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M. Grigorescu

Publications and source records attributed to M. Grigorescu.

At least 19 recordsLinked to original sources
arXiv2021

Mass distributions for the Kepler problem

The regularities in the structure of the planetary system, expressed by the Titius-Bode law, can be accounted also by using a more general formula, derived not by fit but from a logarithmic integrality constraint on the angular momentum (areolar velocity). This work presents the elementary adiabatic invariant used in constraint, the new formula, and applications to the orbit spacing, numbering and mass distributions for planets and the Jupiter satellites.

physics.class-ph↗
arXiv2021

Quantum Distributions for the Electromagnetic Field

The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields", and phase-space distributions of phonons and photons are obtained by Wigner transform. For photons in a thermal environment, the proposed Wigner function evolves towards the Planck equilibrium distribution. It is shown that the free electromagnetic field can also be found in states of definite helicity, described by a complex vector potential.

quant-ph↗
arXiv2018

Coherent Distributions and Quantization

This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that the main difference between classical and quantum behavior arises from the coherence properties of the phase-space distributions known as "action waves" and Wigner functions. The quantum wave functions appear as elementary degrees of freedom for the phase space granularity.

quant-ph↗
arXiv2015

Coherent distributions for the rigid rotator

Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions associated with the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite "zero point" energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schroedinger equation.

quant-ph↗
arXiv2011

Geometrical framework of quantization problem

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship between quantization and discretization of the configuration space is briefly discussed.

math-ph↗
arXiv2010

Electromagnetic 2-forms on space-time

Two field 2-forms on the space-time manifold, in a relationship of duality, are presented and included in the extended phase-space structure used to describe relativistic particles having both electric and magnetic charges. By exterior derivatives, these forms yield the two groups of Maxwell equations, while specific integrality conditions ensure magnetic monopole or electric charge quantization. Some properties of the common characteristic vector of the dual 2-forms are discussed. It is shown that the coupled energy-density continuity equation and the eikonal equation represent a classical, infinite-dimensional Hamiltonian system.

math-ph↗
arXiv2010

Symmetry and collective motion

This work presents the basic elements of the formalism involved in the treatment of Hamiltonian dynamical systems with symmetry and the geometrical description of collective motion.

math-ph↗
arXiv2009

Relativistic probability waves

A canonical structure compatible with the action of the Lorentz group can be obtained considering the energy and time as conjugate variables of an extended phase space. Scalar probability waves, describing free relativistic particles, are associated with functional coherent states for an extended Liouville equation. Relativistic action waves are provided by distributions localized in the momentum space, evolving according to the continuity and Hamilton-Jacobi equations. Presuming the existence of minimum space and time intervals, the action distributions take the form of relativistic Wigner functions. The nonrelativistic quantum dynamics is retrieved approximating the time distribution function by a Gaussian wave packet.

quant-ph↗
arXiv2009

Symplectic dynamics of the nuclear mean-field

Elements of a restricted variational approach to the nuclear mean-field dynamics, providing the microscopic structure of the low energy collective modes, are summarized. The results are illustrated for the isovector states produced by the proton-neutron interactions in deformed and superfluid nuclei.

nucl-th↗
arXiv2008

Structure effects of the two protons - two neutrons correlations

The proton-neutron 2 particles - 2 holes correlations in superfluid nuclei, described by an effective, Josephson-type interaction ~[(P+N-)+(P-N+)], are studied within a boson approximation. The strength of this interaction is estimated using the symmetry energy for an even-even system of nucleons lying on the same degenerate level. The RPA vacuum is obtained explicitly, and the electroexcitation to isovector monopole states of oscillatory pair exchange between the proton and neutron superfluids is briefly discussed.

nucl-th↗
arXiv2008

Classical probability waves

Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, specified by the probability density and the generating function of the Hamilton-Jacobi theory. It is shown that by introducing a minimum distance in the coordinate space, the action distributions aquire the energy dispersion specific to the quantum objects. At finite temperature, probability density waves propagating with the sound velocity are obtained as nonstationary solutions of the classical Fokker-Planck equation. The results suggest that in a system of quantum Brownian particles, a transition from complex to real probability waves could be observed.

