Related papers: Finite-size scaling analysis of eigenstate thermal…
We numerically exhibit strange scaling and temporal evolution of finite-size fluctuation in thermal equilibrium of a simple long-range interacting system. These phenomena are explained from the view point of existence of the Casimirs and…
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…
According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation,…
Fluctuations of thermodynamic quantities become non-negligible and play an important role when the system size is small. We develop finite-time thermodynamics of fluctuations in microscopic heat engines whose environmental temperature and…
A microcanonical finite-size scaling ansatz is discussed. It exploits the existence of a well-defined transition point for systems of finite size in the microcanonical ensemble. The best data collapse obtained for small systems yields…
A Microcanonical Finite Site Ansatz in terms of quantities measurable in a Finite Lattice allows to extend phenomenological renormalization (the so called quotients method) to the microcanonical ensemble. The Ansatz is tested numerically in…
A simple finite-size scaling theory is proposed here for anisotropic percolation models considering the cluster size distribution function as generalized homogeneous function of the system size and two connectivity lengths. The proposed…
In the microcanonical ensemble, suitably defined observables show non-analyticities and power law behaviour even for finite systems. For these observables, a microcanonical finite-size scaling theory is established which facilitates an…
We consider conditions under which an isolated quantum system approaches a microcanonical equilibrium state. A key component is the eigenstate thermalisation hypothesis, which proposes that all energy eigenstates appear thermal. We…
Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often…
Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique to analyze Monte Carlo data at a critical point. It consists in fixing a given renormalization-group invariant quantity to a given value,…
We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared…
We propose a variational quantum algorithm for estimating microcanonical expectation values in models obeying the eigenstate thermalization hypothesis. Using a relaxed criterion for convergence of the variational optimization loop, the…
For models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non-monotonic behaviour of the microcanonical specific heat as a function of the system size. This is in contrast…
Using single cluster flip Monte Carlo simulations we accurately determine new finite size scaling functions which are expressed only in terms the variable $x = \xi_L / L$, where $\xi_L$ is the correlation length in a finite system of size…
In this paper, we study eigenvalue fluctuations of the finite volume Anderson model in the mesoscopic scale. We carry out this study in a regime of exponential localization and prove a central limit theorem for the eigenvalue counting…
The eigenstate thermalization hypothesis (ETH) postulates that the energy eigenstates of an isolated many-body system are thermal, i.e., each of them already yields practically the same expectation values as the microcanonical ensemble at…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
We numerically study the finite-size droplet condensation-evaporation transition in two dimensions. We consider and compare two orthogonal approaches, namely at fixed temperature and at fixed density, making use of parallel multicanonical…
A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number…