Related papers: The Approach to Ergodicity in the Quantum Baker's …
The Walsh-quantized baker's maps are models for quantum chaos on the torus. We show that for all baker's map scaling factors $D\ge2$ except for $D=4$, typically (in the sense of Haar measure on the eigenspaces, which are degenerate) the…
We study the relationship between the spectral properties of diffusive open quantum maps and the classical spectrum of Ruelle-Pollicott resonances. The leading resonances determine the asymptotic time regime for several quantities of…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
At lower energies, the resonances in scattering experiments are often isolated. In quantum chaotic many-body, disordered or generically stochastic systems, the resonances overlap at larger energies. Eventually, the Ericson regime is reached…
We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum…
We give a formulation of quantum ergodicity for Pauli Hamiltonians with arbitrary spin in terms of a Wigner-Weyl calculus. The corresponding classical phase space is the direct product of the phase space of the translational degrees of…
We analyze a randomly perturbed quantum version of the baker's transformation, a prototype of an area-conserving chaotic map. By numerically simulating the perturbed evolution, we estimate the information needed to follow a perturbed…
We present here a canonical quantization for the baker's map. The method we use is quite different from that used in Balazs and Voros (ref. \QCITE{cite}{}{BV}) and Saraceno (ref. \QCITE{cite}{}{S}). We first construct a natural ``baker…
We give an estimate of the quantum variance for $d$-regular graphs quantised with boundary scattering matrices that prohibit back-scattering. For families of graphs that are expanders, with few short cycles, our estimate leads to quantum…
The experimental realization of successive non-demolition measurements on single microscopic systems brings up the question of ergodicity in Quantum Mechanics (QM). We investigate whether time averages over one realization of a single…
We study wave function structure for quantum graphs in the chaotic and disordered regime, using measures such as the wave function intensity distribution and the inverse participation ratio. The result is much less ergodicity than expected…
We prove a strong version of quantum ergodicity for linear hyperbolic maps of the torus (``cat maps''). We show that there is a density one sequence of integers so that as N tends to infinity along this sequence, all eigenfunctions of the…
We consider a sequence of finite quantum graphs with few loops, so that they converge, in the sense of Benjamini-Schramm, to a random infinite quantum tree. We assume these quantum trees are spectrally delocalized in some interval $I$, in…
Operators in ergodic spin-chains are found to grow according to hydrodynamical equations of motion. The study of such operator spreading has aided our understanding of many-body quantum chaos in spin-chains. Here we initiate the study of…
We examine the consequences of classical ergodicity for the localization properties of individual quantum eigenstates in the classical limit. We note that the well known Schnirelman result is a weaker form of quantum ergodicity than the one…
Using the key properties of chaos, i.e. ergodicity and exponential instability, as a resource to control classical dynamics has a long and considerable history. However, in the context of controlling "chaotic" quantum unitary dynamics, the…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
We study the nature and mechanisms of broken ergodicity (BE) in specific random walk models corresponding to diffusion on random potential surfaces, in both one and high dimension. Using both rigorous results and nonrigorous methods, we…
In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities,…
We present a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an…