Related papers: How accurately can the microcanonical ensemble des…
We investigate finite size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy-scale, and the high-energy regime enables…
The anisotropic quantum Heisenberg model with Curie-Weiss-type interactions is studied analytically in several variants of the microcanonical ensemble. (Non)equivalence of microcanonical and canonical ensembles is investigated by studying…
Motivated by recent experiments, we study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson…
We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any sufficiently large time interval. The…
We propose a new approach to justify the use of the microcanonical ensemble for isolated macroscopic quantum systems. Since there are huge number of independent observables in a macroscopic system, we cannot see all of them. Actually what…
A numerically implementable Multi-scale Many-Body approach to strongly correlated electron systems is introduced. An extension to quantum cluster methods, it approximates correlations on any given length-scale commensurate with the strength…
We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of…
A quantum microcanonical postulate is proposed as a basis for the equilibrium properties of small quantum systems. Expressions for the corresponding density of states are derived, and are used to establish the existence of phase transitions…
Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate…
We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum…
We consider a fixed number of noninteracting bosons in a harmonic trap. The determination of the exact microcanonical ground state number fluctuation is a difficult enterprise. There have been several theoretical attempts to solve this…
Representing a strongly interacting multi-particle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave…
We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by…
Hybrid quantum-classical algorithms have begun to leverage quantum devices to efficiently represent many-electron wavefunctions, enabling early demonstrations of molecular simulations on real hardware. A key prerequisite for scalable…
The simulation of quantum many-body systems poses a significant challenge in physics due to the exponential scaling of Hilbert space with the number of particles. Traditional methods often struggle with large system sizes and frustrated…
We consider an isolated, macroscopic quantum system. Let H be a micro-canonical "energy shell," i.e., a subspace of the system's Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + delta E. The…
When a quantum many-body system undergoes a quench, the time-averaged density-matrix $\rho$ governs the time-averaged expectation value of any observable. It is therefore the key object to look at when comparing results with equilibrium…
The microcanonical entropy s(e,m) as a function of the energy e and the magnetization m is computed analytically for the anisotropic quantum Heisenberg model with Curie-Weiss-type interactions. The result shows a number of interesting…
For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and…
We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact…