Related papers: Statistical mechanics model for Clifford random te…
We investigate the critical behavior of three-dimensional ferromagnetic CP(N-1) models, which are characterized by a global U(N) and a local U(1) symmetry. We perform numerical simulations of a lattice model for N=2, 3, and 4. For N=2 we…
We investigate the dynamics of two-dimensional quantum spin systems under the combined effect of random unitary gates and local projective measurements. When considering steady states, a measurement-induced transition occurs between two…
In Ref. [arXiv:1802.05554v3] one of the authors (N.S.M.B.) studies the second quantization of fermions with integer spin while describing the internal degrees of freedom of fermions in Grassmann space. In this contribution we study the…
Fifty years ago the standard model offered an elegant new step towards understanding elementary fermion and boson fields, making several assumptions, suggested by experiments. The assumptions are still waiting for an explanation. There are…
Control landscape phase transitions (CLPTs) occur as abrupt changes in the cost function landscape upon varying a control parameter, and can be revealed by non-analytic points in statistical order parameters. A prime example are quantum…
We define symmetry classes and commutation symmetries in the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites and investigate them by means of tools from the representation theory of symmetric groups S_N such as…
In this paper we establish $L^p$ boundedness properties for maximal operators, Littlewood-Paley functions and variation operators involving Poisson semigroups and resolvent operators associated with nonsymmetric Ornstein-Uhlenbeck…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
Quantum link models provide an extension of Wilson's lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson's parallel transporters,…
A group theoretical description of basic discrete symmetries (space inversion P, time reversal T and charge conjugation C) is given. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex…
We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-$\frac12$ particles. The class of correlations…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
With appropriate boundary conditions the anisotropic $XY$ chain in a magnetic field is known to be invariant under quantum group transformations. We generalize this model defining a class of integrable chains with several fermionic degrees…
By establishing Multiplicative Ergodic Theorem for commutative transformations on a separable infinite dimensional Hilbert space, in this paper, we investigate Pesin's entropy formula and SRB measures of a finitely generated random…
We consider perturbed discrete tight-binding models in $\ell^2(\mathbb{Z_h},\mathcal{G})$ describing union of quantum particles with localized interactions, where $\mathbb{Z_h}$ is the 1D lattice $h\mathbb{Z_h}$, $h > 0$, and $\mathcal G$…
We give an algebraic proof of the spin-statistics connection for the parabosonic and parafermionic quantum topological charges of a theory of local observables with a modular PCT-symmetry. The argument avoids the use of the spinor calculus…
Following on our previous work arXiv:2204.07593 and arXiv:2306.01043 studying the orbits of quantum states under Clifford circuits via `reachability graphs', we introduce `contracted graphs' whose vertices represent classes of quantum…
We study statistical process control (SPC) through charting of $p$-values. When in control (IC), any valid sequence $(P_{t})_{t}$ is super-uniform, a requirement that can hold in nonparametric and two-phase designs without parametric…
We investigate the dynamics of nonstabilizerness - also known as `magic' - in monitored quantum circuits composed of random Clifford unitaries and local projective measurements. For measurements in the computational basis, we derive an…
We study sparse domination for operators defined with respect to an atomic filtration on a space equipped with a general measure $\mu$. In the case of Haar shifts, $L^p$-boundedness is known to require a weak regularity condition, which we…