Quantum Force Research Articles

Quantum force of tunneling macrospins with a mechanical resonator

We study force dynamics of macropsin of molecular magnets coupled to a torsional resonator. In the presence of an ac field and a static field with a gradient, the force is shown to display various types of quantum oscillations which depend upon the coupling strength and the frequency of torsional oscillations. Optimal conditions for observing them will be discussed within the framework of experimentally controllable parameters.

Electromagnetic modes and gravitational instability of spin- 1 / 2 $1/2$ magneto degenerate plasma

We have studied self-gravitational instability using the two fluid model in which the important role of spin effect (due to spin quantum force and spin magnetization current) is established in highly magnetized and degenerate astrophysical environment of pulsar magnetosphere. Along with this; low frequency, high frequency modes of magnetosonic and magnetohydrodynamic waves were carried out discovering its utility in highly magnetized and degenerate astrophysical environments. The plasma is considered to be composed of degenerate electrons and non-degenerate ions and the quantum effects are incorporated via spin and diffraction effects along with the thermal effect of ions. The spin and quantum dominance are discussed analytically and numerically using the dispersion relation in parallel, perpendicular and oblique mode of propagation. The present study can be implemented on highly magnetized white dwarfs, neutron stars and pulsar magnetosphere (with strong magnetic field $B_{0} \le 10^{10}~\mbox{T}$ ) and to degenerate laboratory environments.

The hydrogen atom confined by one and two hard cones

The bound states of the H atom in a semi-infinite space limited by one or two conical boundaries are studied. The exact solution when the nucleus is located at the apex of the conical boundaries is obtained. A rapid increase of the energy when the cone angle opens and tends to π/2 is found. A second situation with the atom separated from the summit of the cone is considered. The changes on the energy and the electronic structure are analyzed. The quantum force is evaluated by calculating the energy derivative versus the distance to the cone vertex. One of the forces exerted on the tip of an Atomic Force Microscope can be modelized by a hard cone probing the electron cloud in the contact mode. Our numerical results show that the quantum force present an important dependence with the cone angle and it vanishes rapidly as the distance increases.

Use of quantum self-friction potentials and forces in standard convention for study of harmonic oscillator

In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the $$L^{{(p_{l}^{ * } )}}$$ -SF Laguerre polynomials ( $$L^{{(p_{l}^{ * } )}}$$ -SFLPs) and $$L^{{(\alpha^{*} )}}$$ -modified SFLPs ( $$L^{{(\alpha^{*} )}}$$ -MSFLPs) in standard convention, the $$V^{{(p_{l}^{ * } )}}$$ -SF potentials ( $$V^{{(p_{l}^{ * } )}}$$ -SFPs), $$V^{{(\alpha^{*} )}}$$ -modified SFPs ( $$V^{{(\alpha^{*} )}}$$ -MSFPs), $$F^{{(p_{l}^{ * } )}}$$ -SF forces ( $$F^{{(p_{l}^{ * } )}}$$ -SFFs) and $$F^{{(\alpha^{*} )}}$$ -modified SFFs ( $$F^{{(\alpha^{*} )}}$$ -MSFFs) are investigated, where $$p_{l}^{ * } = 2l + 2 - \alpha^{*}$$ and $$\,\alpha^{*}$$ is the integer ( $$\alpha^{*} = \alpha$$ , $$\, - \infty < \alpha \le 2)$$ or non-integer ( $$\alpha^{*} \ne \alpha$$ , $$\, - \infty < \alpha < 3)$$ SF quantum number. We note that the potentials ( $$V^{{(p_{l}^{ * } )}}$$ -SFPs and $$V^{{(\alpha^{*} )}}$$ -MSFPs), and forces ( $$F^{{(p_{l}^{ * } )}}$$ -SFFs and $$F^{{(\alpha^{*} )}}$$ -MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., $$V_{num}^{{(p_{l}^{ * } )}} = V_{num}^{{(\alpha^{*} )}}$$ and $$F_{num}^{{(p_{l}^{ * } )}} = F_{num}^{{(\alpha^{*} )}}$$ . The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.

