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Coupled Susy, pseudo-bosons and a deformed su(1, 1) Lie algebra

2021

Abstract In a recent paper a pair of operators a and b satisfying the equations a † a = bb † + γ 1 and aa † = b † b + δ 1 , has been considered, and their nature of ladder operators has been deduced and analyzed. Here, motivated by the spreading interest in non self-adjoint operators in quantum mechanics, we extend this situation to a set of four operators, c, d, r and s, satisfying dc = rs + γ 1 and cd = sr + δ 1 , and we show that they are also ladder operators. We show their connection with biorthogonal families of vectors and with the so-called D -pseudo bosons. Some examples are discussed.

Quantum correlations in generalized spin star system

2006

The problem of detecting quantum signatures in the correlations formed in dynamical evolution of quantum bipartite systems receives a lot of attention in current literature. Generally speaking, the occurrence of correlations between two observables of a system does not necessarily reflect nonclassical behaviour. In this paper, the exact dynamics of a pair of uncoupled spins 1/2 interacting with a common spin 1/2 bath is investigated. Starting from a separable initial condition, the ability of the system to develop purely quantum correlations is brought to light. Physical interpretation of the concurrence function as well as a suggestion on how to measure it are given.

Electron correlation in metal clusters, quantum dots and quantum rings

2009

This short review presents a few case studies of finite electron systems for which strong correlations play a dominant role. In simple metal clusters, the valence electrons determine stability and shape of the clusters. The ionic skeleton of alkali metals is soft, and cluster geometries are often solely determined by electron correlations. In quantum dots and rings, the electrons may be confined by an external electrostatic potential, formed by a gated heterostructure. In the low density limit, the electrons may form so-called Wigner molecules, for which the many-body quantum spectra reveal the classical vibration modes. High rotational states increase the tendency for the electrons to loca…

Spectrum emitted by a trapped electron

2007

We study the behaviour of a homonuclear molecule driven by an intense laser field. Newton's laws are used to describe the dynamics of nuclei while the quantal approach is reserved to the study of the electron. It is observed that the nuclei can oscillate or dissociate according to the degree of ionization of the molecule. In case of low ionization rate it is shown that great amount of information can be obtained by using the simplified approaches of fixed nuclei and of two-state approximation. Under suitable conditions the electron wave function spends a long time localized around one nucleus. The harmonic generation of the molecule is studied and seen to contain even harmonics.

Self-consistent Euclidean-random-matrix theory

2019

Slow-light solitons

2007

We investigate propagation of slow-light solitons in atomic media described by the nonlinear � -model. Under a physical assumption, appropriate to the slow light propagation, we reduce the � -scheme to a simplified nonlinear model, which is also relevant to 2D dilatonic gravity. Exact solutions describing various regimes of stopping slow-light solitons can then be readily derived.

Surface free energy of the open XXZ spin-1/2 chain

2012

We study the boundary free energy of the XXZ spin-$\tf{1}{2}$ chain subject to diagonal boundary fields. We first show that the representation for its finite Trotter number approximant obtained by Bortz, Frahm and G\"{o}hmann is related to the partition function of the six-vertex model with reflecting ends. Building on the Tsuchiya determinant representation for the latter quantity we are able to take the infinite Trotter number limit. This yields a representation for the surface free energy which involves the solution of the non-linear integral equation that governs the thermodynamics of the XXZ spin-1/2 chain subject to periodic boundary conditions. We show that this integral representati…

Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms

2013

We use the quantum separation of variable (SOV) method to construct the eigenstates of the open XXZ chain with the most general boundary terms. The eigenstates in the inhomogeneous case are constructed in terms of solutions of a system of quadratic equations. This SOV representation permits us to compute scalar products and can be used to calculate form factors and correlation functions.

Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables

2014

28 pages; International audience; We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to…

The distribution of velocities in an ensemble of accelerated particles on a surface

2016

An ensemble of particles diffusing with acceleration on a surface is considered as a 2D billiard system. The process of the finite-time diffusion of particles is studied using the balance equation. The probability distribution functions of the velocity and lifetime of particles are obtained analytically and by means of numerical simulations. A thermodynamic interpretation of the process is discussed. The effective temperature and entropy obey the relationship for an ideal gas.