Search results for "Harmonic oscillator"
showing 10 items of 109 documents
Laser control in open molecular systems: STIRAP and Optimal Control
2007
We examine the effect of dissipation on the laser control of a process that transforms a state into a superposed state. We consider a two-dimensional double well of a single potential energy surface. In the context of reactivity, the objective of the control is the localization in a given well, for instance the creation of an enantiomeric form whereas for quantum gates, this control corresponds to one of the transformation of the Hadamard gate. The environment is either modelled by coupling few harmonic oscillators (up to five) to the system or by an effective interaction with an Ohmic bath. In the discrete case, dynamics is carried out exactly by using the coupled harmonic adiabatic channe…
On stability of linear dynamic systems with hysteresis feedback
2020
The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure's problem) can be proved by the well-known circle criterion, the multivalued rate-independent hysteresis poses significant challenges for feedback systems, especially for proof of convergence to an equilibrium state correspondingly set. The dissipative behavior of clockwise input-output hysteresis is considered with two boundary cases of energy losses at reversal cycles. For upper boundary cases of maximal (parallelogram shape) hysteresis loop, an equivalent transformation of the closed-loop system is provided. This allows for the appli…
Magic triangular and tetrahedral clusters
1997
Using the methods of density functional theory and the jellium model we show that clusters with triangular [in two dimensions (2D)] or tetrahedral [in three dimensions (3D)] shapes have a strong shell structure and enhanced stability. Moreover, the shell closings correspond to the lowest magic numbers of a 2D and 3D harmonic oscillator and at the same time to the number of divalent atoms in close-packed triangles and tetrahedrons. Ab initio molecular dynamics simulations for Na and Mg clusters support the results of the jellium model.
Geometric factors in the adiabatic evolution of classical systems
1992
Abstract The adiabatic evolution of the classical time-dependent generalized harmonic oscillator in one dimension is analyzed in detail. In particular, we define the adiabatic approximation, obtain a new derivation of Hannay's angle requiring no averaging principle and point out the existence of a geometric factor accompanying changes in the adiabatic invariant.
Solution of the Skyrme-Hartree–Fock–Bogolyubovequations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): A new version of …
2017
We describe the new version (v2.73y) of the code HFODD which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb ene…
On Functions of Integrable Mean Oscillation
2005
Given we denote by the modulus of mean oscillation given by where is an arc of , stands for the normalized length of , and . Similarly we denote by the modulus of harmonic oscillation given by where and stand for the Poisson kernel and the Poisson integral of respectively. It is shown that, for each , there exists such that
Driven Brownian particle as a paradigm for a nonequilibrium heat bath: Effective temperature and cyclic work extraction
2017
We apply the concept of a frequency-dependent effective temperature based on the fluctuation-dissipation ratio to a driven Brownian particle in a nonequilibrium steady state. Using this system as a thermostat for a weakly coupled harmonic oscillator, the oscillator thermalizes according to a canonical distribution at the respective effective temperature across the entire frequency spectrum. By turning the oscillator from a passive "thermometer" into a heat engine, we realize the cyclic extraction of work from a single thermal reservoir, which is feasible only due to its nonequilibrium nature.
Substituent effect of nitro group on aromaticity of carbazole rings
2014
The molecular geometries of carbazole and its 17 nitro derivatives were optimized at the B3LYP/6-311++G(2d,2p) level of theory. The harmonic oscillator model of aromaticity and nucleus-independent chemical shift descriptors of π-electron delocalization were calculated to estimate the aromaticity of the carbazole five- and six-membered rings. The biggest changes in the value of both descriptors were observed for the pyrrole ring. The nitro group attached to 3 and/or 6 positions of the carbazole ring system exerts only a slight influence on the benzene ring aromaticity.
9-Methyl-3-phenyldiazenyl-9H-carbazole: X-ray and DFT-calculated structures
2006
The title compound, C19H15N3, was prepared by condensation of 3-nitrosocarbazole and aniline with subsequent methylation. The structure is built up of stacks of almost planar molecules. Density functional theory (DFT) calculations predict a completely planar conformation, different from that observed in the crystal lattice. HOMA (harmonic oscillator model of aromaticity) indices, calculated for three aromatic rings, demonstrate the small influence of the azo substituent on π electrons in the carbazole system.
Modeling of the Low-Frequency Noise in Thermal Lens Spectrometry
1998
The low-frequency noise observed in thermal lens spectrometry (TLS) can be modeled by assuming that the heated region, constituted by the thermal lens gradient and associated convective stream, behaves as a weakly damped harmonic oscillator with a natural frequency, vo, which is forced to move at an externally imposed pump frequency, vp. Out-of-phase lower-frequency oscillations of the TLS signal can be produced both by transient events, such as the beginning of the TLS experiment and small changes in the pump beam stability, and by drift of boundary conditions, such as the temperature of the surroundings. A model is developed and checked using 1-(2-pyridylazo)-2-napthol (PAN) solutions in …