Related papers: Quantitative recurrence properties for systems wit…
In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains…
We construct renormalised models of regularity structures by using a recursive formulation for the structure group and for the renormalisation group. This construction covers all the examples of singular SPDEs which have been treated so far…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…
We study chain-recurrence and chain-transitivity in compact dynamical systems without any regularity assumptions on the map. We prove that every compact system has a chain-recurrent point and a closed, invariant, chain-transitive subsystem.…
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…
In principle, all the natural systems such as biological, ecological and economical systems are structure-variable systems (in which some environment parameters are not fixed). In this Letter we show that data sequences from many…
If a quantum experiment includes random processes, then the results of repeated measurements can appear consistent with irreversible decoherence even if the system's evolution prior to measurement was reversible and unitary. Two thought…
Type qualifiers offer a lightweight mechanism for enriching existing type systems to enforce additional, desirable, program invariants. They do so by offering a restricted but effective form of subtyping. While the theory of type qualifiers…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of…
Quantum non-demolition measurements facilitate various quantum technologies, including quantum communication. Notably, their operational structure can be replicated by a classical model--referred to as a noncontextual model--making it…
This paper is devoted to a study of the multiple recurrence of two commuting transformations. We derive a result which is similar but not identical to that of one single transformation established by Bergelson, Host and Kra. We will use the…
For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…
We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on $\ell^p(\mathbb Z)$, $p\geq 1$. Our method uses properties of the difference set of a set with positive upper…
We explore the relationship between subgroups and the possible shifts of finite type (SFTs) that can be defined on the group. In particular, we investigate two group invariants, weak periodicity and strong periodicity, defined via symbolic…
Massive vector fields can be described in a gauge invariant way with the introduction of compensating fields. In the unitary gauge one recovers the original formulation. Although this gauging mechanism can be extended to noncommutative…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras.…
It has been claimed that decoherence of open quantum systems explains the tendency of macroscopic systems to exhibit quasiclassical behavior. We show that quasiclassicality is in fact an unremarkable property, characterizing generic…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…