Related papers: Gibbs states and their classical limit
At large quantum numbers, the probability densities for particle-in-a-box or simple harmonic oscillator converge to the classical result upon coarse-graining the quantum mechanical probability densities by introducing a finite resolution in…
We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled Klein-Gordon-Schr\"odinger equation. Also, we…
We study the classical and quantum KMS conditions within the context of spin lattice systems. Specifically, we define a strict deformation quantization (SDQ) for a $\mathbb{S}^2$-valued spin lattice system over $\mathbb{Z}^d$ generalizing…
Given a uniform, frustration-free family of local Lindbladians defined on a quantum lattice spin system in any spatial dimension, we prove a strong exponential convergence in relative entropy of the system to equilibrium under a condition…
Small spin systems at the interface between analytical studies and experimental application have been intensively studied in recent decades. The spin ring consisting of four spins with uniform antiferromagnetic Heisenberg interaction is an…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
In this paper we study the semiclassical behavior of quantum states acting on the C*-algebra of canonical commutation relations, from a general perspective. The aim is to provide a unified and flexible approach to the semiclassical analysis…
In this letter, we fill a hole in the existing literature about disordered quantum spin systems generated by a random local interaction $\{\mathfrak{h}(Z)\}_{Z\Subset \mathbb{Z}^\nu}$ satisfying a statistical version of translation…
We present an algebraic theory of the states of the infinite classical lattices. The construction follows the Haag-Kastler axioms from quantum field theory. By comparison, the *-algebras of the quantum theory are replaced here with the…
Observables of quantum or classical mechanics form algebras called quantum or classical Hamilton algebras respectively (Grgin E and Petersen A (1974) {\it J Math Phys} {\bf 15} 764\cite{grginpetersen}, Sahoo D (1977) {\it Pramana} {\bf 8}…
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and…
This paper considers states on the Weyl algebra of the canonical commutation relations over the phase space R^{2n}. We show that a state is regular iff its classical limit is a countably additive Borel probability measure on R^{2n}. It…
It is well known that classical and quantum theories carry distinct types of representations, each type of representation corresponding to possible values of generalized charges in the classical or quantum context. This paper demonstrates a…
In the present report we discuss measures of classicality/quantumness of states of finite-dimensional quantum systems, which are based on a deviation of quasiprobability distributions from true statistical distributions. Particularly, the…
I investigate the extent to which the description of quantum systems by Gibbs states can be justified purely on the basis of tomographic data, without recourse to theoretical concepts such as infinite ensembles, environments, information,…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
Using tomographic-probability representation of spin states, quantum behavior of qudits is examined. For a general j-qudit state we propose an explicit formula of quantumness witnetness whose negative average value is incompatible with…
We consider a system of classical particles confined in a box $\Lambda\subset\mathbb{R}^d$ with zero boundary conditions interacting via a stable and regular pair potential. Based on the validity of the cluster expansion for the canonical…
We extend the notion of Gibbsianness for mean-field systems to the set-up of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of…
We consider the dynamics of systems of lattice bosons with infinitely many degrees of freedom. We show that their dynamics defines a group of automorphisms on a $C^*$--algebra introduced by Buchholz, which extends the resolvent algebra of…