We study the Lindbladian dynamics of Sachdev-Ye-Kitaev (SYK) model, where SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in Majorana fermion operators. Here, non-random while sampled from a Gaussian distribution. In limit large $N$, $N$ number operators, and also $M$, $M$ Lindbladians analytically tractable, we obtain their stationary Green'...

In this article we define and exhibit “anticoherent” spin states, which are in a sense “the opposite” of the familiar coherent spin states. Since the familiar coherent states are as “classical” as spin states can be, the anticoherent states may turn out to be better candidates for applications involving non-classical behaviors such as quantum entanglement. Thanks to the Majorana representation ...

A new derivation of the quantum Boltzmann transport equation for the Fermion system from the quantum time evolution equation for the wigner distribution function is presented. The method exhibits the origin of the time - irreversibility of the Boltzmann equation. In the present work, the spin dependent and indistinguishibility of particles are also considered.

We show that long-ranged superconducting order is not necessary to guarantee the existence of Majorana fermion zero modes at the ends of a quantum wire. We formulate a concrete model, which applies, for instance, to a semiconducting quantum wire with strong spin-orbit coupling and Zeeman splitting coupled to a wire with algebraically decaying superconducting fluctuations. We solve this model by...

Nonzero neutrino masses imply the existence of degrees freedom and interactions beyond those in Standard Model. A powerful indicator what these might be is nature massive neutrinos: Dirac fermions versus Majorana fermions. While addressing neutrinos often associated with searches for lepton-number violation, there are several other features that distinguish from Here, we compute great detail ki...

We discuss a general, exact (in that matrix elements are preserved) mapping of fermion pairs to bosons, and find a simple factorization of the boson representation of fermion operators. This leads to boson Hamiltonians that are Hermitian and finite, with no more than two-body operators if the fermion Hamiltonian has at most two-body operators, and one-body boson transition operators if the ferm...

The irreducibility of a representation of a real Lie algebra may depend on whether the representation space is a real or complex Hilbert space. The unitary projective representations of the Poincare group on complex Hilbert spaces were studied by Wigner and many others. Although the Poincare group has a real Lie algebra, we do not know of any study of the orthogonal projective representations o...

The origin of neutrino mass is usually attributed to a seesaw mechanism, either through a heavy Majorana fermion singlet (version 1) or a heavy scalar triplet (version 2). Recently, the idea of using a heavy Majorana fermion triplet (version 3) has gained some attention. This is a review of the basic idea involved, its U(1) gauge extension, and some recent developments.