Related papers: Locality for quantum systems on graphs depends on …
We study the localization properties of bipartite channels, whose action on a subsystem yields a unitary channel. In particular we show that, under such channel, the subsystem must evolve independent of its environment. This point of view…
We consider the spectral and dynamical properties of quantum systems of $n$ particles on the lattice $\Z^d$, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
The effect of repetitive measurement for quantum dynamics of driven by an intensive external force of the simple few-level systems as well as of the multilevel systems that exhibit the quantum localisation of classical chaos is…
Complex potential transformations which add imaginary parts to chosen energy levels are given and qualitatively explained. Unexpected shape similarity of potential perturbations for real and imaginary E-shifts of bound states are exhibited.…
Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
In the present work a general frame for the scattering theory of local, relativistic dipole quantum fields is presented and some models of interacting dipole fields are considered, i.e. local, relativistic quantum fields with indefinite…
In the following we undertake to derive quantum theory as a stochastic low-energy and coarse-grained theory from a more primordial discrete and basically geometric theory living on the Planck scale and which (as we argue) possibly underlies…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
Hidden-variable theories effectively solve the measurement problem. However, a serious issue of this route towards a realistic completion of quantum theory is raised by Bell's proof that the resulting theories are nonlocal. A possible…
We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…