On the conformally coupled scalar field quantum cosmology

We propose a new initial condition for the homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfaces have positive curvature. After solving corresponding Wheeler–DeWitt equation, we obtain exact solutions in both classical and quantum levels. We propose appropriate initial condition for the wave packets which results in a complete classical and quantum correspondence. These wave packets closely follow the classical trajectories and peak on them. We also quantify this correspondence using de Broglie–Bohm interpretation of quantum mechanics. Using this proposal, the quantum potential vanishes along the Bohmian paths and the classical and Bohmian trajectories coincide with each other. We show that the model contains singularities even at the quantum level. Therefore, the resulting wave packets closely follow the classical trajectories from big-bang to big-crunch.     

Gravity-induced geometric spin Hall effect of freely falling quantum particle

We discuss a new gravitational effect that the wave packet of a free-fall quantum particle undergoes a spin-dependent transverse shift in Earth's gravitational field. This effect is similar to the geometric spin Hall effect (GSHE) (Aiello 2009 et al Phys. Rev. Lett. 103 100401 ), and can be called gravity-induced GSHE. This effect suggests that the free-fall wave packets of opposite spin-polarized quantum particles can be split in the direction perpendicular to spin and gravity.     

Wave packets propagation in quantum gravity

Wave packet broadening in usual quantum mechanics is a consequence of dispersion behavior of the medium which the wave propagates in it. In this paper, we consider the problem of wave packet broadening in the framework of Generalized Uncertainty Principle(GUP) of quantum gravity. New dispersion relations are derived in the context of GUP and it has been shown that there exists a gravitational induced dispersion which leads to more broadening of the wave packets. As a result of these dispersion relations, a generalized Klein-Gordon equation is obtained and its interpretation is given.     

Planck Mass Plasma Analog of String Theory

In recent years there had been a growing interest in analog models of general relativity, with certain superfluid solutions simulating black hole solutions of Einstein's gravitational field equation. The quantization of a superfluid, composed of discrete particles (helium atoms), treated as a nonrelativistic many body problem does not lead to divergencies as the quantization of Einstein's field equations. Quantization of gravity is possible in string theory, but only if one introduces the daring hypothesis of higher dimensions. But if the gravitational field is made up of discrete elements as superfluid helium is made up of helium atoms, then gravity can be quantized without difficulty in three space and one time dimension. Such a hypothesis, of course, implies that Lorentz invariance is a dynamic symmetry caused by real rod and clock deformations, as it was assumed in the pre-Einstein theory of relativity by Lorentz and Poincaré, which required the existence of an aether. Making the hypothesis that this aether is a kind of superfluid plasma made up of positive and negative Planck mass particles interacting with the Planck force over a Planck length, one obtains an analog of the standard model, including gravity, which can be quantized as a nonrelativistic many body problem. In this model nonrelativistic vortex rings in three space dimensions and one time dimension simulate the relativistic theory of closed strings in ten space-time dimensions. But because in the vortex lattice, one obtains a large dimensionless number conceivably advancing our understanding of the finestructure constant.     

Nondispersive two-electron wave packets in a helium atom

We demonstrate the existence of stable nondispersing two-electron wave packets in the helium atom in combined magnetic and circularly polarized microwave fields. These packets follow circular orbits and we show that they can also exist in quantum dots. Classically the two electrons follow trajectories which resemble orbits discovered by Langmuir and which were used in attempts at a Bohr-like quantization of the helium atom. Eigenvalues of a generalized Hessian matrix are computed to investigate the classical stability of these states. Diffusion Monte Carlo simulations demonstrate the quantum stability of these two-electron wave packets in the helium atom and quantum-dot helium with an impurity center.     

An Approach to Construct Wave Packets with Complete Classical-Quantum Correspondence in Non-relativistic Quantum Mechanics

We introduce a method to construct wave packets with complete classical and quantum correspondence in one-dimensional non-relativistic quantum mechanics. First, we consider two similar oscillators with equal total energy. In classical domain, we can easily solve this model and obtain the trajectories in the space of variables. This picture in the quantum level is equivalent with a hyperbolic partial differential equation which gives us a freedom for choosing the initial wave function and its initial slope. By taking advantage of this freedom, we propose a method to choose an appropriate initial condition which is independent from the form of the oscillators. We then construct the wave packets for some cases and show that these wave packets closely follow the whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm interpretation of quantum mechanics to quantify this correspondence and show that the resulting Bohmian trajectories are also in complete agreement with their classical counterparts.     

