# Antonio B. NassarUniversity of California, Los Angeles | UCLA · Department of Science and Math

Antonio B. Nassar

PhD

## About

75

Publications

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Introduction

**Skills and Expertise**

## Publications

Publications (75)

In the last decades, many nonlinear extensions of the Schrödinger equation have been proposed in literature either to explore the fundamental aspects of quantum mechanics, with the usual linear theory representing only a limiting case, or to describe open quantum systems. For the description of nonconservative quantum systems, Kostin formulated in...

In this chapter, our purpose is to simply show that Bohmian mechanics is a powerful route to bring about new solutions to problems discussed by conventional quantum mechanical approaches, apart from allowing some striking correspondence between both frameworks. This goal is carried out by choosing some key quantum mechanical problems in the framewo...

Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, was originated in the 1920s by Louis de Broglie, re-discovered and developed in 1952 by David Bohm. No one more eloquently than John Bell has championed this theory in recent decades. Bell and Bernstein also...

Following a phenomenological approach for continuous measurement, a general theory for decoherence in the framework of restricted path integrals (RPI) has been proposed by Mensky. The corresponding propagator is modified according to the information provided by the measurement through the so-called quantum corridors, which correspond to different r...

This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much l...

The discovery of Berry and Balazs in 1979 that the free-particle
Schr\"odinger equation allows a non-dispersive and accelerating Airy-packet
solution has taken the folklore of quantum mechanics by surprise. Over the
years, this intriguing class of wave packets has sparked enormous theoretical
and experimental activities in related areas of optics a...

This Letter proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the dividing line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schrödinger equation is proposed to describe the time evolution of a quantum dissipative system under continuous measu...

The structure of time-dependent Gaussian solutions for the Kostin equation in
dissipative quantum mechanics is analyzed. Expanding the generic external
potential near the center of mass of the wave packet, one conclude that: the
center of mass follows the dynamics of a classical particle under the external
potential and a damping proportional to th...

In this paper we study the Feynman propagators for eight non-linear Schrödinger equations, linearized along a classical trajectory, by using the quantum mechanical formalism of the de Broglie-Bohm.

The study of harmonic scales of musical instruments is discussed in all
introductory physics texts devoted to the science of sound. In this paper, we
present a new piano keyboard to make the so-called Bohlen-Pierce scale more
functional and pleasing for composition and performance.

Unlike most of the research on the Mpemba effect which has focused on
verifying the observation that warm water freezes faster than cold water, our
work quantitatively investigates the rates at which hot and cold water cool and
the point at which hot water reaches a lower temperature than cold water under
a set of external conditions. Using a vacuu...

In this paper we study the quantum wave packet and the Feynman-de
Broglie_Bohm propagator of the linearized Sussmann_Hasse_Albrecht_Kostin_Nassar
equation along a classical trajetory

In this paper we study the quantum wave packet and the Feynman-de Broglie-Bohm propagator of the linearized Schuch-Chung-Hartmann equation along a classical trajetory. Comment: 13 pages

In this paper we study the quantum wave packet and the Feynman-de Broglie-Bohm Propagator of the Schrodinger-Nassar equation for an extended electron. Comment: 15 pages

A new quantum mechanical description of the dynamics of wave packet under continuous measurement is formulated via Bohmian mechanics. The solution to this equation is found through a wave packet approach which establishes a direct correlation between a classical variable with a quantum variable describing the dynamics of the center of mass and the...

In this paper we present the Feynman-de Broglie-Bohm propagator for a semiclassical formulation of the Gross-Pitaeviskii equation. Comment: 6 pages

Although static surface charges on circuit elements are of enormous interest, recent papers and textbooks have only discussed the problem theoretically using analytical or numerical approaches. The only well-known experimental method to visualize the structure of electric fields around circuit elements was reported by Jefimenko almost half a centur...

In this paper we study the quantum wave packet of the non-linear Gross-Pitaevskii equation. Comment: 9 pages

In this paper we study the quantum wave packet of the Schrodinger equation for continuous quantum measurements. Comment: 14 pages

In this work we study the Ramsauer-Townsend effect.First, we use the Quantum Mechanical Formalism of Schrodinger. After, it is calculated with the Quantum Mechanical Formalism of de Broglie-Bohm. In this case, we use the Kostin equation, taking into account the energy dissipation of the electrons scattered by sharp edged potential wells.

