Related papers: Complex-Time Singularity and Locality Estimates fo…
In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the…
For classical lattice systems, the Dobrushin-Lanford-Ruelle theory of boundary conditions states that the restriction of a global equilibrium state to a subsystem can be obtained as an integral over equilibrium states of the subsystem…
The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional…
We study the out-of-equilibrium evolution of a strongly interacting quantum spin chain which is mapped on a system of hard rods that are coherently deposited on and removed from a lattice. We show that this closed quantum system approaches…
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint…
A major challenge of interdisciplinary description of complex system behaviour is whether real systems of higher complexity levels can be understood with at least the same degree of objective, "scientific" rigour and universality as…
We survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
We investigate the non-equilibrium dynamics of a class of isolated one-dimensional systems possessing two degenerate ground states, initialized in a low-energy symmetric phase. We report the emergence of a time-scale separation between fast…
We show that the presented real-number quantum theories, compatible with the independent source assumption, require the inclusion of a nonlocal map. This means that if the independent source assumption holds, in these models, complex-number…
We discuss phenomenology of extra time dimensions in a scenario where the standard model particles are localized in ``our'' time, whereas gravity can propagate in all time dimensions. For an odd number of extra times, at small distances,…
Spatiotemporal complexity is induced in a two dimensional nonlinear disordered lattice through the modulational instability of an initially weakly perturbed excitation. In the course of evolution we observe the formation of transient as…
We discuss the generic slowing down of quantum dynamics in low energy density states of spatially local Hamiltonians. Beginning with quantum walks of a single particle, we prove that for certain classes of Hamiltonians (deformations of…
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression…
Reversible lattice dynamics embody basic features of physics that govern the time evolution of classical information. They have finite resolution in space and time, don't allow information to be erased, and easily accommodate other…
This is a short note on the spatiotemporal complexity of the dynamical state(s) of the universe at subhorizon scales (up to 300 Mpc). There are reasons, based mainly on infrared radiative divergences, to believe that one can encounter a…
We study the light-cone and front dynamics of a single particle continuous time extended quantum walk on a one dimensional lattice with finite range hopping. We show that, in general, for an initially localized state, propagating wave…
We consider growth of local operators under Euclidean time evolution in lattice systems with local interactions. We derive rigorous bounds on the operator norm growth and then proceed to establish an analog of the Lieb-Robinson bound for…
Many physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger than microscopic molecular collision scales and can be considered as in local thermal equilibrium. In…
According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this…