Related papers: Understanding Permutation Symmetry
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…
The statistics of gap ratios between consecutive energy levels is a widely used tool, in particular in the context of many-body physics, to distinguish between chaotic and integrable systems, described respectively by Gaussian ensembles of…
Poisson boundary is a measurable $\Gamma$-space canonically associated with a group $\Gamma$ and a probability measure $\mu$ on it. The collection of all measurable $\Gamma$-equivariant quotients, known as $\mu$-boundaries, of the Poisson…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…
We discuss the the notion of a partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by only a subset of solvable eigenstates, while other eigenstates are strongly mixed. We present an explicit construction of…
We study quantum many-body states of immanons, hypothetical particles that obey an exchange symmetry defined for more than two participating particles. Immanons thereby generalize bosons and fermions, which are defined by their behavior…
Quasi-set theory provides a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the quantum statistics into the scope of quasi-set theory and discuss the…
Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry…
The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from…
Quantum coherence is an exquisitely quantum phenomenon that depends on both probability amplitudes and relative phases. Standard coherence measures quantify superposition within density matrices but cannot distinguish ensembles that produce…
Permutation invariant polynomial functions of matrices have previously been studied as the observables in matrix models invariant under $S_N$, the symmetric group of all permutations of $N$ objects. In this paper, the permutation invariant…
It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons, with the exception of anyons in two dimension. In principle, a second exception known as parastatistics, which…
We investigate the phenomenon of disorder-free localisation in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permutation symmetric many-fermion Hamiltonians and interpret them…
We show that for fermion states, measurements of any two finite outcome particle quantum numbers (e.g.\ spin) are not constrained by a minimum total uncertainty. We begin by defining uncertainties in terms of the outputs of a measurement…
Distinguishability plays a major role in quantum and statistical physics. When particles are identical their wave function must be either symmetric or antisymmetric under permutations and the number of microscopic states, which determines…
In quantum theory, particles in three spatial dimensions come in two different types: bosons or fermions, which exhibit sharply contrasting behaviours due to their different exchange statistics. Could more general forms of probabilistic…
We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial…
The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that \emph{quantum particles} of the same kind (e.g., electrons) are all in exactly the same state and therefore…