On the variational principle for the non-linear Schrödinger equation

While variation of the energy functional yields the Schrödinger equation in the usual, linear case, no such statement can be formulated in the general nonlinear situation when the Hamiltonian depends on its eigenvector. In this latter case, as we illustrate by sample numerical calculations, the points of the energy expectation value hypersurface where the eigenvalue equation is satisfied separate from those where the energy is stationary. We show that the variation of the energy at the eigensolution is determined by a generalized Hellmann–Feynman theorem. Functionals, other than the energy, can, however be constructed, that result the nonlinear Schrödinger equation upon setting their variation zero. The second centralized moment of the Hamiltonian is one example.

The Phase–Space Approach to time Evolution of Quantum States in Confined Systems: the Spectral Split–Operator Method

Using the phase space approach, we consider the quantum dynamics of a wave packet in an isolated confined system with three different potential energy profiles. We solve the Moyal equation of motion for the Wigner function with the highly efficient spectral split-operator method. The main aim of this study is to compare the accuracy of the employed algorithm through analysis of the total energy expectation value, in terms of deviation from its exact value. This comparison is performed for the second and fourth order factorizations of the time evolution operator.

A Service Cost-Base Supply Balance of Sustainable Power Generation

Recently, renewable power sources such as WTG and PV have become viable economic options for generating sustainable energy. However, WTG and PV have an inconstant power production problem. To solve this problem, multi-state models have been proposed. The electricity generated from these units varies with different time scales: hourly, daily and seasonally. Since planning an optimal size generates cost losses to the customer, three models should be built: a load model, generation model, and service cost model. Loss of energy expectation (LOEE) and loss of load expected (LOLE) are calculated for the load and generation model. The reliability value is calculated to determine the number of required renewable generators. As a result, the system is constructed to have sufficient capacity, and the utility cost became the main objective of the total service costs.

Energy Calculation for Excited Lithium Atom in Position Space

The energy expectation values for Li and Li-like ions ( , and ) have been calculated and examined within the ground state and the excited state in position space. The partitioning technique of Hartree-Fock (H-F) has been used for existing wave functions.

Potential Energy Expectation Value for Lithium Excited State (1s2s3s)

The purpose of the present work is to calculate the expectation value of potential energy for different spin states (??? ? ???,??? ? ???) and compared it with spin states (??? , ??? ) for lithium excited state (1s2s3s) and Li- like ions (Be+,B+2) using Hartree-Fock wave function by partitioning techanique .The result of inter particle expectation value shows linear behaviour with atomic number and for each atom and ion the shows the trend ??? < ??? < ??? < ???

An economic prediction of the finer resolution level wavelet coefficients in electronic structure calculations

A highly economic prediction method for fine resolution wavelet coefficients of wave functions and energy expectation values is presented.

Software en MATLAB para la Expansión de Generación Aplicando Criterios de Confiabilidad

El comportamiento de un S.E.P. varía aleatoriamente a través del tiempo por causa de varios factores, es aquí en donde el criterio de confiabilidad basado en un análisis probabilístico y estadístico es indispensable para modelar un sistema con el fin de garantizar el suministro y seguridad del mismo. El siguiente trabajo presenta una aplicación computacional que permite realizar el análisis de confiabilidad del sistemas de generación por medio de la obtención de índices tales como LOLE (loss of load expectation), LOEE (loss of energy expectation) principalmente; los cuales son comparados con la normativa adoptada por la NERC (NORTH AMERICAN ELECTRIC RELIABILITY CORPORATION) la cual establece que el margen de reserva de un sistema debe ser considerando un LOLE menor o igual a 0.1 día por año debido a los factores como la diversidad de carga y la disponibilidad de generación adicional para sostener las contingencias de baja probabilidad. Además el software permite estimar el costo esperado que representaría al país por la energía no suministrada, el cual podría ser considerado como un criterio secundario de decisión para la gestión y directrices que el país deba adoptar en las inversiones del Sistema de Generación durante la etapa de planeación y operación.

CORRELATION ENERGY AND ENTANGLEMENT GAP IN CONTINUOUS MODELS

Our goal is to clarify the relation between entanglement and correlation energy in a bipartite system with infinite dimensional Hilbert space. To this aim, we consider the completely solvable Moshinsky's model of two linearly coupled harmonic oscillators. Also, for small values of the couplings, the entanglement of the ground state is nonlinearly related to the correlation energy, involving logarithmic or algebraic corrections. Then, looking for witness observables of the entanglement, we show how to give a physical interpretation of the correlation energy. In particular, we have proven that there exists a set of separable states, continuously connected with the Hartree–Fock state, which may have a larger overlap with the exact ground state, but also a larger energy expectation value. In this sense, the correlation energy provides an entanglement gap, i.e. an energy scale, under which measurements performed on the 1-particle harmonic sub-system can discriminate the ground state from any other separated state of the system. However, in order to verify the generality of the procedure, we have compared the energy distribution cumulants for the 1-particle harmonic sub-system of the Moshinsky's model with the case of a coupling with a damping Ohmic bath at 0 temperature.

Quantum Energy Expectation in Periodic Time-Dependent Hamiltonians via Green Functions

LetUFbe the Floquet operator of a time periodic HamiltonianH(t). For each positive and discrete observableA(which we call aprobe energy), we derive a formula for the Laplace time average of its expectation value up to timeTin terms of its eigenvalues and Green functions at the circle of radiuse1/T. Some simple applications are provided which support its usefulness.