Related papers: Causal Fermions in Discrete Spacetime
Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum…
The global in time existence of solutions of a system describing the interaction of gravitationally attracting particles with a general diffusion term and fixed energy is proved. The presented theory covers the case of the model with…
In recent years, the picture of discrete space time has been studied in the context of stochastic theory. There are a number of ramifications, which are briefly examined. We argue that the causality of physiics has its roots in the…
We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic…
We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
A quantum cellular automaton (QCA) is an abstract model consisting of an array of finite-dimensional quantum systems that evolves in discrete time by local unitary operations. Here we propose a simple coarse-graining map, where the spatial…
Non-Hermitian Hamiltonians are relevant to describe the features of a broad class of physical phenomena, ranging from photonics and atomic and molecular systems to nuclear physics and mesoscopic electronic systems. An important question…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
A discrete-time Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). In this paper, we study the…
Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an {\it arrow of time} that follows from the fact that…
We present the problematic of controlling the discreteness effects in cosmological N-body simulations. We describe a perturbative treatment which gives an approximation describing the evolution under self-gravity of a lattice perturbed from…
Presented is a quantum lattice gas algorithm to efficiently model a system of Dirac particles interacting through an intermediary gauge field. The algorithm uses a fixed qubit array to represent both the spacetime and the particles…
We begin by describing a sequential growth model in which the universe grows one element at a time in discrete time steps. At each step, the process has the form of a causal set and the "completed" universe is given by a path consisting of…
We study abrupt changes in the dynamics and/or steady state of fermionic dissipative systems produced by small changes of the system parameters. Specifically, we consider open fermionic systems whose dynamics is described by master…
We discuss time dependent quantum systems on bounded domains. Our work may be viewed as a framework for several models, including linear iterations involved in time dependent density functional theory (TDDFT), the Hartree-Fock model, or…
We discuss the phase structure of a higher derivative four-fermion model in four dimensions in curved spacetime in frames of the $\frac{1}{N_c}$-expansion. First, we evaluate in our model the effective potential of two composite scalars in…