Related papers: Telling compositeness at a distance with outer aut…
We study a framework in which fields are labeled by basis elements of a fusion algebra with non-invertible fusion rules. In particular, we consider the case where fields are labeled by conjugacy classes of a finite group rather than its…
Using recent results in mathematics, I point out that free energies and scale-dependent central charges away from criticality can be represented in compact form where modular invariance is manifest. The main example is the near-critical…
In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups $\mathcal{U}$. We encode this large amount of data into a convenient abelian category $\mathcal{A}\mathcal{U}$…
Arthur classified the discrete automorphic representations of symplectic and orthogonal groups over a number field by that of the general linear groups. In this classification, those that are not from endoscopic lifting correspond to pairs…
Let $\Gamma$ be a hyperbolic group and G be the isometry group of a Gromov-hyperbolic, properand geodesic metric space. We study the action of the outer automorphism group Out($\Gamma$) onthe set X($\Gamma$,G) of conjugacy classes of…
Cosmological models that are locally consistent with general relativity and the standard model in which an object transported around the universe undergoes P, C and CP transformations, are constructed. This leads to generalization of the…
Let $1 \le r < n$ be integers. We give a proof that the group $\mathop{\mathrm{Aut}}({X_{n}^{\mathbb{N}}, \sigma_{n}})$ of automorphisms of the one-sided shift on $n$ letters embeds naturally as a subgroup $\mathcal{H}_{n}$ of the outer…
The jamming transition of non-spherical particles is fundamentally different from the spherical case. Non-spherical particles are hypostatic at their jamming points, while isostaticity is ensured in the case of the jamming of spherical…
In this paper we give a number of explicit constructions for II$_1$ factors and II$_1$ equivalence relations that have prescribed fundamental group and outer automorphism group. We construct factors and relations that have uncountable…
We study a bipartite collective spin-$1$ model with exchange interaction between the spins. The bipartite nature of the model manifests itself by the spins being divided into two equal-sized subsystems; within each subsystem the spin-spin…
Semiclassical systems being symmetric under Lie group are studied. A state of a semiclassical system may be viewed as a set (X,f) of a classical state X and a quantum state f in the external classical background X. Therefore, the set of all…
We provide theory, algorithms, and simulations of non-equilibrium quantum systems using a one-dimensional (1D) completely-positive (CP), matrix-product (MP) density-operator ($\rho$) representation. By generalizing the matrix product…
The motivations for the construction of an 8-component representation of fermion fields based on a two dimensional representation of time reversal transformation and CPT invariance are discussed. Some of the elementary properties of the…
We study properties of automorphisms of graph products of groups. We show that graph product $\Gamma\mathcal{G}$ has non-trivial pointwise inner automorphisms if and only if some vertex group corresponding to a central vertex has…
A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. Here, using the tools of resource theory of superposition, we give the conditions for a class of superposition…
We give a classification of gapped quantum phases of one-dimensional systems in the framework of Matrix Product States (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states, and both in…
We investigate quark flavor signals in three different supersymmetric models, the minimal supergravity, the SU(5) SUSY GUT with right handed neutrinos, and the minimal supersymmetric standard model with U(2) flavor symmetry, in order to…
We study flavour physics and CP violation in the context of low energy Supersymmetry with non-universal soft mass terms for sfermions. Large deviations from Standard Model predictions are allowed in B-physics, as shown in two explicit…
It is examined finite state automorphisms of regular rooted trees constructed to represent groups $GL(n,\mathbb{Z})$. The number of states of automorphisms that correspond to elementary matrices is computed. Using the representation of…
A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan $P$ function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify…