Search results for "Names"
showing 10 items of 6843 documents
Quantum graphs with mixed dynamics: the transport/diffusion case
2013
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly nonlocal couplings at the boundary. We provide sufficient conditions for these to be governed by a contractive semigroup on a Hilbert space naturally associated with the system. We show that our setting is also adequate to discuss specific systems of diffusion equations with boundary delays.
Cavity losses for the dissipative Jaynes–Cummings Hamiltonian beyond rotating wave approximation
2007
A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis [Scala M. {\em et al.} 2007 Phys. Rev. A {\bf 75}, 013811], where a microscopic derivation was given in the framework of the Rotating Wave Approximation.
Some results on the rotated infinitely deep potential and its coherent states
2021
The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is because the Swanson Hamiltonian is deeply connected with that of a standard quantum Harmonic oscillator, after a suitable rotation in configuration space is performed. In this paper we consider a rotated version of a different quantum system, the infinitely deep potential, and we consider some of the consequences of this rotation. In particular, we show that differences arise with respect to the Swanson model, mainly because of the technical need of working, he…
Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
2012
Parallels between the notions of nonlinear pseudobosons and of an apparent non-Hermiticity of observables as shown in paper I (arXiv: 1109.0605) are demonstrated to survive the transition to the quantum models based on the use of unbounded metric in the Hilbert space of states.
Frictional quantum decoherence
2007
The dynamics associated with a measurement-based master equation for quantum Brownian motion are investigated. A scheme for obtaining time evolution from general initial conditions is derived. This is applied to analyze dissipation and decoherence in the evolution of both a Gaussian and a Schr\"{o}dinger cat initial state. Dependence on the diffusive terms present in the master equation is discussed with reference to both the coordinate and momentum representations.
Non-Markovian dynamics of interacting qubit pair coupled to two independent bosonic baths
2009
The dynamics of two interacting spins coupled to separate bosonic baths is studied. An analytical solution in Born approximation for arbitrary spectral density functions of the bosonic environments is found. It is shown that in the non-Markovian cases concurrence "lives" longer or reaches greater values.
Self-organization in the A + B → 0 reaction of charged particles
1992
The formalism of many-particle densities developed earlier by the authors is applied to the study of the self-organization phenomena occuring during the course of the bimolecular A + B → 0 reaction between charged particles, interacting via the Coulomb law. Unlike the Debye-Huckel theory, charge screening has an essentially non-equilibrium character. It is shown that for the asymmetric mobility of reactants (DA = 0, DB ≠ 0) similar immobile reactants A form aggregates characterized by a sharp maximum, observed at short distances, in the joint correlation function XA(r, t). Such an aggregation leads to the accelerated particle recombination n ∝ t-54 (nA = nB = n) instead of the generally acc…
Time-dependent perturbation treatment of independent Raman schemes
2007
The problem of a trapped ion subjected to the action of two or more independent Raman schemes is analysed through a suitable time-dependent perturbative approach based on the factorization of the evolution operator in terms of other unitary operators. We show that the dynamics of the system may be traced back to an effective Hamiltonian up to a suitable dressing. Moreover, we give the method to write the master equation corresponding to the case wherein spontaneous decays occur.
Thermalization of Random Motion in Weakly Confining Potentials
2010
We show that in weakly confining conservative force fields, a subclass of diffusion-type (Smoluchowski) processes, admits a family of "heavy-tailed" non-Gaussian equilibrium probability density functions (pdfs), with none or a finite number of moments. These pdfs, in the standard Gibbs-Boltzmann form, can be also inferred directly from an extremum principle, set for Shannon entropy under a constraint that the mean value of the force potential has been a priori prescribed. That enforces the corresponding Lagrange multiplier to play the role of inverse temperature. Weak confining properties of the potentials are manifested in a thermodynamical peculiarity that thermal equilibria can be approa…
(H,ρ)-induced dynamics and large time behaviors
2018
Abstract In some recent papers, the so called ( H , ρ ) -induced dynamics of a system S whose time evolution is deduced adopting an operatorial approach, borrowed in part from quantum mechanics, has been introduced. Here, H is the Hamiltonian for S , while ρ is a certain rule applied periodically (or not) on S . The analysis carried on throughout this paper shows that, replacing the Heisenberg dynamics with the ( H , ρ ) -induced one, we obtain a simple, and somehow natural, way to prove that some relevant dynamical variables of S may converge, for large t , to certain asymptotic values. This cannot be so, for finite dimensional systems, if no rule is considered. In this case, in fact, any …