Emergent phenomena in Nature: a paradox with Theory?

The existence of various physical phenomena stems from the concept called asymptotic emergence, that is, they seem to be exclusively reserved for certain limiting theories. Important examples are spontaneous symmetry breaking (SSB) and phase transitions: these would only occur in the classical or thermodynamic limit of underlying finite quantum systems, since for finite quantum systems, due to the uniqueness of the relevant states, such phenomena are excluded by Theory. In Nature, however, finite quantum systems describing real materials clearly exhibit such effects. In this paper we discuss these apparently ``paradoxical'' phenomena and outline various ideas and mechanisms that encompass both theory and reality, from physical and mathematical points of view.Comment: 21 pages, 5 figure

DLR-KMS correspondence on lattice spin systems

The Dobrushin-Lanford-Ruelle (DLR) condition and the classical Kubo-Martin-Schwinger (KMS) condition are considered in the context of classical lattice systems. In particular, we prove that these conditions are equivalent for the case of a lattice spin system with values in a compact symplectic manifold by showing that infinite volume Gibbs states are in bijection with KMS states.Comment: 13 page

Colorectal liver metastases: Surgery versus thermal ablation (COLLISION) - a phase III single-blind prospective randomized controlled trial

Background: Radiofrequency ablation (RFA) and microwave ablation (MWA) are widely accepted techniques to eliminate small unresectable colorectal liver metastases (CRLM). Although previous studies labelled thermal ablation inferior to surgical resection, the apparent selection bias when comparing patients with unresectable disease to surgical candidates, the superior safety profile, and the competitive overall survival results for the more recent reports mandate the setup of a randomized controlled trial. The objective of the COLLISION trial is to prove non-inferiority of thermal ablation compared to hepatic resection in patients with at least one resectable and ablatable CRLM and no extrahepatic disease. Methods: In this two-arm, single-blind multi-center phase-III clinical trial, six hundred and eighteen patients with at least one CRLM (≤3cm) will be included to undergo either surgical resection or thermal ablation of appointed target lesion(s) (≤3cm). Primary endpoint is OS (overall survival, intention-to-treat analysis). Main secondary endpoints are overall disease-free survival (DFS), time to progression (TTP), time to local progression (TTLP), primary and assisted technique efficacy (PTE, ATE), procedural morbidity and mortality, length of hospital stay, assessment of pain and quality of life (QoL), cost-effectiveness ratio (ICER) and quality-adjusted life years (QALY). Discussion: If thermal ablation proves to be non-inferior in treating lesions ≤3cm, a switch in treatment-method may lead to a reduction of the post-procedural morbidity and mortality, length of hospital stay and incremental costs without compromising oncological outcome for patients with CRLM. Trial registration:NCT03088150 , January 11th 2017

The classical limit and spontaneous symmetry breaking in algebraic quantum theory

In this paper an overview of some recent developments on the classical limit and spontaneous symmetry breaking (SSB) in algebraic quantum theory is given. In such works, based on the theory of $C^*$-algebras, the concept of the classical limit has been formalized in a complete algebraic manner. Additionally, since this setting allows for commutative as well as non-commutative $C^*$-algebras, and hence for classical and quantum theories, it provides an excellent framework to study SBB as an emergent phenomenon when transitioning from the quantum to the classical world by turning off a semi-classical parameter. We summarize the main results and show that this algebraic approach sheds new light on the connection between the classical and the quantum realm, where particular emphasis is placed on the role of SSB in Theory versus Nature. To this end a detailed analysis is carried out and illustrated with three different physical models: Schr\"{o}dinger operators, mean-field quantum spin systems and the Bose-Hubbard model.Comment: 30 page