Related papers: Equilibration properties of small quantum systems:…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
Schelling's model of segregation demonstrates that even in the absence of social or governmental interventions, individuals with mild in-group preferences can self-organize into strongly segregated neighborhoods. Many variants of this…
Spontaneous symmetry breaking (SSB) is a property of Hamiltonian equilibrium states which, in the thermodynamic limit, retain a finite average value of an order parameter even after a field coupled to it is adiabatically turned off. In the…
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…
We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian, and as such connect energy eigenstates from different total quasimomentum sectors. We consider quantum-chaotic and…
The notion of typicality in statistical mechanics is essential to characterize a macroscopic system. An overwhelming majority of the pure state looks almost identical if we neglect macroscopic non-local correlations, suggesting that thermal…
We propose and test a renormalization procedure which acts in Hilbert space. We test its efficiency on strongly correlated quantum spin systems by working out and analyzing the low-energy spectral properties of frustrated quantum spin…
Understanding the equilibration of isolated quantum systems under unitary dynamics is an interesting topic. In this paper, we look at the early time behaviour of periodically and quasi-periodically driven Transverse field Ising chains when…
We introduce an algorithm aimed to reduce the dimensions of Hilbert space. It is used here in order to study the behaviour of low energy states of strongly interacting quantum many-body systems at first order transitions and avoided…
A quantum system subject to continuous measurement and post-selection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the rate of post-selection, this non-Hermitian Hamiltonian undergoes a spectral phase…
Spectral statistics and correlations are the usual way to study the presence or absence of quantum chaos in quantum systems. We present our investigation on the study of the fluctuation average and variance of certain correlation functions…
We consider the properties of an observable (such as a single spin component that squares to the identity) when expressed as a matrix in the basis of energy eigenstates, and then truncated to a microcanonical slice of energies of varying…
The approach to equilibrium is studied for long-range quantum Ising models where the interaction strength decays like r^{-\alpha} at large distances r with an exponent $\alpha$ not exceeding the lattice dimension. For a large class of…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
We study the transition probabilities of a two-point measurement on a quantum system, initially prepared in a thermal state. We find two independent constraints on the difference between transition probabilities when the system is prepared…
The problem of mutual equilibration between two finite, identical quantum systems, A and B, prepared initially at different temperatures is elucidated. We show that the process of energy exchange between the two systems leads to accurate…
Consider $D$ random systems that are modeled by independent $N\times N$ complex Hermitian Wigner matrices. Suppose they are lying on a circle and the neighboring systems interact with each other through a deterministic matrix $A$. We prove…
We analyze the behavior of a non-Hermitian opened one-dimensional quantum system with $\mathcal{PT}$ symmetry. This system is built by a dimer, with balanced gains and losses described by a parameter $\gamma$. By varying $\gamma$ the system…
Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…
Many theoretical and experimental results show that even isolated quantum systems evolving unitarily may equilibrate, since the evolution of some observables may be around an equilibrium value with negligible fluctuations most of the time.…