共查询到20条相似文献,搜索用时 15 毫秒
1.
Bruno Galvan 《Journal of statistical physics》2008,131(6):1155-1167
An extension of the Born rule, the quantum typicality rule, has recently been proposed [B. Galvan in Found. Phys. 37:1540–1562 (2007)]. Roughly speaking, this rule states that if the
wave function of a particle is split into non-overlapping wave packets, the particle stays approximately inside the support
of one of the wave packets, without jumping to the others.
In this paper a formal definition of this rule is given in terms of imprecise probability. An imprecise probability space is a measurable space
endowed with a set of probability measures ℘. The quantum formalism and the quantum typicality rule allow us to define a set of probabilities
on (X
T
,ℱ), where X is the configuration space of a quantum system, T is a time interval and ℱ is the σ-algebra generated by the cylinder sets. Thus, it is proposed that a quantum system can be represented as the imprecise stochastic process
, which is a canonical stochastic process in which the single probability measure is replaced by a set of measures. It is
argued that this mathematical model, when used to represent macroscopic systems, has sufficient predictive power to explain
both the results of the statistical experiments and the quasi-classical structure of the macroscopic evolution. 相似文献
2.
Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of
quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set
theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get
a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified.
We build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable
elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them,
reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to
follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic)
theory, coping also with the physical theory’s underlying logic and mathematics.
G. Domenech is a fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina.
D. Krause is a fellow of the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. 相似文献
3.
REN De-Ming 《理论物理通讯》2004,41(5):685-688
The Newton equation of motion is derived from quantum
mechanics. 相似文献
4.
The Conditional Probability Interpretation of Quantum Mechanics replaces the abstract notion of time used in standard Quantum
Mechanics by the time that can be read off from a physical clock. The use of physical clocks leads to apparent non-unitary
and decoherence. Here we show that a close approximation to standard Quantum Mechanics can be recovered from conditional Quantum
Mechanics for semi-classical clocks, and we use these clocks to compute the minimum decoherence predicted by the Conditional
Probability Interpretation. 相似文献
5.
Manuel Bächtold 《Foundations of Physics》2008,38(9):843-868
The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter
consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions
any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum
mechanics is the only theory which fulfils exactly these functions.
This work received financial support from the European Union (Marie Curie Actions). 相似文献
6.
General classical statistical uncertainty relation is deduced and generalized to quantum uncertainty relation. We give a general unification theory of the classical statistical and quantum uncertainty relations, and prove that the classical limit of quantum mechanics is just classical statistical mechanics. It is shown that the classical limit of the general quantum uncertainty relation is the general classical uncertainty relation. Also, some specific applications show that the obtained theory is self-consistent and coincides with those from physical experiments. 相似文献
7.
Mario Bunge 《International Journal of Theoretical Physics》2003,42(1):135-142
According to both Dirac's and Kemmer's relativistic quantum theories, the eigenvalues of the velocity operator are +c and –c. This false result is avoided if certain alternative particle coordinates are adopted. Another advantage is that the new coordinates occur in additional constants of the motion. These are sui generis angular momenta obtained by taking the vector product of the nonstandard coordinates with the linear momentum. An additional virtue of the new velocity operator is that, like in classical mechanics, it is proportional to the linear momentum. Besides, the zeroth component of the new set of coordinates does not commute with the hamiltonian, which results in a genuine indeterminacy relation between time and energy. 相似文献
8.
Pulak Ranjan Giri 《International Journal of Theoretical Physics》2008,47(7):2095-2100
We show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial
state, i.e., making a round trip along the great circle over S
2, must have a lower bound in quantum mechanics, if the difference between two eigenstates of the 2×2 Hamiltonian is kept fixed.
Even the non-hermitian quantum mechanics can not reduce it to arbitrarily small value. In fact, we show that whether one uses
a hermitian Hamiltonian or a non-hermitian, the required minimal total time of evolution is same. It is argued that in hermitian
quantum mechanics the condition for minimal time evolution can be understood as a constraint coming from the orthogonality
of the polarization vector P of the evolving quantum state
with the vector
of the 2×2 hermitian Hamiltonians
and it is shown that the Hamiltonian H can be parameterized by two independent parameters
and Θ. 相似文献
9.
Franklin E. Schroeck Jr. 《International Journal of Theoretical Physics》2008,47(1):175-184
On any quantum mechanical Hilbert space, the phase space localization operators form a set of operators that are both physically
motivated and form the groundwork for a C* algebra. This set is shown to be informationally complete in the original Hilbert
space. We also revisit the relation between having a complete set of eigenvectors, commutability and compatibility.
Dedicated to G.G. Emch. 相似文献
10.
Gabriel Catren 《Foundations of Physics》2008,38(5):470-487
We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do
so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful—or equivariant—realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical
states is not incomplete, but rather that the classical notion is overdetermined. 相似文献
11.
Florian Hulpke Uffe V. Poulsen Anna Sanpera Aditi Sen Ujjwal Sen Maciej Lewenstein 《Foundations of Physics》2006,36(4):477-499
The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived from other principles has been often considered. In this contribution, we show that unitary evolutions arise as a consequences of demanding preservation of entropy in the evolution of a single pure quantum system, and preservation of entanglement in the evolution of composite quantum systems.