Quantum force of nanomagnets loosely fastened to the matrix in a magnetic field gradient

We study nanomagnets that exhibit quantum forces, but are not firmly fixed to the substrate. The Hamiltonian of a rotating spin system is derived in the presence of a microwave field and a transverse field gradient, and analytic expressions for the forces are obtained. We show that the period of the oscillating force depends upon the coupling constant of the system to the matrix and the total angular momentum, and we discuss the conditions under which they can be observed within the framework of experimentally controllable parameters.

Understanding How Isotopes Affect Charge Transfer in P3HT/PCBM: A Quantum Trajectory-Electronic Structure Study with Nonlinear Quantum Corrections.

The experimentally observed effect of selective deuterium substitution on the open circuit voltage for a blend of poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM; Nat. Commun. 2014, 5, 3180) is explored using a 221-atom model of a polymer-wrapped PCBM molecule. The protonic and deuteronic wave functions for the H/D isotopologues of the hexyl side chains are described within a quantum trajectory/electronic structure approach where the dynamics is performed with newly developed nonlinear corrections to the quantum forces, necessary to describe the nuclear wave functions; the classical forces are generated with a density functional tight binding method. The resulting protonic and deuteronic time-dependent wave functions are used to assess the effects of isotopic substitution (deuteration) on the energy gaps relevant to the charge transfer for the donor and acceptor electronic states. While the isotope effect on the electronic energy levels is found negligible, the quantum-induced fluctuations of the energy gap between the charge transfer and charge separated states due to nuclear wave functions may account for experimental trends by promoting charge transfer in P3HT:PCBM and increasing charge recombination on the donor in the deuterium substituted P3HT:PCBM.

A Bohmian approach to the perturbations of non-linear Klein–Gordon equation

In the framework of Bohmian quantum mechanics, the Klein–Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave ϕ(x) in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein–Gordon equation? We examine this approach for ϕ 4(x) and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.

Force sensing based on coherent quantum noise cancellation in a hybrid optomechanical cavity with squeezed-vacuum injection

We propose and analyse a feasible experimental scheme for a quantum force sensor based on the elimination of backaction noise through coherent quantum noise cancellation (CQNC) in a hybrid atom-cavity optomechanical setup assisted with squeezed vacuum injection. The force detector, which allows for a continuous, broadband detection of weak forces well below the standard quantum limit (SQL), is formed by a single optical cavity simultaneously coupled to a mechanical oscillator and to an ensemble of ultracold atoms. The latter acts as a negative-mass oscillator so that atomic noise exactly cancels the backaction noise from the mechanical oscillator due to destructive quantum interference. Squeezed vacuum injection enforces this cancellation and allows sub-SQL sensitivity to be reached in a very wide frequency band, and at much lower input laser powers.

Quantum Gravitational Force Between Polarizable Objects.

Since general relativity is a consistent low energy effective field theory, it is possible to compute quantum corrections to classical forces. Here we compute a quantum correction to the gravitational potential between a pair of polarizable objects. We study two distant bodies and compute a quantum force from their induced quadrupole moments due to two-graviton exchange. The effect is in close analogy to the Casimir-Polder and London-van der Waals forces between a pair of atoms from their induced dipole moments due to two photon exchange. The new effect is computed from the shift in vacuum energy of metric fluctuations due to the polarizability of the objects. We compute the potential energy at arbitrary distances compared to the wavelengths in the system, including the far and near regimes. In the far distance, or retarded, regime, the potential energy takes on a particularly simple form: V(r)=-3987ℏcG^{2}α_{1S}α_{2S}/(4πr^{11}), where α_{1S}, α_{2S} are the static gravitational quadrupole polarizabilities of each object. We provide estimates of this effect.

