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1.
There are four reasons why our present knowledge and understanding of quantum mechanics can be regarded as incomplete. (1)
The principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than
about a thousand atoms. (2) There is no universally agreed upon explanation for the process of quantum measurement. (3) There
is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of
position eigenstates. (4) Most importantly, the concept of time is classical and hence external to quantum mechanics: there
should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we
argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important
at the Planck mass scale. Such a nonlinearity can provide insights into the aforesaid problems. We use a physically motivated
model for a nonlinear Schr?dinger equation to show that nonlinearity can help in understanding quantum measurement. We also
show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a
quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain
the observed absence of position superpositions in macroscopic objects (lifetime is too small). It also suggests that ongoing
laboratory experiments may be able to detect the finite superposition lifetime for mesoscopic objects in the near future. 相似文献
2.
3.
Vieri Benci 《Foundations of Physics》1999,29(1):1-28
This work is part of a program which has the aim to investigate which phenomena can be explained by nonlinear effects in classical mechanics and which ones require the new axioms of quantum mechanics. In this paper, we construct a nonlinear field equation which admits soliton solutions. These solitons exibit a dynamics which is similar to that of quantum particles. 相似文献
4.
Sudhanshu S Jha 《Pramana》1984,22(3-4):173-182
A general nonlinear response theory for the case of linear coupling of physical systems to arbitrary external fields is formulated
for applications in different branches of physics. This is done within the framework of non-relativistic density matrix approach
of quantum mechanics. Some simple properties of response functions and other related functions, which are introduced here
for convenience, are studied to obtain suitable representations of the nonlinear response functions, including important sum-rules.
As an example, the sum rule for the second-order response function is applied to electronic dipole nonlinearity at optical
frequencies which includes both the Raman nonlinearity arising from perturbation to the electronic motion from external ionic
displacement field and the usual optical sum, difference and harmonic generations. This immediately allows us to visualize
a rigorous connection between these two types of non-linearities. 相似文献
5.
V. P. Bykov 《Physics of Wave Phenomena》2014,22(1):1-9
Modern concepts of the physical phenomenon described by the term “photon”, which was introduced simultaneously with the acceptance of quantum concepts in physics, are presented. Since that time, this term is a necessary component of each discussion about the physical meaning of quantum mechanics. These discussions are generally carried out within the concepts that are 50 or even 100 years old. At the same time, new fields of science have arisen and been developed in the last century: quantum mechanics and quantum electrodynamics, nonlinear optics, theory of dynamic chaos, etc. The experimental potential has been significantly increased, especially when highly coherent lasers were developed. As a result, the difficult problems of quantum mechanics have become aggravated and enriched. In this paper, we discuss two different approaches to gaining insight into the photon nature, which differ radically. An especially urgent problem is the difference in the estimates of the length of light states that are put into correspondence with photons: laser photons are many orders of magnitude longer than the photons put into correspondence with photocounts. Correspondingly, the spectrum of photocounts is many orders of magnitude wider than the lasing spectrum. The author believes that a photocount cannot be put into correspondence with a photon, because the former is a manifestation of the Coulomb nonlinearity of photodetector. The final solution of the question of the photon nature is expected to be obtained experimentally. 相似文献
6.
The difference between strong and weak nonlinear systems is discussed. A classification of strong nonlinearities is given. It is based on the divergence or inanity of series expansions of the equation of state commonly used in the study of weak nonlinear phenomena. Such power or functional series cannot be used in three cases: (i) if the equation of state contains a singularity; (ii) if the series diverges for strong disturbances; (iii) if the linear term is absent, and higher nonlinearity dominates. Strong nonlinearities are known in acoustics, optics, mechanics and in quantum field theory. Mathematical models, solutions and observed phenomena are presented. For example, an equation of Heisenberg type and its generalization for strongly nonlinear wave system are given. In particular, exact solutions of new “quadratically cubic” Burgers and Riemann-Hopf equations are discovered. 相似文献
7.
