Quantum Dynamics Of Particles Research Articles

Global monopole effects on exact s-state solution under trigonometric Pöschl–Teller potential

In this paper, we address into the quantum dynamics of quantum particles interacting with a trigonometric potential within the context of a space-time background featuring a point-like global monopole. Our aim is to derive exact s-states eigenvalue solutions. To achieve this, we first derive the angular and radial wave equations of the Schrödinger equation within this particular geometry, considering Pöschl–Teller potential. While the angular solutions are well-known, the radial wave equation necessitates the utilisation of special functions for its solution. Our analysis demonstrates that the presence of the global monopole induces modifications in both the exact energy eigenvalues and the corresponding wave functions of quantum particles. Consequently, these modifications deviate from the behaviour typically observed in flat space when considering this potential. Afterwards, we compute Shannon entropy for this quantum systems and show the influences of various parameters.

Improving the proof of the Born rule using a physical requirement on the dynamics of quantum particles

We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time Δt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta t$$\\end{document} between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to produce the Born rule in its explicit form by improving the result given in [1]. While the proposed postulate is still not part of the quantum mechanics postulates, every experiment obeys it, and it cannot be deduced using the standard postulates of quantum mechanics.

Effective Theory of Classical and Quantum Particle Dynamics in Rapidly Oscillating Fields.

We study the large-scale dynamics of charged particles in a rapidly oscillating field and formulate its classical and quantum effective theory description. The high-order perturbative results for the effective action are presented. Remarkably, the action models the effects of post-Newtonian general relativity on the motion of nonrelativistic particles, with the values of the emergent curvature and speed of light determined by the field spatial distribution and frequency. Our results can be applied to a wide range of physical problems including the high-precision analysis and design of the charged particle traps and Floquet quantum materials.

Intrinsic quantum dynamics of particles in brane gravity

The Newtonian dynamics of particles in brane gravity is investigated. Due to the coupling of the particles’ energy–momentum tensor to the tension of the brane, the particle is semi-confined and oscillates along the extra dimension. We demonstrate that the frequency of these oscillations is proportional to the kinetic energy of the particle in the brane. We show that the classical stability of particle trajectories on the brane gives us the Bohr–Sommerfeld quantization condition. The particle’s motion along the extra dimension allows us to formulate a geometrical version of the uncertainty principle. Furthermore, we exhibited that the particle’s motion along the extra dimension is identical to the time-independent Schrödinger equation. The dynamics of a free particle, particles in a box, a harmonic oscillator, a bouncing particle, and tunneling are re-examined. We show that the particle’s motion along the extra dimension yields a quantized energy spectrum for bound states.

Dynamics and uncertainty for maximally entangled bipartite system constrained on a helicoid

The classical and quantum dynamics of particles constrained on a right helicoid is discussed via Dirac approach. We show how the uncertainty in measurement for observables of maximally entangled system is affected by the total number of constrained particles sigma , external magnetic field vec {mathcal {B}}; as well as by geometric parameters like the pitchrho and the radial position of particles. In doing so we also highlight numeric bounds on the external field strengths to tune both intraparticle and bipartite entanglement and we remark that the bipartite entanglement is more robust to changes in the fields than the intraparticle entanglement, in this framework. We also highlight specific parameter regimes which lead the uncertainty (in measurement) to achieve respective parameter independence and, for a particular subset of commutation relations, the system remains confined in the quantum regime even in the limit sigma rightarrow infty . It is observed that the uncertainties are strongly influenced by the geometric parameters e.g., rho , and the strength of bipartite as well as intraparticle entanglement might be controllable through rho . The energy equation for this setup is obtained and the additional terms are discussed which arise due to quantum correlations, orbit–orbit interaction and the normal Zeeman effect, which leads to the splitting of the energy level into 11 non-degenerate levels. Finally we comment that, a linkage of this phenomenology with Aharonov–Bohm like effect might be possible by strictly confining vec {mathcal {B}} along the central axis of the helicoid.

Quantum operations with indefinite time direction

The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental question is whether it is possible, at least in principle, to conceive a broader set of operations that probe quantum processes in the backward direction, from the future to the past, or more generally, in a combination of the forward and backward directions. Here we introduce a mathematical framework for operations that are not constrained to a definite time direction. More generally, we introduce a set of multipartite operations that include indefinite time direction as well as indefinite causal order, providing a framework for potential extensions of quantum theory.

