Related papers: Weak Quantum Ergodicity
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the…
In this work we report on a loss of ergodicity in a simple hopping model, motivated by the Hubbard Hamiltonian, of a many body quantum system at zero temperature, quantized in Euclidean time. We show that this quantum system may lose…
This paper is a continuation of Poiret-Robert-Thomann (2013) where we studied a randomisation method based on the Laplacian with harmonic potential. Here we extend our previous results to the case of any polynomial and confining potential…
We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.
We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically-constrained models of classical glasses. Through a combination of analytics, exact diagonalization and…
We consider a qubit governed by a sequence of weak measurements, with the measurement strength modified in a time- and state-dependent manner. The resulting trajectory of the qubit in the phase space can be weakly controlled without any…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
We analyze the dynamics of a quantum kicked rotor (QKR) driven with a binary Fibonacci sequence of two distinct drive amplitudes. While the dynamics at low drive frequencies is found to be diffusive, a long-lived pre-ergodic regime emerges…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…
We characterize the points that satisfy Birkhoff's ergodic theorem under certain computability conditions in terms of algorithmic randomness. First, we use the method of cutting and stacking to show that if an element x of the Cantor space…
We analyze a class of one-dimensional quantum systems characterized by a position-dependent kinetic term arising as the continuum limit of an inhomogeneous tight-binding model with spatially varying hopping amplitudes. In this limit, the…
Reduced transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, but may also emerge from the influence of a few controllable defects. We show here how a single defect profoundly…
Geometric analogs of Bloch oscillations studied so far have relied on Berry curvature. We show that a weakly inhomogeneous electric field adds a distinct quantum-metric term to semiclassical wavepacket dynamics, generating an oscillatory…
We show that in systems with highly degenerate energy spectra, such as the 2D transverse-field Ising model (2DTFIM) in the strong-field limit, quantum chaos can emerge in finite systems for arbitrary small perturbations. In this regime, the…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
In this paper we construct a sequence of eigenfunctions of the ``quantum Arnold's cat map'' that, in the semiclassical limit, show a strong scarring phenomenon on the periodic orbits of the dynamics. More precisely, those states have a…
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…
The notion of trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any…
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…