Xiao-feng Pang 《Frontiers of Physics in China》2008,3(2):205-237
In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems
in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear
quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of
the solution of the nonlinear Schr?dinger equation, the stability of microscopic particles described by NLQM, invariances
and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and
Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the
features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as
well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass,
energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws
of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of
motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They
have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule
of motion and conservation laws of energy, momentum and mass, satisfy minimum uncertainty relation, can be localized due to
the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that
rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical
theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic
particles in nonlinear systems, which can solve problems disputed for about a century by scientists in the LQM field. Hence,
the NLQM built is very necessary and correct. The NLQM established can promote the development of physics and can enhance
and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that nonlinear quantum
mechanics has extensive applications in physics, chemistry, biology and polymers, etc.
相似文献
8.
PANG Xiao-feng 《Frontiers of Physics》2008,3(2):205
In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of the solution of the nonlinear Schrödinger equation, the stability of microscopic particles described by NLQM, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass, energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule of motion and conservation laws of energy,momentum and mass, satisfy minimum uncertainty relation, can be localized due to the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems, which can solve problems disputed for about a century by scientists in the LQM field. Hence, the NLQM built is very necessary and correct. The NLQM established can promote the development of physics and can enhance and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that nonlinear quantum mechanics has extensive applications in physics, chemistry, biology and polymers, etc. 相似文献
9.
We consider the quantum above-barrier reflection of a particle by the one-dimensional Rosen-Morse potential well, for the nonlinear Schrödinger equation (the Gross-Pitaevskii equation) with a small nonlinearity. The most interesting case is realized in resonances when the reflection coefficient is exactly equal to zero for the linear Schrödinger equation. Then the reflection is determined by only a small nonlinear term in the Gross-Pitaevskii equation. The simple analytic expression is obtained for the reflection coefficient produced only by the nonlinearity. The analytic condition is found for the common action of the potential well and the nonlinearity to produce the zero reflection coefficient. The reflection coefficient is also derived analytically in the vicinity of a resonance shifted by the nonlinearity. 相似文献
10.
11.
The Klein-Gordon equation arises in many scientific areas of quantum mechanics and quantum field theory.In this paper a novel method based on spectral method and Jacobian free Newton method composed by generalized minimum residual(JFNGMRes) method with adaptive preconditioner will be introduced to solve nonlinear Klein-Gordon equation. In this work the nonlinear Klein-Gordon equation has been converted to a nonlinear system of algebraic equations using collocation method based on Bessel functions without any linearization, discretization and getting help of any other methods. Finally, by using JFNGMRes, solution of the nonlinear algebraic system will be achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the Klein-Gordon equation and compare our results with other methods. 相似文献
12.
A. V. Belinskii 《Journal of Russian Laser Research》1991,12(6):464-479
An exact solution of the Schrödinger quantum equation is used to investigate the evolution of a fundamental optical soliton in its proper waveguide having a Kerr nonlinearity. It is established that the quantum fluctuations grow unceasingly over the entire length of the nonlinear propagation, so that the soliton is ultimately annihilated. A four-photon interaction model is used to clarify the physical nature of this phenomenon. It is shown that the effects considered restrict the possibility of producing quantum squeezed states of a light pulse.Presented at the International Workshop on Squeezed and Correlated States, Moscow, December 3–7, 1990. 相似文献
13.
The adiabatic approximation is an important concept in quantum mechanics. In linear systems, the adiabatic condition is derived with the help of the instantaneous eigenvalues and eigenstates of the Hamiltonian, a procedure that breaks down in the presence of nonlinearity. Using an explicit example relevant to photoassociation of atoms into diatomic molecules, we demonstrate that the proper way to derive the adiabatic condition for nonlinear mean-field (or classical) systems is through a linearization procedure, using which an analytic adiabatic condition is obtained for the nonlinear model under study. 相似文献
14.
