Related papers: Ergodic Theorems for Quantum Trajectories under Di…
This work develops tools to understand how quantum information spreads, scrambles, and is reshaped by measurements in many-body systems. First, I study scrambling and pseudorandomness in the Brownian Sachdev-Ye-Kitaev (SYK) model,…
This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand…
For appropriately chosen weights, temporal averages in chaotic systems can be approximated as a weighted sum of averages over reference states, such as unstable periodic orbits. Under strict assumptions, such as completeness of the orbit…
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for parametrically driven waves. The motion of the defects is traced in detail yielding their life-times, annihilation partners, and distances traveled. In a regime in…
A quantum particle propagates subdiffusively on a strongly disordered chain when it is coupled to itinerant hard-core bosons. We establish a generalized Einstein relation (GER) that relates such subdiffusive spread to an unusual…
A concurrent system is defined as a monoid action of a trace monoid on a finite set of states. Concurrent systems represent state models where the state is distributed and where state changes are local. Starting from a spectral property on…
Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this…
In this paper, we define random quasi-periodic paths for random dynamical systems and quasi-periodic measures for Markovian semigroups. We give a sufficient condition for the existence and uniqueness of random quasi-periodic paths and…
In quantum mechanics, randomness is postulated as a separate axiom. De Broglie's theory allows one to reproduce quantum phenomena from completely deterministic formalism. But the question of the quantum randomness emergency in the de…
The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the…
The quantum chaos conjecture associates the spectral statistics of a quantum system with abstract notions of quantum ergodicity. Such associations are taken to be of fundamental and sometimes defining importance for quantum chaos, but their…
We study quantum Markov chains on graphs, described by completely positive maps, following the model due to S. Gudder (J. Math. Phys. 49, 072105, 2008) and which includes the dynamics given by open quantum random walks as defined by S.…
We develop an analytical theory for quantum phase transitions driven by disorder in magnets and superconductors. We study these transitions with a cavity approximation which becomes exact on a Bethe lattice with large branching number. We…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
We investigate the time-dependent, coherent, and dissipative dynamics of bound particles in single multilevel quantum dots in the presence of sequential tunnelling transport. We focus on the nonequilibrium regime where several channels are…
We study the quantum mechanics of a generalized version of the baker's map. We show that the Ruelle resonances (which govern the approach to ergodicity of classical distributions on phase space) also appear in the quantum correlation…
This is a comprehensive review of the random-matrix approach to the theory of phase-coherent conduction in mesocopic systems. The theory is applied to a variety of physical phenomena in quantum dots and disordered wires, including universal…
The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach -- essentially a fusion of the $G…
In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For these graphs, we compute the limiting distribution of the walk…
Macroscopic realism is a set of assumptions about how we experience the world at a classical level. While the Leggett-Garg inequalities are temporal correlations that are violated by quantum systems not obeying such macrorealism, the…