Related papers: The Anderson transition in quantum chaos
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
This article examines the relationship between classical and quantum propagation of chaos. (In this context, "chaos" refers to the Boltzmann's Ansatz of molecular disorder, not to chaotic dynamics.) Classical propagation of chaos is shown…
Independent studies by different authors have proposed that classicality may be induced in quantum objects by cosmological constraints presented by an expanding universe of finite extent in space-time. Cosmological effects on a quantum…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
We study classical and quantum maps on the torus phase space, in the presence of noise. We focus on the spectral properties of the noisy evolution operator, and prove that for any amount of noise, the quantum spectrum converges to the…
While there is strong evidence for advantages of quantum over classical computation, the repertoire of computational primitives with proven or conjectured quantum advantage remains limited. A big challenge of quantum algorithmic design is a…
We investigate the previously unexplored quantum dynamics of non-relativistic, spinless particles propagating in curved spaces with torsion. Our findings demonstrate that while torsion has been predominantly associated with spin, it can…
Disorder, noise and interaction play a crucial role in the transport properties of real systems, but they are typically hard to control and study both theoretically and experimentally, especially in the quantum case. Here we explore a…
We present a theory of quantum work statistics in generic chaotic, disordered Fermi liquid systems within a driven random matrix formalism. By extending P. W. Anderson's orthogonality determinant formula to compute quantum work…
We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
The perturbations in the early universe are generated as a result of the interplay between quantum field theory and gravitation. Since these primordial perturbations lead to the anisotropies in the cosmic microwave background and eventually…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…
We have combined two remarkable phenomena: resonance tunneling and Anderson localization. It results in unexpected spectrum reverse to usual notions. It is demonstrated by the quantum system with chaotic distribution of potential resonance…
We study quantum chaos in a non-KAM system, i.e. a kicked particle in a one-dimensional infinite square potential well. Within the perturbative regime the classical phase space displays stochastic web structures, and the diffusion…
Loop quantum gravity introduces strong non-perturbative modifications to the dynamical equations in the semi-classical regime, which are responsible for various novel effects, including resolution of the classical singularity in a Friedman…
We explore various properties of classical one-dimensional Wigner solids in the presence of disorder at T=0 in the context of a recently discovered Anderson transition of plasma modes in the random potential system. The extent to which the…
All quantum field theories that describe interacting bosonic elementary particles, share the feature that the zeroth order perturbation expansion describes non-interacting harmonic oscillators. This is explained in the paper. We then…
The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…