Related papers: Comparison of typicality in quantum and classical …
Equilibrium properties of many-body systems with a large number of degrees of freedom are generally expected to be described by statistical mechanics. Such expectations are closely tied to the observation of thermalization, as manifested…
Dynamical typicality refers to the property that two pure states, which initially exhibit (almost) the same expectation value for some given observable $A$, are very likely to exhibit also very similar expectation values when evolving in…
The phenomenon of universality is one of the most striking in many-body physics. Despite having sometimes wildly different microscopic constituents, systems can nonetheless behave in precisely the same way, with only the variable names…
If the state of a quantum system is sampled out of a suitable ensemble, the measurement of some observables will yield (almost) always the same result. This leads us to the notion of quantum typicality: for some quantities the initial…
Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems, made up of microscopic particles, in terms of a small number of macroscopic quantities, such as…
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed…
A quantum field model for an experiment describes thermal fluctuations explicitly and quantum fluctuations implicitly, whereas a comparable continuous random field model would describe both thermal and quantum fluctuations explicitly. An…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging…
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the…
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization.…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
The response of a quantum system in a pure state to an external force is investigated by reconsidering the standard statistical approach to quantum dynamics on the light of the statistical description of equilibrium based on typicality. We…
The nonzero ground-state energy of the quantum mechanical harmonic oscillator implies quantum fluctuations around the minimum of the potential with the mean square value proportional to Planck's constant. In classical mechanics thermal…
Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems.…
In the classical world one can construct two identical systems which have identical behavior and give identical measurement results. We show this to be impossible in the quantum domain. We prove that after the same quantum measurement two…
An analytical prediction is established of how an isolated many-body quantum system relaxes towards its thermal long-time limit under the action of a time-independent perturbation, but still remaining sufficiently close to a reference case…
We consider a quantum system with $N$ degrees of freedom which is classically chaotic. When $N$ is large, and both $\hbar$ and the quantum energy uncertainty $\Delta E$ are small, quantum chaos theory can be used to demonstrate the…