Related papers: Random product states at high temperature equilibr…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
Considering any Hamiltonian, any initial state, and measurements with a small number of possible outcomes compared to the dimension, we show that most measurements are already equilibrated. To investigate non-trivial equilibration we…
Recently, there have been significant new insights concerning conditions under which closed systems equilibrate locally. The question if subsystems thermalize---if the equilibrium state is independent of the initial state---is however much…
We consider a finite chain of non-linear oscillators coupled at its ends to two infinite heat baths which are at different temperatures. Using our earlier results about the existence of a stationary state, we show rigorously that for…
We use simple spectral perturbation theory to show that the positive partial transpose property is stable under bounded perturbations of the Hamiltonian, for equilibrium states in infinite dimensions. The result holds provided the…
We show that states of macroscopic systems with purported absolute negative temperatures are not stable under small, yet arbitrary, perturbations. We prove the previous statement using the fact that, in equilibrium, the entropy takes its…
In how far does an non-equilibrium initial ensemble evolve towards a stationary long time behavior for an isolated macroscopic quantum system? We demonstrate that deviations from a steady state indeed become unmeasurably small or…
We consider the problem of estimating the maximal energy of quantum $p$-local spin glass random Hamiltonians, the quantum analogues of widely studied classical spin glass models. Denoting by $E^*(p)$ the (appropriately normalized) maximal…
We show that thermal states of local Hamiltonians are separable above a constant temperature. Specifically, for a local Hamiltonian $H$ on a graph with degree $\mathfrak{d}$, its Gibbs state at inverse temperature $\beta$, denoted by $\rho…
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…
We provide here an explicit example of Khinchin's idea that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics. This point of view is supported by extensive numerical…
Temperature of a finite-sized system fluctuates due to the thermal fluctuations. However, a systematic mathematical framework for measuring or estimating the temperature is still underdeveloped. Here, we incorporate the estimation theory in…
Equilibrium states of infinite extended lattice systems at high temperature are studied with respect to their entanglement. Two notions of separability are offered. They coincide for finite systems but differ for infinitely extended ones.…
This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of…
We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are…
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…
Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
We discuss the possibility of defining an emergent local temperature in extended quantum many-body systems evolving out of equilibrium. For the most simple case of free-fermionic systems, we give an explicit formula for the effective…