The Quantum Mechanics of Israeli Totalitarianism

This article argues that Israel's occupation of Palestinian territory represents criminalized state behaviour at the most systematic, intricately planned and executed. Evoking the quantum physics of Israel's matrix of control, the article argues that to understand how it feels to live as a Palestinian today requires the mindset of a particle physicist, not a social scientist. Life in Israel/Palestine involves negotiating a host of forces over which the average Palestinian has as much control as the average electron or proton does over the nuclear and quantum forces determining its path. The power embodied in Israel's matrix of control lies in the state's ability to shift rules, tactics, amplitude and frequency of the forces, strategies and techniques and technologies of occupation. The article argues that the Occupation and the conditions it creates have become normalized, and that maintaining a situation of confusion and ambiguity is key to making the Occupation effectively permanent.

Does Bohm’s Quantum Force Have a Classical Origin?

In the de Broglie - Bohm formulation of quantum mechanics, the electron is stationary in the ground state of the hydrogen atom, because the quantum force exactly cancels the Coulomb attraction of the electron to the proton. In this paper it is shown that classical electrodynamics similarly predicts the Coulomb force can be effectively canceled by part of the magnetic force that occurs between two similar particles each consisting of a point charge moving with circulatory motion at the speed of light. Supposition of such motion is the basis of the {\em Zitterbewegung} interpretation of quantum mechanics. The magnetic force between two luminally-circulating charges for separation large compared to their circulatory motions contains a radial inverse square law part with magnitude equal to the Coulomb force, sinusoidally modulated by the phase difference between the circulatory motions. When the particles have equal mass and their circulatory motions are aligned but out of phase, part of the magnetic force is equal but opposite the Coulomb force. This raises a possibility that the quantum force of Bohmian mechanics may be attributable to the magnetic force of classical electrodynamics. It is further shown that non-relativistic relative motion between the particles leads to modulation of the magnetic force with spatial period equal to the de Broglie wavelength.

Electron excitation from ground state to first excited state: Bohmian mechanics method**Project supported by the Doctoral Research Start-up Funding of Northeast Dianli University, China (Grant No. BSJXM-201332), the National Natural Science Foundation of China (Grant Nos. 11547114, 11534004, 11474129, 11274141, 11447192, and 11304116), and the Graduate Innovation Fund of Jilin University, China (Grant No. 2015091).

The excitation process of electrons from the ground state to the first excited state via the resonant laser pulse is investigated by the Bohmian mechanics method. It is found that the Bohmian particles far away from the nucleus are easier to be excited and are excited firstly, while the Bohmian particles in the ground state is subject to a strong quantum force at a certain moment, being excited to the first excited state instantaneously. A detailed analysis for one of the trajectories is made, and finally we present the space and energy distribution of 2000 Bohmian particles at several typical instants and analyze their dynamical process at these moments.

Effect of quantum force discontinuity on electron transmission across abrupt heterojunctions

Matching conditions for the envelope function in the effective mass approximation are determined based on the feasibility of exactly solving the effective mass Schrodinger equation. The transmission and reflection probabilities for these conditions at an abrupt heterojunction are determined for a step mass and step potential and an alternative description of transport across the heterojunction based on the interplay between discontinuities of the quantum force and the effective mass is discussed.

Quantum Forces in a Relativistic Entangled &amp;quot;Space-Time&amp;quot; State in Complex Hamiltonian Dynamics

Based on complex quantum Hamilton-Jacobi theory and its natural complex spacetime configuration, we realized new states for both positive and negative values of energy and momentum, and we discuss this complex configuration in a relativistic entangled "space-time" state and the resultant 12 extra wave functions than the four solutions of Dirac equation for a free particle. Accordingly, we calculate the quantum forces between particles and antiparticles in a relativistic entangled "space-time" state.

Nonlinear interaction between surface plasmons and ion oscillations in a semi-bounded collisional quantum plasma

In this paper, we have investigated the nonlinear interaction between high-frequency surface plasmons and low-frequency ion oscillations in a semi-bounded collisional quantum plasma. By coupling the nonlinear Schrodinger equation and quantum hydrodynamic model, and taking into account the ponderomotive force, the dispersion equation is obtained. By solving this equation, it is shown that there is a modulational instability in the system, and collisions and quantum forces play significant roles on this instability. The quantum tunneling increases the phase and group velocities of the modulated waves and collisions increase the growth rate of the modulational instability. It is also shown that the effect of quantum forces and collisions is more significant in high modulated wavenumber regions.

