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arXiv:nucl-th/0011047

Macroconstraints from Microsymmetries of Macrosystems

L. Turko, Johann Rafelski A

Published Nov 13, 2000• 2 citations
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Abstract

The dynamics governing the evolution of a many body system is constrained by a nonabelian local symmetry. We obtain a general form of the global macroscopic conditions assuring that at the microscopic level the evolution respects the overall symmetry constraint. These conditions does not depend on detailed dynamics of the system. It is shown that a nonabelian internal symmetry leads to the new subsidiary condition imposed on the system. A structure of constraints is analysed.

DOI
10.48550/arxiv.nucl-th/0011047

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The dynamics governing the evolution of a many body system is constrained by a nonabelian local symmetry. We obtain a general form of the global macroscopic conditions assuring that at the microscopic level the evolution respects the overall symmetry constraint. These conditions does not depend on detailed dynamics of the system. It is shown that a nonabelian internal symmetry leads to the new subsidiary condition imposed on the system. A structure of constraints is analysed.
Deterministic microscopic laws constrain physical systems through conservation laws and boundary conditions, yet macroscopic evolution routinely exhibits irreversible collapse, destruction, and path dependence. We analyze deterministic classical and quantum systems admitting multiple metastable macroscopic trajectories under fixed global constraints and show that deterministic dynamics generally underdetermine macroscopic history. We introduce a distinction between constraint-defined macroscopic equivalence classes, fixed by invariant quantities, and metastable macroscopic trajectories, defined by dynamical stability. Using stability and basin-of-attraction arguments, we characterize collapse as a deterministic loss of metastability in which an entire macroscopic trajectory becomes dynamically inaccessible without violation of microscopic reversibility or conservation laws. Irreversible destruction corresponds to elimination of physically realizable paths rather than loss of information or coarse-grained inaccessibility. We show that explanations based solely on coarse-graining or decoherence are insufficient to account for such trajectory elimination, as they preserve admissibility of erased histories. In contrast, instability-driven trajectory destruction constitutes an ontic dynamical process, directly realized in many-body and condensed matter systems. The framework provides a unified account of irreversible macroscopic change and causal differentiation within deterministic dynamics, without invoking stochasticity, modified laws, or observer-dependent mechanisms. Deterministic laws constrain admissible macroscopic states, while instability and metastability govern the physically realizable histories connecting them.
We derive general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries, and show that MBL is not possible with symmetry groups that protect multiplets (e.g., all non-Abelian symmetry groups). Based on simple representation theoretic considerations, we derive general Mermin-Wagner--type principles governing the possible alternative fates of nonequilibrium dynamics in isolated, strongly disordered quantum systems. Our results rule out the existence of MBL symmetry-protected topological phases with non-Abelian symmetry groups, as well as time-reversal symmetry-protected electronic topological insulators, and in fact all fermion topological insulators and superconductors in the 10-fold way classification. Moreover, extending our arguments to systems with intrinsic topological order, we rule out MBL phases with non-Abelian anyons as well as certain classes of symmetry-enriched topological orders.
Symmetry principles have played a crucial role in the development of modern physics and underpin our most fundamental theories of nature. The present thesis is concerned with the analysis of symmetries in the context of quantum information theory. Whenever a quantum mechanical system interacts with its environment it is subjected to decoherence, a process that is typically irreversible and most generally treated abstractly using the concept of quantum operations. If there is an underlying symmetry principle, additional structures emerge. The central question we address is, What are the consequences of global or local gauge symmetry on the structure of many-body quantum processes?This leads us to a diagrammatic framework of decomposing quantum operations into terms that respond to the symmetry principle in particular ways and respect the causal structures involved. We present two core applications. First, we address the interplay between irreversibility and repeatable use of coherent resources under symmetry constraints. Second, we give an information-theoretic perspective on gauging globally symmetric dynamics to a local symmetry applicable even in the presence of irreversibility and thus it goes beyond the usual Lagrangian formulation. Finally, we analyse the departure from conservation laws under symmetric dynamics subject to decoherence.
In a recent article, Alli and Sewell [J. Math. Phys. 36, 5598 (1995)] formulated a new version of the Dicke–Hepp–Lieb laser model in terms of quantum dynamical semigroups, and thereby extended the macroscopic picture of the model. In the present article, we complement that picture with a corresponding microscopic one, which carries the following new results. (a) The local microscopic dynamics of the model is piloted by the classical, macroscopic field, generated by the collective action of its components; (b) the global state of the system carries no correlations between its constituent atoms after transient effects have died out; and (c) in the latter situation, the state of the system at any time t maximizes its entropy density, subject to the constraints imposed by the instantaneous values of its macroscopic variables.