共查询到20条相似文献,搜索用时 15 毫秒
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A recently developed unified theory of classical and quantum chaos, based on the de Broglie-Bohm (Hamilton-Jacobi) formulation
of quantum mechanics is presented and its consequences are discussed. The quantum dynamics is rigorously defined to be chaotic
if the Lyapunov number, associated with the quantum trajectories in de Broglie-Bohm phase space, is positive definite. This
definition of quantum chaos which under classical conditions goes over to the well-known definition of classical chaos in
terms of positivity of Lyapunov numbers, provides a rigorous unified definition of chaos on the same footing for both the
dynamics. A demonstration of the existence of positive Lyapunov numbers in a simple quantum system is given analytically,
proving the existence of quantum chaos. Breaking of the time-reversal symmetry in the corresponding quantum dynamics under
chaotic evolution is demonstrated. It is shown that the rigorous deterministic quantum chaos provides an intrinsic mechanism
towards irreversibility of the Schrodinger evolution of the wave function, without invoking ‘wave function collapse’ or ‘measurements’ 相似文献
3.
The problem of quantum friction in the framework of Bohmian quantum mechanics is studied. The appropriate equations for such
a system is written and solved exactly for some cases. Also two approximate solutions are found which represent the transition
of a system from an upper state to the ground state caused by the friction. The physical nature of these solutions are examined. 相似文献
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Partha Ghose 《Pramana》2001,56(2-3):211-215
An experiment is suggested that is capable of distinguishing between the de Broglie-Bohm theory and standard quantum mechanics. 相似文献
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Gonzalo García de Polavieja 《Physics letters. A》1996,220(6):303-314
The causal theory for the coherent state representation of quantum mechanics is derived. The general conditions for the classical limit are given and it is shown that phase space classical mechanics can be obtained as a limit even for stationary states, in contrast to the de Broglie-Bohm quantum theory of motion. 相似文献
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We show that, in a relativistic quantum theory in which the mass shell is not sharp, and positive and negative energy states are admissable, causal propagation is possible, and Hegerfeldt's theorem can be avoided. The conditions under which this is true have simple physical interpretation.1. On sabbatical leave from School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel. This work was supported in part by a grant from the Ambrose Monell Foundation. 相似文献
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The principles of the causal interpretation are embodied in a conformally invariant theory in Weyl space. The particle is represented by a spherically symmetric thin-shell solution to Einstein's equations. Use of the Gauss-Mainardi-Codazzi formalism yields new insights into the issues of nonlocality, the quantum potential, and the guidance mechanism.1. The issue of negative probabilities associated with second-order wave equations in the causal interpretation is discussed in Ref. 19. 相似文献
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We examine “de Broglie-Bohm” causal trajectories for the two electrons in a nonrelativistic helium atom, taking into account
the spin-dependent momentum terms that arise from the Pauli current. Given that this many-body problem is not exactly solvable,
we examine approximations to various helium eigenstates provided by a low-dimensional basis comprised of tensor products of
one-particle hydrogenic eigenstates.
First to be considered are the simplest approximations to the ground and first-excited electronic states found in every introductory
quantum mechanics textbook. For example, the trajectories associated with the simple 1s(1)1s(2) approximation to the ground state are, to say the least, nontrivial and nonclassical.
We then examine higher-dimensional approximations, i.e., eigenstates Ψ
α
of the Hamiltonian in this truncated basis, and show that ∇
i
S
α
=0 for both particles, implying that only the spin-dependent momentum term contributes to electronic motion. This result is
independent of the size of the truncated basis set, implying that the qualitative features of the trajectories will be the
same, regardless of the accuracy of the eigenfunction approximation.
The electronic motion associated with these eigenstates is quite specialized due to the condition that the spins of the two
electrons comprise a two-spin eigenfunction of the total spin operator. The electrons either (i) remain stationary or (ii)
execute circular orbits around the z-axis with constant velocity. 相似文献
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The de Broglie-Bohm causal theory of quantum mechanics is applied to the hydrogen atom in the fully spin-dependent and relativistic framework of the Dirac equation, and in the nonrelativistic but spin-dependent framework of the Pauli equation. Eigenstates are chosen which are simultaneous eigenstates of the energy H, total angular momentum M, and z component of the total angular momentum M
z. We find the trajectories of the electron, and show that in these eigenstates, motion is circular about the z-axis, with constant angular velocity. We compute the rates of revolution for the ground (n=1) state and the n=2 states, and show that there is agreement in the relevant cases between the Dirac and Pauli results, and with earlier results on the Schrödinger equation. 相似文献
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M. Roncadelli 《Il Nuovo Cimento D》1989,11(1-2):73-99
Summary We present in a rather pedagogical way a new formulation of quantum mechanics. Our starting point is the path integral representation
of the quantum-mechanical propagator analytically continued to imaginary timeW(X″, s″|X′, s′). We view the set of random paths contributing toW(X″, s″|X′, s′) as the manifold of solutions of a Langevin equation with a Gaussian white noise. We thus obtainW(X″, s″|X′, s′) as the noise-average of a suitable functional of the solution of the Langevin equation. The standard quantum-mechanical propagator
is finally recovered by analytically continuingW(X″, s″|X′, s′) back to real time. The present approach allows for a straightforward application of standard methods of classical stochastic
processes to quantum-mechanical problems and offers a new promising way to perform computer simulations of quantum-dynamical
systems.