In this work we study the Ermakov-Lewis invariants of the non-linear Gross-Pitaeviskii equation

In this work we study the Ermakov-Lewis invariants of the Schrodinger equation continuous measurement.

This paper presents an alternative proposal to the teaching of physics applied to Amazon problems. It is based on the need of qualified personal to deal with quite different areas which form the engineering in this region. The plan takes into account fundamental aspects of the formation of a engineer with strong scientific basis. The organization o...

Resumo: O grande desafio enfrentado na região amazônica está hoje intimamente relacionado com as contínuas e profundas transformações sociais ocasionadas pela velocidade com que têm sido gerados novos conhecimentos científicos e tecnológicos. A Universidade Federal do Pará/UFPA enquanto agente de transformação, interligada com essas questões, procu...

This paper presents an alternative proposal to the teaching of physics applied to Amazon problems. It is based on the need of qualified personal to deal with quite different areas which form the engineering in this region. The plan takes into account fundamental aspects of the formation of a engineer with strong scientific basis. The organization o...

A new quantum mechanical wave equation describing the dynamics of an extended electron is derived via Bohmian mechanics. The
solution to this equation is found through a wave packet approach which establishes a direct correlation between a classical
variable with a quantum variable describing the dynamics of the center of mass and the width of the...

Via the hydrodynamical formulation of quantum mechanics, we propose new boundary conditions to the problem of tunneling through sharp-edged potential barriers with and without dissipation. Above all, these boundary conditions can be matched without assuming continuity of the wave function at a surface sigma where the potential undergoes a, finite j...

In this paper we calculate the magnetic suscetibility (chi) of Bateman-Caldirola-Kanai dissipative systems.

Although the use of fluorescent lamps has been increasing due to their
energy-saving advantages, discussions about them are rarely found in
introductory physics texts. Although most of the disadvantages of
fluorescent lamps have begun to be remedied, there still exist some
problems that need to be solved. Two of the problems involve buzz and
high-f...

We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developped formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities.

We find a condition on the parameter controlling the strength of the nonlinearity of a nonlinear Schrödinger equation which grants the possibility of nonspreading Gaussian wave packet solutions for an inverted parabolic potential. Our analysis is performed using the de Broglie-Bohm formalism.

New generalized squeezed states for the time-dependent harmonic
oscillator are found through the theory of invariants. Our method gives
a comparatively clearer picture than methods using evolution operators
because we can establish a direct connection between the classical and
quantum solutions. The additional significance of our method is that it...

In this paper we calculate the specific heat (Cv) of Bateman-Caldirola-Kanai dissipative systems.

Via quantum fluid dynamics the author presents a general method to obtain a solution of the nonlinear Schrodinger-Langevin equation with a multiterm potential for the description of interactions in non-conservative systems. The nonlinear complete set of equations forming the basis of the model are derived. The corresponding solutions are exhibited...

The author recasts a generalised Schrodinger-Langevin equation into a set of hydro-dynamical equations and draws some analogies with a classical (plasma) fluid theory describing the motion of charged particles in a neutralised background.

A Fokker-Plank equation describing the relative motion of two particles in a dissipative spacetime correlated turbulent force-field flow is derived, and the clump lifetime of the correlated motion for two adjacent particles with a small initial separation is found and compared with Dupree's results (1972) for the dissipationless case.

This work provides a step-by-step guideline for the construction of a
simple, low-cost generator of a nonpropagating hydrodynamic soliton.

Via the de Broglie-Bohm causal interpretation of quantum mechanics, we develop a protocol to obtain a propagator for the guiding wave function where the features of the quantum potential are kept. Our analysis is extended to include a friction mechanism.

We present the solution of Schrödinger's equation for time-dependent quadratic potentials in terms of an Airy packet. We demonstrate new features of the Airy packet in light of its apparent unfamiliar properties discovered by Berry and Balazs (who found a nonspreading and accelerating Airy packet to be a unique solution to the free-particle Schrödi...