Generalized Bloch oscillations of ultracold lattice atoms subject to higher-order gradients

The standard Bloch oscillation normally refers to the oscillatory tunneling dynamics of quantum particles in a periodic lattice plus a linear gradient. In this work we theoretically investigate the generalized form of the Bloch oscillation in the presence of additional higher order gradients, and demonstrate that the higher order gradients can significantly modify the tunneling dynamics, particularly in the spectrum of the density oscillation. The spectrum of the standard Bloch oscillation is composed of a single prime frequency and its higher harmonics, while the higher-order gradients in the external potential give rise to fine structures in the spectrum around each of these Bloch frequencies, which are composed of serieses of frequency peaks. Our investigation leads to a twofold consequence to the applications of Bloch oscillations for measuring external forces: For one thing, under a limited resolution of the measured spectrum, the fine structures would manifest as a blur to the spectrum, and leads to intrinsic errors to the measurement. For another, given that the fine structures could be experimentally resolved, they can supply more information of the external force than the strength of the linear gradient, and be used to measure more complicated forces.

Simulation and Analytical Modeling of Quantum Gas Dynamics Taking Into Account the Temperature and Electric Fields and Frictional Forces

The article investigates the questions of calculating the dynamics of quantum gases on the basis of the stochastic interpretation of Schrodinger equation. A comparison of several appropriate methods for solve of equations of quantum mechanics – based on the method of simulating the dynamics of quantum particles as a Brownian motion, using an analytical solution of the equations of quantum hydrodynamics and directly the Schrodinger equation. An example of modeling the gas flow of quantum particles with allowance for the temperature and electric fields and friction forces is considered. The influence of the form factor of the initial distribution of the gas density, temperature, and parameters of the computational method is studied.

Quantum dynamics of a parity-time-symmetric kicked particle in a 1D box

We study quantum particle dynamics in a box and driven by a parity-time (PT)-symmetric, delta-kicking complex potential. The dynamical characteristics, identified by the average kinetic energy as a function of time, and quasi-energy are computed for different values of the kicking parameters. Breaking of the PT-symmetry at certain values of the non-Hermitian kicking parameter is shown. Experimental realization of the model is also discussed.

Quantum Mechanics as a Fourier Representation of a Relativistic Quantum Particle

The starting point of this research is a representation of a quantum particle according to the Schrodinger equation of the conventional quantum mechanics. In this representation, a quantum particle is described by a wave packet in the coordinate space and the conjugated wave packet in the momentum space. The problem is that while in the coordinate space the group velocity is in agreement with one of the Hamilton equations, the group velocity in the momentum space is in contradiction with the other Hamilton equation - a minus sign is missing. Group velocities in agreement with the Hamilton equations are obtained only when in the time dependent phase of a quantum particle wave packet, instead of the Hamiltonian coming from the conventional Schrodinger equation, the Lagrangian is considered. This suggests us to consider the relativistic Lagrangian in the time dependent phase. In this way, the conventional relativistic principle of invariance of the time-space interval gets the more physically understandable form of the invariance of the time dependent phase of a quantum particle - the time dependent phase of a quantum particle is the same in any system of coordinates. Based on the relativistic time dependent phase invariance of a quantum particle, from the group velocities of this particle the relativistic kinematics and dynamics are obtained. The interaction with an electromagnetic field is described by a modification of the time dependent phase with a scalar potential conjugated to time and a vector potential conjugated to the space coordinates. In this paper, we find that, according to the formalism of the general relativity, any matter element in a field of forces is accelerated only perpendicularly to its velocity. This means that the matter propagation of a quantum particle can be conceived in planes perpendicular to velocity, while the mater distribution can be considered in a Fourier representation - quantum waves. We study the quantum particle dynamics in gravitational waves and derive the graviton spin. We consider a quantum particle in electromagnetic field and obtain a Schrödinger-Dirac-type equation, with additional terms describing the velocity dependence of the particle dynamics.

Schrödinger and Dirac dynamics on time-dependent quantum graph

Quantum graphs with varying edges lengths are constructed. We deal with two types of operators on the graph edges: the Schrodinger and the Dirac operators. The dynamics of quantum particles for these two cases is compared. From the physical point of view, the Schrodinger dynamics corresponds to nonrelativistic particle and the Dirac dynamics to the relativistic one.

