Related papers: Examples of Pseudo-bosons in quantum mechanics
We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different,…
Pseudo-Hermitian system is a class of non-Hermitian system with Hamiltonian satisfying the condition $\eta^{-1}H^\dagger\eta=H$. We develop the in-in and Schwinger Keldysh formalism to calculate cosmological correlators for pseudo-Hermitian…
In the context of two particularly interesting non-Hermitian models in quantum mechanics we explore the relationship between the original Hamiltonian H and its Hermitian counterpart h, obtained from H by a similarity transformation, as…
In this paper we consider squares of pseudo-bosonic ladder operators and we use them to produce explicit examples of eigenstates of certain operators satisfying a deformed $\mathfrak{su}(1,1)$ Lie algebra. We show how these eigenstates may,…
In a recent Letter, Gopalakrishnan, Martin, and Demler [Phys. Rev. Lett. 111 (2013) 185304] show that quasi-two-dimensional dipolar Bose gases, subject to a Rashba spin-orbit coupling, exhibit a variety of spatially ordered, or crystalline,…
We analyze the possible types of ordering in a boson--fermion model. The Hamiltonian is inherently related to the Bose--Hubbard model for vector two-species bosons in optical lattices. We show that such model can be reduced to the…
Para-particles are fascinating because they are neither bosons nor fermions. While unlikely to be found in nature, they might represent accurate descriptions of physical phenomena like topological phases of matter. We report the quantum…
In the study of bi-Hamiltonian systems (both classical and quantum) one starts with a given dynamics and looks for all alternative Hamiltonian descriptions it admits.In this paper we start with two compatible Hermitian structures (the…
Quantum Algebras (q-algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and…
We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of…
We study the 2010 specific version of the 2002 proposed $U(1)_X$ extension of the supersymmetric standard model, which has no $\mu$ term and conserves baryon number and lepton number separately and automatically. We consider in detail the…
The problems of the standard model are briefly reviewed and the motivations for introducing supersymmetry are discussed. Two realistic supersymmetric models; the Minimal SuperSymmetric Model, MSSM, and its proposed extension NMSSM are…
We advocate the sparsification of bosonic SYK models as a promising arena for the exploration of quantum advantage. We initiate the study of quantum simulations of the models, both in classical simulators and on quantum devices implemented…
We study a generalized scheme of Swanson Hamiltonian from a second-derivative pseudosupersymmetric approach. We discuss plausible choices of the underlying quasi-Hamiltonian and consider the viability of applications to systems like the…
We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy…
Various forms of the $q$-boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator. Both the one-component and the multicomponent $q$-bosons are discussed. As a byproduct, we obtain a new…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
We study the role of fermionic resonances in realistic composite Higgs models. We consider the low energy effective description of a model in which the Higgs arises as the pseudo-Goldstone boson of an SO(5)/SO(4) global symmetry breaking…
Quantum computing has recently been emerging in theoretical chemistry as a realistic avenue meant to offer computational speedup to challenging eigenproblems in the context of strongly-correlated molecular systems or extended materials.…
We demonstrate that not all generalized Bogoliubov transformations lead to $\cal D$-pseudo-bosons and prove that a correspondence between the two can only be achieved with the imposition of specific constraints on the parameters defining…