相关论文: Canonical Typicality
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
We consider a system weakly interacting with a bath as a thermodynamic setting to establish a quantum foundation of statistical physics. It is shown that even if the composite system is initially in an arbitrary nonequilibrium pure quantum…
We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal…
It is typically assumed, without justification, that a weak coupling between a system and a bath is a necessary condition for the equivalence of a canonical ensemble and a microcanonical ensemble. For instance, in a canonical ensemble,…
We propose a definition of microcanonical and canonical statistical ensembles based on the concept of density of states. This definition applies both to the classical and the quantum case. For the microcanonical case this allows for a…
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 compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and…
In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic…
Two approaches to describe the thermodynamics of a subsystem that interacts with a thermal bath are considered. Within the first approach, the mean system energy $E_{S}$ is identified with the expectation value of the system Hamiltonian,…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented…
For quantum systems that are weakly coupled to a much 'bigger' environment, thermalization of possibly far from equilibrium initial ensembles is demonstrated: for sufficiently large times, the ensemble is for all practical purposes…
In this article it is shown that in a classical equilibrium canonical ensemble of molecules with $s$-body interaction full Gibbs distribution can be uniquely expressed in terms of a reduced s-particle distribution function. This means that…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that…
While the canonical ensemble has been tremendously successful in capturing thermal statistics of macroscopic systems, deviations from canonical behavior exhibited by small systems are not well understood. Here, using a small two dimensional…
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…
The microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…
According to thermodynamics, the specific heat of Boltzmannian short-range interacting systems is a positive quantity. Less intuitive properties are instead displayed by systems characterized by long-range interactions. In that case, the…
We study the role of the system-bath coupling for the generalized canonical thermalization [S. Popescu, et al., Nature Physics 2,754(2006) and S. Goldstein et al., Phys. Rev. Lett. 96, 050403(2006)] that reduces almost all the pure states…
In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is…