Entanglement in fermionic chains and bispectrality

Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a tridiagonal matrix commuting with the entanglement Hamiltonian can be found using the algebraic Heun operator construct in instances when there is an underlying bispectral problem. Cases corresponding to the Lie algebras [Formula: see text] and [Formula: see text] as well as to the q-deformed algebra [Formula: see text] at [Formula: see text] a root of unity are presented.

L∞ - derivations and the argument shift method for deformation quantization algebras

The argument shift method is a well-known method for generating commutative families of functions in Poisson algebras from central elements and a vector field, verifying a special condition with respect to the Poisson bracket. In this notice we give an analogous construction, which gives one a way to create commutative subalgebras of a deformed algebra from its center (which is as it is well known describable in the terms of the center of the Poisson algebra) and an L∞-differentiation of the algebra of Hochschild cochains, verifying some additional conditions with respect to the Poisson structure.

Generalized deformed SU(2) algebras in Nuclear Physics

A generalized deformed algebra SUφ(2), characterized by a structure function Φ. is obtained. The usual SU(2) and SUq(2) algebras correspond to specific choices of the structure function Φ. The action of the generators of the algebra on the relevant basis vectors, as well as the eigenvalues of the Casimir operator, are easily obtained. Possible applications in improving phenomenological nuclear models are discussed.

Parafermion theory from the q-deformed algebra with q a root of unity

In this paper, we find the [Formula: see text]-deformed algebra with the finite- and infinite-dimensional Fock space and both the fermionic limit and the bosonic limit. Using the cardinality of set theory, we propose the Hamiltonian interpolating bosonic case and fermionic case, which enables us to construct the proper partition function and internal energy. As examples, we discuss the specific heat of free [Formula: see text] parafermion gas model and [Formula: see text] parafermion star.

(1+1)-dimensional Dirac oscillator with deformed algebra with minimal uncertainty in position and maximal in momentum

[Formula: see text]-dimensional Dirac oscillator with minimal uncertainty in position and maximal in momentum is investigated. To obtain energy spectrum, SUSY QM technique is applied. It is shown that the Dirac oscillator has two branches of spectrum, the first one gives the standard spectrum of the Dirac oscillator when the parameter of deformation goes to zero and the second branch does not have nondeformed limit. Maximal momentum brings an upper bound for the energy and it gives rise to the conclusion that the energy spectrum contains a finite number of eigenvalues. We also calculate partition function for the spectrum of the first type. The partition function allows us to derive thermodynamic functions of the oscillator which are obtained numerically.

Statistical Entropy of Quantum Black Holes in the Presence of Quantum Gravity Effects

We investigate the effects of deformed algebra, admitted from minimal length, on canonical description of quantum black holes. Using the modified partition function in the presence of all orders of the Planck length, we calculate the thermodynamical properties of quantum black holes. Moreover, after obtaining some thermodynamical quantities including internal energy, entropy, and heat capacity, we conclude that, at high temperature limits due to the decreasing of the number of microstates, the entropy tends to upper bounds.

Radiation of quantum black holes and modified uncertainty relation

In this paper, using a deformed algebra [Formula: see text] which is originated from various theories of gravity, we study thermodynamical properties of quantum black holes (BHs) in canonical ensembles. We exactly calculate the modified internal energy, entropy and heat capacity. Moreover, we investigate a tunneling mechanism of massless particle in phase space. In this regard, the tunneling radiation of BH receives new corrections and the exact radiant spectrum is no longer precisely thermal. In addition, we show that our results are compatible with other quantum gravity (QG) approaches.

Snyder-like modified gravity in Newton's spacetime

This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder-like deformation in the background of the Kepler problem. In order to accomplish that task, a Newtonian spacetime is used. Newtonian spacetime is not a metric manifold, but allows to introduce a torsion-free connection in order to interpret the dynamic equations of the deformed Kepler problem as geodesics in a curved spacetime. These geodesics and the curvature terms of the Riemann and Ricci tensors show a mass and a fundamental length dependence as expected, but are velocity-independent that is a feature present in other classical approaches to the problem. In this sense, the effect of introducing a deformed algebra is examined and the corresponding curvature terms calculated, as well as the modifications of the integrals of motion.