Related papers: Universal relation for operator complexity
We investigate Krylov state complexity as a probe of the quantum Mpemba effect in quantum spin chains. For models without global $U(1)$ symmetry, Krylov complexity exhibits clear Mpemba-like crossings, consistent with conventional…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
A theoretical framework bridging General Relativity (GR) and Quantum Dynamics (QD) is introduced through the application of Kripke semantics and linear logic. While conventional unification efforts often rely on structural or geometrical…
The structure of the Heisenberg evolution of operators plays a key role in explaining diverse processes in quantum many-body systems. In this paper, we discuss a new universal feature of operator evolution: an operator can develop a void…
Nonstabilizerness is a quantum property of states associated with the non-Clifford resources required for their preparation. As a resource, nonstabilizerness complements entanglement, and the interplay between these two concepts has…
We investigate the analyticity of the attractors of a class of Kuramoto-Sivashinsky type pseudo-differential equations in higher dimensions, which are periodic in all spatial variables and possess a universal attractor. This is done by…
We study Krylov complexity in Schr\"odinger field theory in the grand canonical ensemble with chemical potential $\mu$, with an emphasis on the qualitatively new features that arise for $\mu>0$. In this regime the fermionic Wightman power…
We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large $s$, $s$…
We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are…
It is demonstrated that almost any S-matrix of quantum field theory in curved spaces posses an infinite set of complex poles (or branch cuts). These poles can be transformed into complex eigenvalues, the corresponding eigenvectors being…
We investigate the time evolution of the complexity of the operator by the Sachdev-Ye-Kitaev (SYK) model with $N$ Majorana fermions. We follow Nielsen's idea of complexity geometry and geodesics thereof. We show that it is possible that the…
Logarithmic corrections to the entropy of extremal black holes have proven effective in precisely matching the microscopic degeneracies obtained from string-theoretic as well as a non-perturbative quantum correction manifests as an…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…
In various contexts in mathematical physics one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the…
In classical chaotic systems the entropy, averaged over initial phase space distributions, follows an universal behavior. While approaching thermal equilibrium it passes through a stage where it grows linearly, while the growth rate, the…
The competitive growth models involving only one kind of particles (CGM), are a mixture of two processes one with probability $p$ and the other with probability $1-p$. The $p-$dependance produce crossovers between two different regimes. We…
An entropic approach to formulating uncertainty relations for the number-annihilation pair is considered. We construct some normal operator that traces the annihilation operator as well as commuting quadratures with a complete system of…
Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle…
The extension problem asks whether positive semi-definite functions on a symmetric unital subset of a discrete group can be extended to positive semi-definite functions on the whole group. It has been known at least since the work of Rudin…
Building on the duality between Krylov complexity and geodesic length in Jackiw-Teitelboim and sine-dilaton gravity, we develop a precise holographic dictionary for quantities in the Krylov subspace of the double-scaled Sachdev-Ye-Kitaev…