Contextual Wavefunction collapse: an integrated theory of quantum measurement

This paper is an in depth implementation of the proposal (Ellis 2012 Ann. Phys. NY 327 1890–932) that the quantum measurement issue can be resolved by carefully looking at top-down contextual effects within realistic measurement contexts. The specific setup of the measurement apparatus determines the possible events that can take place. The interaction of local heat baths with a quantum system plays a key role in the process. In contrast to the usual attempts to explain quantum measurement by decoherence, we argue that the heat bath follows unitary time evolution only over limited length and time scales (Drossel 2017 His. Phil. Sci. B 58 12–21) and thus leads to localization and stochastic dynamics of quantum particles that interact with it. We show furthermore that a theory that describes all the steps from the initial arrival of the quantum particle to the final pointer deflection must use elements from classical physics. This proposal also provides a contextual answer to the puzzle of the origin of the arrow of time when quantum measurements take place: it derives from the cosmological direction of time. Overall, our proposal is for contextual wavefunction collapse.

Analysis of lense‐governed Wigner signed particle quantum dynamics (Phys. Status Solidi RRL 7/2017)

Analysis of lense‐governed Wigner signed particle quantum dynamics (Phys. Status Solidi RRL 7/2017)

Analysis of lense‐governed Wigner signed particle quantum dynamics

We present a Wigner signed particles analysis of the lense‐governed electron state dynamics based on the quantitative theory of coherence reformulated in phase space terms. Electrostatic lenses are used for manipulating electron evolution and are therefore attractive for applications in novel engineering disciplines like entangletronics. The signed particle model of Wigner evolution enables physically intuitive insights into the processes maintaining coherence. Both, coherent processes and scattering‐caused transitions to classical dynamics are unified by a scattering‐aware particle model of the lense‐controlled state evolution. Our approach bridges the fairly new theory of coherence with the Wigner signed particle method.

Finding quantum effects in strong classical potentials

The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified framework. The current, semiclassical methods to describe the dynamics of quantum particles in strong classical fields also provide the theoretical framework for fundamental questions in gravity and hadron–hadron collisions, including Hawking radiation, cosmological particle production and thermalization of particles created in heavy-ion collisions. However, as we show, these methods break down for highly relativistic particles propagating in strong fields. They must therefore be improved and adapted for the description of laser–plasma experiments that typically involve the acceleration of electrons. Theory developed from quantum electrodynamics, together with dedicated experimental efforts, offer the best controllable context to establish a robust, experimentally validated foundation for the fundamental theory of quantum effects in strong classical potentials.

Ponderomotive dynamics of waves in quasiperiodically modulated media

Similarly to how charged particles experience time-averaged ponderomotive forces in high-frequency fields, linear waves also experience time-averaged refraction in modulated media. Here we propose a covariant variational theory of this "ponderomotive effect on waves" for a general nondissipative linear medium. Using the Weyl calculus, our formulation accommodates waves with temporal and spatial period comparable to that of the modulation (provided that parametric resonances are avoided). Our theory also shows that any wave is, in fact, a polarizable object that contributes to the linear dielectric tensor of the ambient medium. The dynamics of quantum particles is subsumed as a special case. As an illustration, ponderomotive Hamiltonians of quantum particles and photons are calculated within a number of models. We also explain a fundamental connection between these results and the commonly known expression for the electrostatic dielectric tensor of quantum plasmas.

Control of quantum particle dynamics by impulses of magnetic field

The problem of control of quantum dynamics particle has been studied. The general equations have obtained for a description of this problem. The criteria for optimal time, reaching the desired point, have been obtained and have analyzed. The different types of spectrum of acting fields using for control, from impulse form of the field to the power form and Gauss distribution force spectrums, have been studied.

Classical and quantum particle dynamics in univariate background fields

We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or spacelike field dependence. For a special scenario in the classical regime we show how the radiation spectrum in the spacelike (undulator) case becomes well-approximated by the plane wave model in the high energy limit, despite the two systems being Lorentz inequivalent. In the quantum problem, there is no analogue of the WKB-exact Volkov solution. Nevertheless, WKB and uniform-WKB approaches give good approximations in all cases considered. Other approaches that reduce the underlying differential equations from second to first order are found to miss the correct physics for situations corresponding to barrier transmission and wide-angle scattering.

Динамика квантовой частицы в возмущенном двумерном параболическом потенциале

Динамика квантовой частицы в возмущенном двумерном параболическом потенциале

Dynamics of particles with anisotropic mass depending on time and position

Representations of solutions of equations describing the diffusion and quantum dynamics of particles in a Riemannian manifold are discussed under the assumption that the mass of particles is anisotropic and depends on both time and position. These equations are evolution differential equations with secondorder elliptic operators, in which the coefficients depend on time and position. The Riemannian manifold is assumed to be isometrically embedded into Euclidean space, and the solutions are represented by Feynman formulas; the representation of a solution depends on the embedding.