Discusses a well-known optical refraction problem where the depth of an object in a liquid is determined. Proposes that many texts incorrectly solve the problem. Provides theory, equations, and diagrams. (MVL)

An approach to the problem of tunneling through sharp-edged potential
barriers with and without dissipation was developed. Boundary conditions
can be matched without assuming continuity of the wave function. The
effect of a small friction mechanism on the tunneling of a particle
through a single, sharp-edged rectangular barrier diminishes the
trans...

The problem of scattering in multilayer systems is addressed from the standpoint of quantum hydrodynamics. A general formula for the transmission coefficient is found in terms of the invariants of the problem. We find that the transmission coefficient for a N-layer sharp-edged parabolic superlattice composed of discrete steps has a complex structur...

The clump lifetime of the correlated motion for two adjacent particles in a dissipative space-time-correlated stochastic field with a small initial separation is found to have a remarkable feature. Despite its monotonic long-time diffusive behavior, this work predicts that if the motion of these two particles undergoes dissipation, the formation of...

A kinetic equation for the quantum Brownian motion is derived by starting from the quantum Liouville equation for a N-particle density matrix. The friction coefficient presented through the kinetic approach is derived self-consistently within the theory and expressed in terms of the intermolecular forces acting on the Brownian particle. Particular...

Via the Schwinger action principle, we derive a formula for the transformation function (or propagator) of time-dependent systems that can be expressed into a quadratic form. We present also a new type of two-time rotation-translation of coordinates which makes it possible to evaluate the exact transformation function of the three-dimensional time-...

A new approach to the problem of scattering is presented via the exact invariants of quantum hydrodynamics, where the solution preserves information about the quantum potential which accounts for quantum-wave features such as interference and diffraction effects. Within this formalism, a formula for the transmission coefficient of a steady flux of...

The time spent by a quantum particle in a scattering event or a tunneling process (the traversal time) through a rectangular barrier is calculated from the viewpoint of the stochastic formulation of quantum mechanics. Comparison with previous results is also provided.

Quantum fluctuations occurring in tunneling processes are studied via the operator Hamilton-Jacobi (HJ) formalism, generated from the principles of Feynman and Schwinger. It is shown that due to these quantum fluctuations and the ordering procedure, the operator HJ equation does not transform likewise its classical counterpart, and that two kinds o...

The authors provide physical and mathematical reasons by which propagators associated with non-local actions may not satisfy the composition property and may not be of the Van Vleck-Pauli formula either. Furthermore, they demonstrate that the Feynman and Schwinger principles, at least when applied to non-local quadratic actions, yield identical for...

We show that, by using a convenient space-time transformation, we can considerably simplify the evaluation of the exact transformation function (or propagator) for a time-dependent mass, subject to a time-varying, forced harmonic oscillator potential, obtained through the Schwinger action principle. Overall, we demonstrate that such a transformatio...

We discuss a method for constructing analytically solvable second-order linear differential equations with n-parameter variable coefficients (periodic or not). We show that an exact solution to this problem is possible if one can find another solution to a related subset problem (a subset equation formed with one of the variable coefficients). In t...

Via Nelson's stochastic mechanics, a method for the solution of the hydrodynamical version of the logarithmic nonlinear Schrödinger equation (LNLSE), with a time-dependent forced-harmonic-oscillator potential, is presented. Based on a new interpretation of the interplay between dispersion and nonlinearity, a revealing general spreading-wave-packet...

We evaluate the exact propagator for the time-dependent two-dimensional charged harmonic oscillator in a time-varying magnetic field, by taking direct recourse to the corresponding Schrödinger equation. Through the usage of an appropriate space-time transformation, we show that such a propagator can be obtained from the free propagator in the new s...

DOI:https://doi.org/10.1103/PhysRevA.35.1444.2

Via the quantum‐hydrodynamical method, a time‐dependent invariant associated to the quantum dissipative time‐dependent harmonic oscillator (TDHO), described by two classes of nonlinear Schrödinger–Langevin equations with the following frictional nonlinear terms is constructed: (i) W1=−iℏν(ln ψ−〈ln ψ〉), which is the Schuch–Chung–Hartman frictional n...

