Related papers: Sub-bosonic (deformed) ladder operators

Sub-bosonic (deformed) ladder operators

URL: http://arxiv.org/abs/2009.06392v2
Date: Wed, 23 Jun 2021 15:55:08 GMT
Title: Sub-bosonic (deformed) ladder operators
Authors: J. Damastor Serafim, Ricardo Ximenes, and Fernando Parisio
Abstract summary: We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
Score: 62.997667081978825
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The canonical operator $\hat{a}^{\dagger}$ ($\hat{a}$) represents the ideal process of adding (subtracting) an {\it exact} amount of energy $E$ to (from) a physical system in both elementary quantum mechanics and quantum field theory. This is a ``sharp'' notion in the sense that no variability around $E$ is possible at the operator level. In this work, we present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.

Related papers

Features, paradoxes and amendments of perturbative non-Hermitian quantum mechanics [0.0]
Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. In our paper it is shown that all of these three obstacles can be circumvented via just a mild amendment of the Rayleigh-Schr"odinger perturbation-expansion approach.
arXiv Detail & Related papers (2024-05-03T12:08:25Z)
The $\mathfrak S_k$-circular limit of random tensor flattenings [1.2891210250935143]
We show the convergence toward an operator-valued circular system with amalgamation on permutation group algebras. As an application we describe the law of large random density matrix of bosonic quantum states.
arXiv Detail & Related papers (2023-07-21T08:59:33Z)
Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
arXiv Detail & Related papers (2023-05-22T11:00:25Z)
Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
arXiv Detail & Related papers (2023-02-03T19:17:37Z)
Quantum teleportation in the commuting operator framework [63.69764116066747]
We present unbiased teleportation schemes for relative commutants $N'cap M$ of a large class of finite-index inclusions $Nsubseteq M$ of tracial von Neumann algebras. We show that any tight teleportation scheme for $N$ necessarily arises from an orthonormal unitary Pimsner-Popa basis of $M_n(mathbbC)$ over $N'$.
arXiv Detail & Related papers (2022-08-02T00:20:46Z)
An Introduction to Scattering Theory [0.0]
Part A defines the theoretical playground, and develops basic concepts of scattering theory in the time domain. Part B is then to build up, in a step-by-step fashion, the time independent scattering theory in energy domain. Part C elaborates the nonhermitian scattering theory (Siegert pseudostate formalism)
arXiv Detail & Related papers (2022-04-08T11:41:24Z)
The classical limit of Schr\"{o}dinger operators in the framework of Berezin quantization and spontaneous symmetry breaking as emergent phenomenon [0.0]
A strict deformation quantization is analysed on the classical phase space $bR2n$. The existence of this classical limit is in particular proved for ground states of a wide class of Schr"odinger operators. The support of the classical state is included in certain orbits in $bR2n$ depending on the symmetry of the potential.
arXiv Detail & Related papers (2021-03-22T14:55:57Z)
Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
arXiv Detail & Related papers (2020-10-13T15:50:49Z)
Are quantum spins but small perturbations of ontological Ising spins? [0.0]
The dynamics-from-permutations of classical Ising spins is generalized here for an arbitrarily long chain. We deduce the corresponding Hamiltonian operator and show that it generates an exact terminating Baker-Campbell-Hausdorff formula. It is striking that (in principle arbitrarily) small deformations of the model turn it into a genuine quantum theory.
arXiv Detail & Related papers (2020-08-04T17:52:25Z)
Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.