quant-ph↗
arXiv2008

Coherent tunneling and quantum coherence oscillations at the atomic level

The evolution of the quantum wave packet describing an atom trapped in the surface-tip junction of the scanning tunneling microscope is investigated by using the time-dependent Schroedinger equation, and by a quasi-classical Hamiltonian approach. The estimates concern a Xe atom in a biased double-well junction potential. The exact treatment shows that quantum coherence oscillations of the metastable ground state may occur at particular resonant values of the bias voltage. The effect of decoherence by partial localization is studied within the quasi-classical frame.

quant-ph↗
arXiv2007

Variational Principle for Mixed Classical-Quantum Systems

An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical variables are expressed in the form of a quantum state vector which includes the action of the classical subsystem in its phase factor. It is shown that the statistical ensemble of Brownian state vectors for a quantum particle in a classical thermal environment can be described by a density matrix evolving according to a nonlinear quantum Fokker-Planck equation. Exact solutions of this equation are obtained for a two-level system in the limit of high temperatures, considering both stationary and nonstationary initial states. A treatment of the common time shared by the quantum system and its classical environment, as a collective variable rather than as a parameter, is presented in the Appendix.

quant-ph↗
arXiv2007

Constrained evolution in Hilbert space and requantization

The quantum dynamics generated by time-dependent variational calculations is discussed from the perspective of geometric quantization. On examples, it is shown that approximate energy eigenstates can be associated to the quantized periodic orbits.

math-ph↗
arXiv2006

Energy and time as conjugate dynamical variables

The energy and time variables of the elementary classical dynamical systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group on this space is canonical, but not Hamiltonian equivariant. Although it has no effect at classical level, the lack of equivariance makes the Galilei action inconsistent with the canonical quantization. A Hamiltonian equivariant action can be obtained by assuming that the inertial parameter in the extended phase-space is quasi-isotropic. This condition leads naturally to the Lorentz transformations between moving frames as a particular case of symplectic transformations. The limit speed appears as a constant factor relating the two additional canonical coordinates to the energy and time. Its value is identified with the speed of light by using the relationship between the electromagnetic potentials and the symplectic form of the extended phase-space.

math-ph↗
arXiv2005

Low-lying isovector monopole resonances

The mass difference between the even-even isobaric nuclei having the valence nucleons on the same degenerate level is attributed to a Josephson-type interaction between pairs of protons and pairs of neutrons. This interaction can be understood as an isospin symmetry-breaking mean field for a four-particle interaction separable in the two particles-two holes channel. The strength of this mean field is estimated within an o(5) algebraic model, by using the experimental value of the inertial parameter for the collective isorotation induced by the breaking of the isospin symmetry. In superfluid nuclei, the presumed interaction between the proton and neutron condensates leads to coupled oscillations of the BCS gauge angles, which should appear in the excitation spectrum as low-lying isovector monopole resonances.

nucl-th↗
arXiv2005

Decoherence and Dissipation in Quantum Two-State Systems

The Brownian dynamics of the density operator for a quantum system interacting with a classical heat bath is described using a stochastic, non-linear Liouville equation obtained from a variational principle. The environment's degrees of freedom are simulated by classical harmonic oscillators, while the dynamical variables of the quantum system are two non-hermitian "square root operators" defined by a Gauss-like decomposition of the density operator. The rate of the noise-induced transitions is expressed as a function of the environmental spectral density, and is discussed for the case of the white noise and blackbody radiation. The result is compared with the rate determined by a quantum environment, calculated by partial tracing in the whole Hilbert space. The time-dependence of the von Neumann entropy and of the dissipated energy is obtained numerically for a system of two quantum states. These are the ground and first excited state of the center of mass vibrations for an ion confined in a harmonic trap.

quant-ph↗