Dispersionless forces and the Aharonov-Bohm effect

The independence of the Aharonov-Bohm phase shift on particle velocity is one of its defining properties. The classical counterpart to this dispersionless behavior is the absence of forces along the direction of motion of the particle. A reevaluation of the experimental demonstration that forces are absent in the AB physical system is given, including previously unpublished data. It is shown that the debate on the presence or absence of forces is not settled. Experiments that measure the influence of magnetic permeability on forces and search for dispersionless quantum forces are proposed.

Atom-based coherent quantum-noise cancellation in optomechanics

We analyze a quantum force sensor that uses coherent quantum noise cancellation (CQNC) to beat the Standard Quantum Limit (SQL). This sensor, which allows for the continuous, broad-band detection of feeble forces, is a hybrid dual-cavity system comprised of a mesoscopic mechanical resonator optically coupled to an ensemble of ultracold atoms. In contrast to the stringent constraints on dissipation typically associated with purely optical schemes of CQNC, the dissipation rate of the mechanical resonator only needs to be matched to the decoherence rate of the atomic ensemble -- a condition that is experimentally achievable even for the technologically relevant regime of low frequency mechanical resonators with large quality factors. The modular nature of the system further allows the atomic ensemble to aid in the cooling of the mechanical resonator, thereby combining atom-mediated state preparation with sensing deep in the quantum regime.

Gold/Benzenedithiolate/Gold Molecular Junction: A Driven Dynamics Simulation on Structural Evolution and Breaking Force under Pulling

Dynamic evolutions of molecular binding structures and breaking forces of gold/thiolate molecular junctions under pulling are still not well understood. We perform driven dynamics simulations to show that there are essentially two distinct breaking force traces corresponding to the Au–Au and Au–S bond ruptures. The latter is attributed to the formation and breaking of an additional “–Au–SR–Au–” unit in the molecular junction. The force histogram shows two force quanta at 1.5 and 2.0 nN, corresponding to the Au–Au and Au–S bond breaking. Our findings provide new molecular insights into the gold–thiolate interactions. The intermediate metal–molecule–metal binding structures could be used for further molecular transport calculations.

Nonlinear hydrodynamics of axion dark matter: Relative velocity effects and quantum forces

The non-linear hydrodynamic equations for axion/scalar field dark matter (DM) in the non-relativistic Madelung-Shcr\"{o}dinger form are derived in a simple manner, including the effects of universal expansion and Hubble drag. The hydrodynamic equations are used to investigate the relative velocity between axion DM and baryons, and the moving-background perturbation theory (MBPT) derived. Axions massive enough to be all of the DM do not affect the coherence length of the relative velocity, but the MBPT equations are modified by the inclusion of the axion effective sound speed. These MBPT equations are necessary for accurately modelling the effects of axion DM on the formation of the first cosmic structures, and suggest that the 21cm power spectrum could improve constraints on axion mass by up to four orders of magnitude with respect to the current best constraints. A further application of these results uses the "quantum force" analogy to model scalar field gradient energy in a smoothed-particle hydrodynamics model of axion DM. Such a model can treat axion DM in the non-linear regime and could be incorporated into existing N-body codes.

Estimation of the Ground State Energy of an Atomic Solid by Employing Quantum Trajectory Dynamics with Friction.

Evolution with energy dissipation can be used to obtain the ground state of a quantum-mechanical system. This dissipation is introduced in the quantum trajectory framework by adding an empirical friction force to the equations of motion for the trajectories, which, as an ensemble, represent a wave function. The quantum effects in dynamics are incorporated via the quantum force derived from the properties of this ensemble. For scalability to large systems, the quantum force is computed approximately yet with sufficient accuracy to describe the strongly anharmonic ground state of solid (4)He represented by a simulation cell of 180 atoms.