Related papers: Operator Spreading in the Memory Matrix Formalism
The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle corresponding, in its simplest form, to the Maximum…
Fluctuations in biochemical networks, e.g., in a living cell, have a complex origin that precludes a description of such systems in terms of bipartite or multipartite processes, as is usually done in the framework of stochastic and/or…
Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum…
We present a general theory of quantum information propagation in chaotic quantum many-body systems. The generic expectation in such systems is that quantum information does not propagate in localized form; instead, it tends to spread out…
The hydrodynamic representation of quantum mechanics describes virtual flow as if a quantum system were fluid in motion. This formulation illustrates pointlike vortices when the phase of a wavefunction becomes nonintegrable at nodal points.…
Quantum parallelism implies a spread of information over the space in contradistinction to the classical mechanical situation where the information is "centered" on a fixed trajectory of a classical particle. This means that a quantum state…
The emergence of quantum technologies has brought much attention to the characterization of quantum resources as well as the classical simulatability of quantum processes. Quantum resources, as quantified by non-stabilizerness, have in one…
We systematically investigate whether classical hydrodynamic field theories can predict the long-time dynamics of many-particle quantum systems. We study both numerically and analytically the time evolution of a chain of spins (or qubits)…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
Out-of-Time-Order Correlators (OTOCs) quantify quantum information scrambling, but their connection to localized phase-space structures, such as chemical transition states, requires formal development. We derive a leading-order…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affecting the particle's speed and the other its direction. These…
Understanding the spreading of quantum correlations in out-of-equilibrium many-body systems is one of the major challenges in physics. For {\it isolated} systems, a hydrodynamic theory explains the origin and spreading of entanglement via…
Entanglement is a defining feature of many-body quantum systems and is an essential requirement for quantum computing. It is therefore useful to study physical processes which generate entanglement within a large system, as they maybe…
Commonly, the notion of "quantum chaos'' refers to the fast scrambling of information throughout complex quantum systems undergoing unitary evolution. Motivated by the Krylov complexity and the operator growth hypothesis, we demonstrate…
The growth of bubbles in cosmological first-order phase transitions involves nontrivial hydrodynamics. For that reason, the study of the propagation of phase transition fronts often requires several approximations. A frequently used…
Thermodynamic behaviors in a quantum Brownian motion coupled to a classical heat bath is studied. We then define a heat operator by generalizing the stochastic energetics and show the energy balance (first law) and the upper bound of the…
Fluctuation theorems establish exact relations for nonequilibrium dynamics, profoundly advancing the field of stochastic thermodynamics. In this work, we extend quantum fluctuation theorems beyond the traditional thermodynamic framework to…
In this work, we quantify the time scales and information flow associated with multiscale energy transfer in a weakly turbulent system. This is done through a greedy optimization algorithm which finds the maximum conditional-mutual…
Information spreads in time. For example, correlations dissipate when the correlated system locally couples to a third party, such as the environment. This simple but important fact forms the known quantum data-processing inequality. Here…