To speed up publication, the author has agreed not to receive proofs which have been supervised by the Scientific Committee. 相似文献
12.
The classical and quantum physics seem to divide nature into two domains macroscopic and microscopic. It is also certain that
they accurately predict experimental results in their respective regions. However, the reduction theory, namely, the general
derivation of classical results from the quantum mechanics is still a far cry. The outcome of some recent investigations suggests
that there possibly does not exist any universal method for obtaining classical results from quantum mechanics. In the present
work we intend to investigate the problem phenomenonwise and address specifically the phenomenon of scattering. We suggest
a general approach to obtain the classical limit formula from the phase shiftδ
l, in the limiting value of a suitable parameter on whichδ
l depends. The classical result has been derived for three different potential fields in which the phase shifts are exactly
known. Unlike the current wisdom that the classical limit can be reached only in the high energy regime it is found that the
classical limit parameter in addition to other factors depends on the details of the potential fields. In the last section
we have discussed the implications of the results obtained. 相似文献
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Nicolay V. Lunin 《Journal of Russian Laser Research》2008,29(5):441-459
The complete set of observables (bilinear Hermitian forms) is determined for the Schrödinger equation and their connection with the curvature and torsion of the curves, where conservation laws are fulfilled, is established. It is shown that these curves for a free particle, in the general case, are spiral lines with the radius and step length defined by the observables at the initial point (both parameters are proportional to the de Broglie wavelength). A spiral line turns to a straight line under some conditions. The trajectory variations are considered in the problem with a potential step and a rectangular barrier. It is shown that spiral lines can be transformed into straight lines and vice versa. All observables, which are changed along the potential barrier, can be restored under some constraints on the potential. The Hermitian transformations at the potential step are connected with the Lorentz transformations. A qualitative explanation of the double-slit experiment for extremely low intensity of the particles' source in the absence of the interference conditions is suggested. 相似文献
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There exists a coassociative and cocommutative coproduct in the linear space spanned by the two algebraic products of a classical
Hamilton algebra (the algebraic structure underlying classical mechanics [1]). The transition from classical to quantum Hamilton
algebra (the algebraic structure underlying quantum mechanics) is anħ-deformation which preserves not only the Lie property of the classical Hamilton algebra but also the coassociativity and
cocommutativity of the above coproduct. By explicit construction we obtain the algebraic structures of theq-deformed Hamilton algebras which preserve the said properties of the coproduct. Some algorithms of these structures are obtained
and their implications discussed. The problem of consistency of time evolution with theq-deformed kinematical structure is discussed. A characteristic distinction between the parametersħ andq is brought out to stress the fact thatq cannot be regarded as a fundamental constant. 相似文献
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R. H. Rietdijk 《Journal of Geometry and Physics》1993,11(1-4):545-551
We consider the classical mechanics of the spinning particle and investigate which Abelian interactions can be added without breaking supersymmetry. A quantum theory is presented. The well known index theorem for the Dirac operator is extended to take into account the effect of anti-symmetric Abelian tensor fields. Furthermore interactions with non-Abelian anti-symmetric tensor fields are investigated. It turns out in both cases that these fields do not give any non-trivial contributions to the index. 相似文献
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In this paper a new version of the DHN (Dashen–Hasslacher–Neveu) formula, which is used to compute the one-loop order kink mass correction in (1+1)-dimensional scalar field theory models, is constructed. The new expression is written in terms of the spectral data coming from the supersymmetric partner operator of the second-order small kink fluctuation operator and allows us to compute the kink mass quantum shift in new models for which this calculation was out of reach by means of the old formula. 相似文献
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A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation. 相似文献
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We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering ‘mass’ as
a function of coordinates. Its usefulness in solving potential problems is discussed with specific examples. We also discuss
the ‘physical’ significance of the supersymmetric states in this formalism. 相似文献
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