NOTAS DE FÍSICA

Detectores em Física de Altas Energias

Alberto Reis — 2025-08-11

Detectores em Física de Altas Energias.

Interação da radiação com a matéria

Alberto Reis — 2025-08-06

Interação da radiação com a matéria.

Braided QM and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework

Zhanna Kuznetsova — 2025-02-12

We introduce {\it color} Heisenberg-Lie (super)algebras graded by the abelian groups $\zthree^2$, $\ztwo^p\times\zthree^2$ for $p=1,2,3$, and investigate the properties of their associated multi-particle quantum
paraoscillators.\par In the Rittenberg-Wyler's color Lie (super)algebras framework the above abelian groups are the simplest ones which induce {\it mixed brackets} interpolating commutators and anticommutators. These mixed brackets allow to accommodate two types of parastatistics: one based on the permutation group (beyond bosons and fermions in any space dimension) and an anyonic parastatistics based on the braid group. In both such cases the two broad classes of paraparticles are given by parabosons and parafermions.\par Mixed-bracket parafermions are created by nilpotent operators; they satisfy a generalized Pauli exclusion principle leading to roots-of-unity truncations in their multi-particle energy spectrum (braided Majorana qubits and their Gentile-type parastatistics are recovered in this color Lie superalgebra setting). \par Mixed-bracket parabosons do not admit truncations of the spectrum; the minimal detectable signature of their parastatistics is encoded in the measurable probability density of two indistinguishable parabosonic oscillators in a given energy eigenstate.

As transformações de Galileu a partir das leis de Newton

Francisco Caruso — 2025-02-20

Mostra-se que as express\~{o}es matem\'{a}ticas das transforma\c{c}\~{o}es lineares de Galileu podem ser deduzidas a partir do pressuposto que tal transforma\c{c}\~{a}o exista e da imposi\c{c}\~{a}o do princ\'{\i}pio da invari\^{a}ncia de Galileu \`{a}s leis de Newton, sem necessariamente considerar as hip\'{o}teses de homogeneidade e isotropia do espa\c{c}o, e da homogeneidade do tempo.

Múons atmosféricos

Alberto Reis — 2025-08-07

Múons atmosféricos.

Integrable $\mathbb{Z}_2^2$-graded super-Liouville Equation and Induced $\mathbb{Z}_2^2$-graded super-Virasoro Algebra

Naruhiko Aizawa — 2025-12-23

We present a framework for enlarging the construction of $\Z2$-graded classical Toda theory from the class of $\Z2$-graded Lie algebras to the class of $\Z2$-graded Lie superalgebras. This scheme is applied to derive a $\Z2$-graded extension of the super-Liouville equation based on a $\Z2$-graded extension of $\osp(1|2).$ The mathematical tools employed in this work are a $\Z2$-graded version of the zero-curvature formalism and of the Polyakov's soldering procedure. It is demonstrated that both methods yield the same $\Z2$-graded super-Liouville equation. An algebraic construction of solutions to the resulting equations is also presented, together with their B\"acklund transformations. Furthermore, three distinct new $\Z2$-graded extensions of the super-Virasoro algebra are obtained via Hamiltonian reduction of the WZNW currents defined for $\Z2$-$\osp(1|2).$

Braided Majorana qubits as a minimal setting for Topological Quantum Computation?

Francesco Toppan — 2025-04-03

I point out that a possible minimal setting to realize Kitaev's proposal of a Topological Quantum Computation which offers topological protection from decoherence could in principle be realized by braided Majorana qubits.
Majorana qubits and their braiding were introduced in Nucl. Phys. B 980, 115834 (2022) and further analyzed in J. Phys. A: Math. Theor. 57, 435203 (2024). Braided Majorana qubits implement a Gentile-type parastatistics with at most $s-1$ excited states accommodated in a multiparticle sector (the integer $s=2,3,4,\ldots$ labels quantum group reps at roots of unity).
It is argued that braided Majorana qubits could play, for topological quantum computers, the same role as standard bits for ordinary computers and as qubits for ``ordinary" quantum computers.