超流氦浴中的热波传热研究

热波传热机制是超流氦传热非常重要的一个方面.在小热流密度的情况下,超流氦中的热波完全保持加热热流的波形,热量的传输完全靠热波来完成;随着热流密度的增加到一定程度,会在超流氦浴中激发量子涡旋.量子涡旋使热波发展成为热激波.在开放氦浴中,热波的波形不同于狭窄通道里的热波,在热波的尾部会出现一个冷却波;并且随着加热时间的变化,冷却波的形状和幅度会发生很大的变化.运用二流体模型和涡旋方程对超流氦中的热波进行了计算,实验结果与计算结果吻合得较好. 关键词： 超流氦 热波 量子涡旋 热激波     

Equivalent Forms of Dirac Equations in Curved Space-times and Generalized de Broglie Relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved space-time. This canonical form is needed to apply Whitham’s Lagrangian method. The latter method, unlike the Wentzel–Kramers–Brillouin method, places no restriction on the magnitude of Planck’s constant to obtain wave packets and furthermore preserves the symmetries of the Dirac Lagrangian. We show by using canonical Dirac fields in a curved space-time that the probability current has a Gordon decomposition into a convection current and a spin current and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck’s constant. We further discuss the classical-quantum correspondence in a curved space-time based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved space-time are a direct consequence of Whitham’s Lagrangian method and not just a physical hypothesis as introduced by Einstein and de Broglie and by many quantum mechanics textbooks.     

Quantum Gauge General Relativity

Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein‘s field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.     

Gravitational radiation antennas using the Sagnac effect

A new class of gravitational antennas that utilize the general relativistic Sagnac effect is proposed. These antennas may be more efficient than the Weber bar by a factor of (c/v_s)⁴ 10¹⁹, wherev _sis the velocity of sound in the bar. A specific case of such an antenna consisting of a superfluid helium Josephson interferometer is considered. A general relativistic theory of the interaction of the superfluid with the gravitational field is given. Using this theory, the phase shift due to a gravitational plane wave on one such antenna is obtained. More generally, the proposed interferometer involves the interplay of general relativity and quantum theory and may afford the possibility of testing general relativity in the laboratory at the quantum mechanical level. The possibility of detecting gravitons, assuming nearly unit coupling efficiency for the antenna, is explored.This essay received the second award from the Gravity Research Foundation for the year 1981-Ed.Research was supported by NSF grant No. PHY 79-13146.Research was supported by NSF grant No. ECS-8009834.     

Propagation of General Wave Packets in Some Classical and Quantum Systems

In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no precise counterpart to the center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for the electromagnetic wave. We propose a center-of-energy velocity to describe the entire motion of general wave packets in classical physical systems. It is a measurable quantity, and is well defined for both continuous and discrete systems. For electromagnetic wave packets it is a generalization of the velocity of energy transport. General wave packets in several classical systems are studied and the center-of-energy velocity is calculated and expressed in terms of the dispersion relation and the Fourier coefficients. These systems include string subject to an external force, monatomic chain and diatomic chain in one dimension, and classical Heisenberg model in one dimension. In most cases the center-of-energy velocity reduces to the group velocity for quasi-monochromatic wave packets. Thus it also appears to be the generalization of the group velocity. Wave packets of the relativistic Dirac equation are discussed briefly.     

Quantum hydrodynamics

Quantum hydrodynamics in superfluid helium and atomic Bose–Einstein condensates (BECs) has been recently one of the most important topics in low temperature physics. In these systems, a macroscopic wave function (order parameter) appears because of Bose–Einstein condensation, which creates quantized vortices. Turbulence consisting of quantized vortices is called quantum turbulence (QT). The study of quantized vortices and QT has increased in intensity for two reasons. The first is that recent studies of QT are considerably advanced over older studies, which were chiefly limited to thermal counterflow in ⁴${}^4$He, which has no analog with classical traditional turbulence, whereas new studies on QT are focused on a comparison between QT and classical turbulence. The second reason is the realization of atomic BECs in 1995, for which modern optical techniques enable the direct control and visualization of the condensate and can even change the interaction; such direct control is impossible in other quantum condensates like superfluid helium and superconductors. Our group has made many important theoretical and numerical contributions to the field of quantum hydrodynamics of both superfluid helium and atomic BECs. In this article, we review some of the important topics in detail. The topics of quantum hydrodynamics are diverse, so we have not attempted to cover all these topics in this article. We also ensure that the scope of this article does not overlap with our recent review article (arXiv:1004.5458), “Quantized vortices in superfluid helium and atomic Bose–Einstein condensates”, and other review articles.     

