Related papers: On quantum to classical comparison for Davies gene…
The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to…
We develop the connection between large deviation theory and more applied approaches to stochastic hybrid systems by highlighting a common underlying Hamiltonian structure. A stochastic hybrid system involves the coupling between a…
We examine quantum normal typicality and ergodicity properties for quantum systems whose dynamics are generated by Hamiltonians which have residual degeneracy in their spectrum and resonance in their energy gaps. Such systems can be…
We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic)…
We introduce a systematic protocol for constructing quantum Hilbert-space-fragmented Hamiltonians, whose Krylov-sector structure, unlike in classically fragmented models, can be fully resolved only in an entangled basis. The protocol takes…
It is shown that for any given quantum system evolving unitarily with the Hamiltonian, $\hat{H} = \hat{\bf p}^2/(2m) + U({\bf q})$, [bold letters denote $D$-dimensional ($D \geqslant 3$) vectors] and with a sufficiently smooth potential…
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
Decoherence is a well established process for the emergence of classical mechanics in open quantum systems. However, it can have two different origins or mechanisms depending on the dynamics one is considering, speaking then about intrinsic…
Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…
It is shown that generators of single-particle, translation-invariant Lindblad operators on the infinite line are unitarily equivalent to direct integrals of finite-range bi-infinite Laurent operator with finite-range perturbations. This…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the…
In the context of dissipative systems, we show that for any quantum chaotic attractor a corre- sponding classical chaotic attractor can always be found. We provide with a general way to locate them, rooted in the structure of the parameter…
In chaotic quantum systems, an initially localized quantum state can deviate strongly from the corresponding classical phase-space distribution after the Ehrenfest time $t_{\mathrm{E}} \sim \log(\hbar^{-1})$, even in the limit $\hbar \to…
We investigate the relation between non-Hermitian Hamiltonian and Lindblad dynamics in nonequilibrium open quantum systems. Non-Hermitian models can extend phase diagrams and enable sensing advantages, but such effects often rely on…
Analog Quantum Simulators offer a route to exploring strongly correlated many-body dynamics beyond classical computation, but their predictive power remains limited by the absence of quantitative error estimation. Establishing rigorous…
We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…