Search results for "Quantum Mechanics"
showing 10 items of 2468 documents
Magnetic exchange between metal ions with unquenched orbital angular momenta: basic concepts and relevance to molecular magnetism
2010
This review article is a first attempt to give a systematic and comprehensive description (in the framework of the unified theoretical approach) of the exchange interactions in polynuclear systems based on orbitally degenerate metal ions in the context of their relevance to the modern molecular magnetism. Interest in these systems is related to the fundamental problems of magnetism and at the same time steered by a number of impressive potential applications of molecular magnets, like high-density memory storage units, nanoscale qubits, spintronics and photoswitchable devices. In the presence of orbital degeneracy, the conventional spin Hamiltonian (Heisenberg–Dirac–van Vleck model) becomes…
Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule
2016
We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of $\Phi$-derivability for the self-energy $\Sigma$ to a larger class of diagrammatic terms in which only some of the Green's function lines contain the fully dressed Green's function $G$. We call the corresponding approximations for $\Sigma$ partially $\Phi$-derivable. A special subclass of such approximations, which are gauge-invariant, is obtained by dressing loops in the diagrammatic expansion of $\Phi$ consistently with $G$. These approximations are number conserving but do not have to fulfill other conservation laws, such…
Anharmonicity deformation and curvature in supersymmetric potentials
1994
An algebraic description of the class of 1D supersymmetric shape invariant potentials is investigated in terms of the shape-invariant-potential (SIP) deformed algebra, the generators of which act both on the dynamical variable and on the parameters of the potentials. The phase space geometry associated with SIP's is studied by means of a coherent state (SIP-CS) path integral and the ray metric of the SIP-CS manifold. The anharmonicity of SIP's results in a inhomogeneous phase space manifold with one Killing vector and with a modified symplectic Kahler structure, and it induces a non constant curvature into the generalized phase space. Analogous results from the phase space geometry of someq…
A new mathematical tool for an exact treatment of open quantum system dynamics
2005
A new method to obtain an operatorial exact solution of a wide class of Markovian master equations is presented. Its key point is the existence of a constant of motion partitioning the Hilbert space into finite-dimensional subspaces. The consequent possibility of representing the reduced density operator as a block diagonal matrix is shown. Each “block operator” evolves under the action of a non-unitary operator explicitly derived. Our mathematical approach is illustrated applying it to simple physical systems.
Three periodic solutions for perturbed second order Hamiltonian systems
2009
AbstractIn this paper we study the existence of three distinct solutions for the following problem−u¨+A(t)u=∇F(t,u)+λ∇G(t,u)a.e. in [0,T],u(T)−u(0)=u˙(T)−u˙(0)=0, where λ∈R, T is a real positive number, A:[0,T]→RN×N is a continuous map from the interval [0,T] to the set of N-order symmetric matrices. We propose sufficient conditions only on the potential F. More precisely, we assume that G satisfies only a usual growth condition which allows us to use a variational approach.
Fractional calculus in solid mechanics: local versus non-local approach
2009
Several enriched continuum mechanics theories have been proposed by the scientific community in order to develop models capable of describing microstructural effects. The aim of the present paper is to revisit and compare two of these models, whose common denominator is the use of fractional calculus operators. The former was proposed to investigate damage in materials exhibiting a fractal-like microstructure. It makes use of the local fractional derivative, which turns out to be a powerful tool to describe irregular patterns such as strain localization in heterogeneous materials. On the other hand, the latter is a non-local approach that models long-range interactions between particles by …
Revealing non-classical behaviours in the oscillatory motion of a trapped ion
2003
The possibility of revealing non-classical behaviours in the dynamics of a trapped ion via measurements of the mean value of suitable operators is reported. In particular we focus on the manifestation known as `` Parity Effect\rq\rq which may be observed \emph{directly measuring} the expectation value of an appropriate correlation operator. The experimental feasibility of our proposal is discussed.
Exact Coulomb cutoff technique for supercell calculations in two dimensions
2009
We present a reciprocal space technique for the calculation of the Coulomb integral in two dimensions in systems with reduced periodicity, i.e., finite systems, or systems that are periodic only in one dimension. The technique consists in cutting off the long-range part of the interaction by modifying the expression for the Coulomb operator in reciprocal space. The physical result amounts in an effective screening of the spurious interactions originated by the presence of ghost periodic replicas of the system. This work extends a previous report [C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006)], where three-dimensional systems were considered. We show that the use of the cutoffs dramatic…
Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory
2006
To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning's hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to impro…
Perturbative calculation of spin-orbit splittings using the equation-of-motion ionization-potential coupled-cluster ansatz.
2008
Spin-orbit splittings for (2)Pi states are calculated within coupled-cluster (CC) theory via first-order degenerate perturbation theory. Using the equation-of-motion CC variant for ionization potentials (EOMIP-CC), the two components of the considered (2)Pi state are treated in a balanced way by generating both radical states via annihilation of one electron out of the CC wave function of the corresponding anion. We report on the implementation of the described approach within the CC singles and doubles approximation. To ensure computational efficiency, an atomic mean-field approximation for the spin-orbit integrals is used, resulting in a formulation in terms of one-electron transition-den…