Nondispersive two-electron wave packets in driven helium

We provide a detailed quantum treatment of the spectral characteristics and of the dynamics of nondispersive two-electron wave packets along the periodically driven, collinear frozen planet configuration of helium. These highly correlated, long-lived wave packets arise as a quantum manifestation of regular islands in a mixed classical phase space, which are induced by nonlinear resonances between the external driving and the unperturbed dynamics of the frozen-planet configuration. Particular emphasis is given to the dependence of the ionization rates of the wave packet states on the driving field parameters and on the quantum mechanical phase space resolution, preceded by a comparison of 1D and 3D life times of the unperturbed frozen planet. Furthermore, we study the effect of a superimposed static electric field component, which, on the grounds of classical considerations, is expected to stabilize the real 3D dynamics against large (and possibly ionizing) deviations from collinearity. Received 7 November 2002 / Received in final form 2 December 2002 Published online 28 January 2003     

Semiclassical Cosmological Perturbations Generated During Inflation

Interaction with the environment may induce stochastic semiclassical dynamicsin open quantum systems. In the gravitational context, stress-energy fluctuationsof quantum matter fields give rise to a stochastic behavior in the spacetimegeometry. The Einstein—Langevin equation is a suitable tool to take these effectsinto account when addressing the backreaction problem in semiclassical gravity.We analyze within this framework the generation of gravitational fluctuationsduring inflation, which are of great interest for large-scale structure formationin cosmology.     

Interaction between gravity and moving superconductors

We propose a unified phenomenological theory to investigate the interaction between arbitrarily moving superconductors and gravitational fields including the Newtonian gravity, gravitational waves, vector transverse gravitoelectric fields, and vector gravitomagnetic fields. In the limit of weak field and low velocity, the expressions for the induced electromagnetic and gravitational fields in the interior of a moving superconductor are obtained. The Meissner effect, London moment, DeWitt effect, effects of gravitational wave on a superconductor, and induced electric fields in the interior of a freely vibrating superconductor are recovered from these two expressions. We demonstrate that the weak equivalence principle is valid in superconductivity, that Newtonian gravity and gravitational waves will penetrate either a moving superconductor or a superconductor at rest, and that a superconductor at rest cannot shield either vector gravitomagnetic fields or vector transverse gravitoelectric fields.     

Ordinary SQUID interferometers and superfluid helium matter wave interferometers: The role of quantum fluctuations

When comparing the operation of a superfluid helium matter wave quantum interferometer (He SQUID) with that of an ordinary direct-current quantum interferometer (dc SQUID), we estimate their resolution limitation that correspond to quantum fluctuations. An alternative mode of operation of the interferometer as a unified macroquantum system is considered.     

Gauge Model with Massive Gravitons

Gauge theory of gravity is formulated based on principle of local gauge invariance. Because the model hasstrict local gravitational gauge symmetry, and gauge theory of gravity is a perturbatively renormalizable quantum model.However, in the original model, all gauge gravitons are massless. We want to ask whether there exist massive gravitonsin Nature. In this paper, we will propose a gauge model with massive gravitons. The mass term of gravitational gaugefield is introduced into the theory without violating the strict local gravitational gauge symmetry. Massive gravitons canbe considered to be possible origin of dark energy and dark matter in the Universe.     

Self-accelerated Universe Induced by Repulsive Effects as an Alternative to Dark Energy and Modified Gravities

The existence of current–time universe’s acceleration is usually modeled by means of two main strategies. The first makes use of a dark energy barotropic fluid entering by hand the energy–momentum tensor of Einstein’s theory. The second lies on extending the Hilbert–Einstein action giving rise to the class of extended theories of gravity. In this work, we propose a third approach, derived as an intrinsic geometrical effect of space–time, which provides repulsive regions under certain circumstances. We demonstrate that the effects of repulsive gravity naturally emerge in the field of a homogeneous and isotropic universe. To this end, we use an invariant definition of repulsive gravity based upon the behavior of the curvature eigenvalues. Moreover, we show that repulsive gravity counterbalances the standard gravitational attraction influencing both late and early times of the universe evolution. This phenomenon leads to the present speed up and to the fast expansion due to the inflationary epoch. In so doing, we are able to unify both dark energy and inflation in a single scheme, showing that the universe changes its dynamics when \({\ddot{H}\over H}=-2 \dot{H}\), at the repulsion onset time where this condition is satisfied. Further, we argue that the spatial scalar curvature can be taken as vanishing because it does not affect at all the emergence of repulsive gravity. We check the goodness of our approach through two cosmological fits involving the most recent union 2.1 supernova compilation.     

Gravity-Related Wave Function Collapse

The gravity-related model of spontaneous wave function collapse, a longtime hypothesis, damps the massive Schrödinger Cat states in quantum theory. We extend the hypothesis and assume that spontaneous wave function collapses are responsible for the emergence of Newton interaction. Superfluid helium would then show significant and testable gravitational anomalies.     

Nonlinear wave interactions in porous media filled with a quantum fluid

The problem of the nonlinear interaction between the fourth sound and an acoustic wave propagating in a porous medium filled with superfluid helium is solved. Based on the Landau equations of quantum fluid dynamics and on the Biot theory of mechanical waves in a porous medium, nonlinear wave equations are derived for studying the aforementioned interaction. An expression is obtained for the vertex that determines the excitation of an acoustic wave by two waves of the fourth sound. The possibility of an experimental observation of this process is estimated.