spacetime as a function spatial geometry. The we consider are Dirac fermion, conformally-coupled scalar, and holographic CFT, take geometry to be axisymmetric deformation round sphere. energies fermion scalar computed numerically using heat kernel methods; CFT is from static, asymptotically AdS dual novel approach introduce here. find that two theories qualitatively similar...