Related papers: Quantum baker map on the sphere

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…

A non-Hermitian PT-symmetric version of the kicked top is introduced to study the interplay of quantum chaos with balanced loss and gain. The classical dynamics arising from the quantum dynamics of the angular momentum expectation values…

Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…

We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…

The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum…

We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure…

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…

We study a special kind of semiclassical limit of quantum dynamics on a circle and in a box (infinite potential well with hard walls) as the Planck constant tends to zero and time tends to infinity. The results give detailed information…

We present two complementary ways in which Saraceno's symmetric version of the quantum baker's map can be written as a shift map on a string of quantum bits. One of these representations leads naturally to a family of quantizations of the…

Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…

We present a broad family of quantum baker maps that generalize the proposal of Schack and Caves to any even Hilbert space with arbitrary boundary conditions. We identify a structure, common to all maps consisting of a simple kernel…

Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…

We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum…

We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…

The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…

We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…

The correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin, and which appear in the spectra of actions of the classical periodic orbits of the corresponding classical…

We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…

Time-reversal symmetry is of fundamental importance to physics. In the classical theory of time-reversal symmetry, the time-reversal symmetry of a quantum system is described by an anti-unitary operator, which is known as the time-reversal…

This work exploits a framework whereby a graph (in the mathematical sense) serves to connect a classical system to a state space that we call `quantum-like' (QL). The QL states comprise arbitrary superpositions of states in a tensor product…