The authors demonstrate that the use of a spacetime transformation can greatly simplify the evaluation of the propagator for the problem of a particle with time-dependent mass, subject to a time-varying forced harmonic oscillator potential. They show that such a propagator can be easily obtained from the free propagator in the new spacetime coordin...

We evaluate the exact propagator for the time-dependent three-dimensional charged harmonic oscillator in a time-varying magnetic field. We show that such a propagator can be obtained from that for a charged particle in a constant magnetic field.

We evaluate the exact propagator for the time-dependent three-dimensional charged harmonic oscillator in a time-varying magnetic field. We show that such a propagator can be obtained from that for a charged particle in a constant magnetic field.

Summary We derive the quantum-mechanical Green’s function for the problem of a time-dependent variable mass particle subject to a
time-dependent forced harmonic-oscillator potential by taking direct recourse of the corresponding Schrödinger equation. Through
the usage of the nonlinear superposition law of Ray and Reid, we show that such a Green’s f...

DOI:https://doi.org/10.1103/PhysRevA.33.4433

We investigate special types of solutions of the hydrodynamical version
of a generalized Schrödinger-Langevin equation (GNLSLE), derived in
an earlier work, via stochastic mechanics. Within the same scheme of
stochastic differential equations, we decompose the stochastic process
associated with the GNLSLE into two independent processes: a classical...

Via the hydrodynamical formulation of quantum mechanics, a unified protocol to treat the quantum time‐dependent harmonic oscillator with friction is presented, described by two different models: an explicitly time‐dependent, linear Schrödinger equation (Caldirola–Kanai model) and a logarithmic nonlinear Schrödinger equation (Kostin model). For the...

We demonstrate the usefulness of the nonlinear superposition law of Ray and Reid in connection with the Feynman propagator. We derive the propagator for the problem of a time-dependent variable mass particle subject to a harmonic potential with a time-dependent frequency by taking direct recourse to the corresponding Schrödinger equation.

The Ermakov problem of finding an exact invariant of the time-dependent harmonic oscillator is derived and solved within the framework of Nelson's stochastic mechanics.

Within the framework of the Nelson-de la Peña stochastic mechanics a generalized nonlinear Schrödinger-Langevin equation is derived. Then, by taking proper limits, results of previous works are fully recovered.

A simple, direct, alternative derivation of the magnetohydrodynamic force law from an action principle is presented.

Summary The quantum friction problem described, by the Caldirola-Kanai time-dependent Hamiltonian is treated via the quantum fluid
dynamics. The nonlinear complete set of equations forming the basis of the hydrodynamical model are derived. Exact solutions
are exhibited in closed form for the case of the potential force-free motion.

The brownian motion of a quantum particle described by the Caldirola-Kanai model of a Langevin system is studied via quantum fluid dynamics. The nonlinear complete set of equations forming the basis of the model are derived. Exact solutions are exhibited in closed form for a field-free fluid-particle motion interacting with a randomly fluctuating m...

Neste artigo apresentamos aspectos fundamentais da Mec^ anica Estat stica Qu^ antica. Usando os propagadores de Feynman, calculamos a matriz densidade, a fun c~ ao de parti c~ ao, a energia livre e o calor espec co a volume constante para sistemas dissipativos representados pela Hamiltoni-ana de Bateman-Caldirola-Kanai. Os c alculos s~ ao efetuados...

Este trabalho apresenta uma proposta alternativa para o ensino de f´ isica aplicada aos problemas amazonicos. Baseia-se inicialmente na necessidade de pessoal qualificado para atuar nas diversificadasareas que compoem atualmente a engenharia nessa regiao. A proposta leva em conta os aspectos fundamentais da formacao de um profissional que possua as...

Via the hydrodynamical formulation of quantum mechanics, an approach to the problem of tunneling through sharp-edged potential barriers is developed. Above all, it is shown how more general boundary conditions follow from the continuity of mass, momentum, and energy.

Some of the key components in basic education nowadays are: the use of information technology, and to know how to use it effectively. This article reveals several drawbacks with the pedagogical techniques used by most teachers in the Brazilian classroom. First, students come to school with patchy, flawed knowledge and information acquired from the...