Two decades ago, standard quantum mechanics entered into a new territory called space-fractional quantum mechanics, in which wave dynamics and effects are described by the fractional Schrödinger equation. Such territory is now a key and hot topic in diverse branches of physics, particularly in optics driven by the recent theoretical proposal for emulating the fractional Schrödinger equation. However, the light-wave propagation in saturable nonlinear media with space fractional derivatives is yet to be clearly disclosed. Here, such nonlinear optics phenomenon is theoretically investigated based on the nonlinear fractional Schrödinger equation with nonlinear lattices—periodic distributions of either focusing cubic (Kerr) or quintic saturable nonlinearities—and the existence and evolution of localized wave structures allowed by the model are addressed. The model upholds two kinds of one-dimensional soliton families, including fundamental solitons (single peak) and higher-order solitonic structures consisting of two-hump solitons (in-phase) and dipole ones (anti-phase). Notably, the dipole solitons can be robust stable physical objects localized merely within a single well of the nonlinear lattices—previously thought impossible. Linear-stability analysis and direct simulations are executed for both soliton families, and their stability regions are acquired. The predicted solutions can be readily observed in optical experiments and beyond. 相似文献
15.
H. Dekker 《Physica A》1976,84(1):205-211
A simple sum over paths will be considered for the general nonlinear diffusion process described by complex coordinates. In order to derive the corresponding stochastic differential equation the Feynman method used in quantum mechanics will be generalised for the present case of a coordinate dependent variance or diffusion function by means of a nonlinear coordinate transformation. The resulting equation will be seen to be the general nonlinear Fokker-Planck equation. The relevance of the present formulation for nonequilibrium phenomena, such as for example those occuring in nonlinear quantum optics, will be discussed. 相似文献
16.
Laskin N 《Chaos (Woodbury, N.Y.)》2000,10(4):780-790
A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical particle has been established, and the Levy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a free particle quantum-mechanical kernel using Fox's H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a free particle in a square infinite potential well, the fractional "Bohr atom" and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics. (c) 2000 American Institute of Physics. 相似文献
17.
Agung Budiyono 《International Journal of Theoretical Physics》2014,53(4):1276-1298
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of local causality. By contrast, here we shall show that the Schrödinger equation with Born’s statistical interpretation of wave function and uncertainty relation can be derived from a statistical model of microscopic stochastic deviation from classical mechanics which is selected uniquely, up to a free parameter, by the principle of Local Causality. Quantization is thus argued to be physical and Planck constant acquires an interpretation as the average stochastic deviation from classical mechanics in a microscopic time scale. Unlike canonical quantization, the resulting quantum system always has a definite configuration all the time as in classical mechanics, fluctuating randomly along a continuous trajectory. The average of the relevant physical quantities over the distribution of the configuration are shown to be equal numerically to the quantum mechanical average of the corresponding Hermitian operators over a quantum state. 相似文献
18.
Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameterγ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rateγ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r=C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. 相似文献
19.
When the nonlinearity of nanomechanical resonator is not negligible, the quantum decoherence of charge qubit is studied analytically. Using nonlinear Jaynes-Cummings model, one explores the possibility of being quantum data bus for nonlinear nanomechanical resonator, the nonlinearity destroys the dynamical quantum information-storage and maintains the revival of quantum coherence of charge qubit. With the calculation of decoherence factor, we demonstrate the influence of the nonlinearity of nanomechanical resonator on engineered decoherence of charge qubit. 相似文献
20.
Wm. C. McHarris 《Acta Physica Hungarica A》2004,19(3-4):289-295
Alternative, parallel explanations for a number of counter-intuitive concepts connected with the foundations of quantum mechanics can be constructed in terms of nonlinear dynamics. These include ideas as diverse as the statistical exponential decay law and spontaneous symmetry breaking to decoherence itself and the inference from violations of Bell’s inequality that local reality is ruled out in hidden variable extensions of quantum mechanics. Such alternative explanations must not be taken as demonstrations of nonlinear underpinnings for quantum mechanics, but they do raise the possibility of their existence. In this article I delve a bit into ideas connected with the exponential decay law and with Bell’s inequality as demonstrations. Then an investigation of the Klein-Gordon equation shows that it should not come as a complete surprise that quantum mechanics just might contain fundamental nonlinearities. 相似文献