Related papers: Dynamic symmetry approach to entanglement
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
In open quantum systems, entanglement can vanish faster than coherence. This phenomenon is usually called sudden death of entanglement. In this paper sudden death of entanglement is discussed from a geometrical point of view, in the context…
We focus on various dynamical invariants associated to toric correspondences, using algebraic geometry or arithmetic. We find a formula for the dynamical degrees, relate the exponential growth of the degree sequences with a strict…
Giving a new form of the vortex mode equation by a proper change of parameter, our aim is to analyze the point and contact symmetries of the new equation. Fundamental invariants and a form of general solutions of point transformations along…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector…
We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of…
We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising from our recent work: entanglement measures, for characterising…
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how…
These notes, based on lectures given at various schools over the last few years, aim to provide an introduction to entanglement entropies in quantum field theories, including holographic ones. We explore basic properties and simple examples…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
Recent developments in the study of shape-invariant Hamiltonians are briefly summarized. Relations between certain exactly solvable problems in many-body physics and shape-invariance are explored. Connection between Gaudin algebras and…
In this paper, we show that when two systems of differential equations admitting a symmetry group are related by a point transformation it is always possible to generate invariant schemes, one for each system, that are also related by the…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems and we introduce the notion of coefficient of quantum correlations. Our presentation stems from rigorous…
Finite group symmetry is commonplace in Physics, in particular through crystallographic groups occurring in condensed matter physics -- but also through the inversions (C,P,T and their combinations) occurring in high energy physics and…
The aim of this dissertation is to clarify the structure of entanglement, a type of quantum correlations, in various quantum systems with a large number of degrees of freedom for holography between generic quantum systems and spacetimes…