Related papers: Classical and Quantum Discrete Dynamical Systems
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
We discuss the dynamics of finite systems within molecular dynamics models. Signatures of a critical behavior are analyzed and compared to experimental data both in nucleus-nucleus and metallic cluster collisions. We suggest the possibility…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
Recent advances in quantum technologies have enabled quantum simulation of gauge theories -- some of the most fundamental frameworks of nature -- in regimes far from equilibrium, where classical computation is severely limited. These…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present…
The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of non-relativistic quantum field theory is proposed, to describe both coherent and incoherent…
The purpose of physics is to describe nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this spectrum of events is desirable, this would…
We show that if a discrete quantum gravity is not classical, then it cannot be generated by an isometric dynamics. In particular, we show that if the quantum measure {\mu} (or equivalently the decoherence functional) is generated by an…
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime…
Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry.…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…