Search results for "operators"
showing 10 items of 228 documents
Scalable and effective multi-level entangled photon states: a promising tool to boost quantum technologies
2021
Abstract Multi-level (qudit) entangled photon states are a key resource for both fundamental physics and advanced applied science, as they can significantly boost the capabilities of novel technologies such as quantum communications, cryptography, sensing, metrology, and computing. The benefits of using photons for advanced applications draw on their unique properties: photons can propagate over long distances while preserving state coherence, and they possess multiple degrees of freedom (such as time and frequency) that allow scalable access to higher dimensional state encoding, all while maintaining low platform footprint and complexity. In the context of out-of-lab use, photon generation…
An operator-like description of love affairs
2010
We adopt the so--called \emph{occupation number representation}, originally used in quantum mechanics and recently considered in the description of stock markets, in the analysis of the dynamics of love relations. We start with a simple model, involving two actors (Alice and Bob): in the linear case we obtain periodic dynamics, whereas in the nonlinear regime either periodic or quasiperiodic solutions are found. Then we extend the model to a love triangle involving Alice, Bob and a third actress, Carla. Interesting features appear, and in particular we find analytical conditions for the linear model of love triangle to have periodic or quasiperiodic solutions. Numerical solutions are exhibi…
A Phenomenological Operator Description of Dynamics of Crowds: Escape Strategies
2015
Abstract We adopt an operatorial method, based on creation, annihilation and number operators, to describe one or two populations mutually interacting and moving in a two-dimensional region. In particular, we discuss how the two populations, contained in a certain two-dimensional region with a non-trivial topology, react when some alarm occurs. We consider the cases of both low and high densities of the populations, and discuss what is changing as the strength of the interaction increases. We also analyze what happens when the region has either a single exit or two ways out.
Correlations between a Hawking particle and its partner in a 1+1D Bose-Einstein condensate analog black hole
2020
The Fourier transform of the density-density correlation function in a Bose-Einstein condensate (BEC) analog black hole is a useful tool to investigate correlations between the Hawking particles and their partners. It can be expressed in terms of $⟨{^{\mathrm{out}}\stackrel{^}{a}}_{\mathrm{up}}^{\mathrm{ext}}\text{ }\text{ }{^{\mathrm{out}}\stackrel{^}{a}}_{\mathrm{up}}^{\mathrm{int}}⟩$, where ${^{\mathrm{out}}\stackrel{^}{a}}_{\mathrm{up}}^{\mathrm{ext}}$ is the annihilation operator for the Hawking particle and ${^{\mathrm{out}}\stackrel{^}{a}}_{\mathrm{up}}^{\mathrm{int}}$ is the corresponding one for the partner. This basic quantity is calculated for three different models for the BEC f…
Occupation Number Representation
2007
The first two chapters of this book presented angular momentum algebra as the basic tool of nuclear theory. That includes angular momentum coupling coefficients, spherical tensor operators and reduced matrix elements. In the preceding chapter we introduced the mean-field concept, along with associated many-nucleon wave functions, Slater determinants, describing configurations of non-interacting particles in mean-field single-particle orbitals.
Spheroidal and hyperspheroidal coordinates in the adiabatic representation of scattering states for the Coulomb three-body problem
2009
Recently, an involved approach has been used by Abramov (2008 J. Phys. B: At. Mol. Opt. Phys. 41 175201) to introduce a separable adiabatic basis into the hyperradial adiabatic (HA) approximation. The aim was to combine the separability of the Born–Oppenheimer (BO) adiabatic basis and the better asymptotic properties of the HA approach. Generalizing these results we present here three more different separable bases of the same type by making use of a previously introduced adiabatic Hamiltonian expressed in hyperspheroidal coordinates (Matveenko 1983 Phys. Lett. B 129 11). In addition, we propose a robust procedure which accounts in a stepwise procedure for the unphysical couplings that are …
Dynamics of Confined Crowd Modelled Using Fermionic Operators
2014
An operatorial method based on fermionic operators is used to describe the dynamics of a crowd made of different kind of populations mutually interacting and moving in a two–dimensional bounded closed region. The densities of the populations are recovered through the Heisenberg equation and the diffusion process is driven by the Hamiltonian operator defined by requiring that the populations move along optimal paths. We apply the model obtained in a concrete situation and we discuss the effect of the interaction between the populations during their motion.
Existence results for a nonlinear nonautonomous transmission problem via domain perturbation
2021
In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$. First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$.
Ground-state properties of generalized Heisenberg chains with composite spin.
1988
We consider in detail the ground-state properties of recently introduced generalized Heisenberg models which can have several spin operators at each site and which interpolate smoothly between Heisenberg chains of different spin lengths. We show that the mappings to field-theoretical models used to describe the critical properties of the Heisenberg model remain valid in the composite-spin model. In models which interpolate between the spin-(1/2 and the spin-1 behavior, these mappings predict an extended singlet phase around the isotropic antiferromagnetic point whenever the models move away from the spin-(1/2 point. Numerical calculations on finite chains seem to confirm the existence of th…
Electromagnetic properties of some positive parity dipole states described in terms of quadrupole and octupole interacting bosons
1990
The first three positive parity dipole states predicted by a phenomenological quadrupole-octupole boson Hamiltonian are extensively studied. Their coupling to the neighboring positive and negative parity states, due to the {ital M}1 and {ital E}{lambda} ({lambda}=1,3) transitions, respectively, are considered. Special attention is paid to the lowest two states which are of collective {ital M}1 nature. The signature which distinguishes them from the {ital M}1 state describing the scissors mode is also discussed.