6
We would also like to dedicate this work to the memory of Asher Peres, whose contributions and sharp comments guided the first steps of the present article. 相似文献
12.
B.B. Kadomtsev 《Physics letters. A》1996,210(6):371-376
The use of Einstein-Podolsky-Rosen (EPR) correlated microparticles for telecommunication purposes is considered from a new point of view. In spite of the fact that the usual nonlocality of EPR pairs is not controllable, the use of irreversible quantum systems opens new possibilities. A concrete scheme for a controllable correlated quantum system is considered. It might be used for non-wave-type communication over not very large distances. 相似文献
13.
David T. Pegg 《Foundations of Physics》2008,38(7):648-658
A retrocausal interpretation of quantum mechanics is examined and is applied to the problem of measuring an optical qubit
before the qubit is actually created. Although the predictions of the retrocausal interpretation are the same as for the conventional
causal picture, it provides a new perspective which should give a useful way of understanding some quantum mechanical processes. 相似文献
14.
Based on the statistical concept of the median, we propose a quantum uncertainty relation between semi-interquartile ranges of the position and momentum distributions of arbitrary quantum states. The relation is universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We show that the median-based one is not saturated for Gaussian distributions in position. Instead, the Cauchy-Lorentz distributions in position turn out to be the one with the minimal uncertainty, among the states inspected, implying that the minimum-uncertainty state is not unique but depends on the measure of spread used. Even the ordering of the states with respect to the distance from the minimum uncertainty state is altered by a change in the measure. We invoke the completeness of Hermite polynomials in the space of all quantum states to probe the median-based relation. The results have potential applications in a variety of studies including those on the quantum-to-classical boundary and on quantum cryptography. 相似文献
15.
James B. Hartle 《International Journal of Theoretical Physics》2006,45(8):1390-1396
Familiar quantum mechanics assumes a fixed spacetime geometry. Quantummechanics must therefore be generalized for quantum gravity where spacetime geometry is not fixed but rather a quantum variable. This extended abstract sketches a fully fourdimensional generalized quantum mechnics of cosmological spacetime geometries that is one such generalization.This contribution to the proceedings of the Glafka Conference is an extended abstract of the author's talk there. More details can be found in the references cited at the end of the abstract expecially (Hartle, 1995). 相似文献
16.
John Harding 《International Journal of Theoretical Physics》2009,48(3):769-802
Abramsky and Coecke (Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, pp. 415–425, IEEE Comput.
Soc., New York, 2004) have recently introduced an approach to finite dimensional quantum mechanics based on strongly compact closed categories
with biproducts. In this note it is shown that the projections of any object A in such a category form an orthoalgebra Proj
A. Sufficient conditions are given to ensure this orthoalgebra is an orthomodular poset. A notion of a preparation for such
an object is given by Abramsky and Coecke, and it is shown that each preparation induces a finitely additive map from Proj
A to the unit interval of the semiring of scalars for this category. The tensor product for the category is shown to induce
an orthoalgebra bimorphism Proj
A×Proj
B→Proj (A
⊗
B) that shares some of the properties required of a tensor product of orthoalgebras.
These results are established in a setting more general than that of strongly compact closed categories. Many are valid in
dagger biproduct categories, others require also a symmetric monoidal tensor compatible with the dagger and biproducts. Examples
are considered for several familiar strongly compact closed categories. 相似文献
17.
S. D. Purohit 《advances in applied mathematics and mechanics.》2013,5(5):639-651
The aim of this article is to investigate the solutions of generalized fractional
partial differential equations involving Hilfer time fractional derivative and the
space fractional generalized Laplace operators, occurring in quantum mechanics. The
solutions of these equations are obtained by employing the joint Laplace and Fourier
transforms, in terms of the Fox's $H$-function. Several special cases as solutions of
one dimensional non-homogeneous fractional equations occurring in the quantum mechanics
are presented. The results given earlier by Saxena
et al. [Fract. Calc. Appl. Anal., 13(2) (2010), pp. 177-190]
and Purohit and Kalla [J. Phys. A Math. Theor., 44 (4) (2011), 045202]
follow as special cases of our findings. 相似文献
18.
F. Strocchi 《Foundations of Physics》2004,34(3):501-527
The problems which arise for a relativistic quantum mechanics are reviewed and critically examined in connection with the foundations of quantum field theory. The conflict between the quantum mechanical Hilbert space structure, the locality property and the gauge invariance encoded in the Gauss' law is discussed in connection with the various quantization choices for gauge fields. 相似文献
19.
U. Mohrhoff 《Foundations of Physics》2009,39(2):137-155
This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves,
Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion
beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including
the claim that different pure states may legitimately be assigned to the same system at the same time, and the claim that
the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard
the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads
to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are
neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible
outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the
only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these
are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation
of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic.
This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory.
Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various
reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify
an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians
refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the
macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests
itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental
in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in
the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms
of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe
its manifestation. 相似文献
20.
We review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics recently proposed in refs. 1–7. In the algebraic formalism of quantum statistical mechanics we introduce notions of non-equilibrium steady states, entropy production and heat fluxes, and study their properties. Our basic paradigm is a model of a small (finite) quantum system coupled to several independent thermal reservoirs. We exhibit examples of such systems which have strictly positive entropy production. 相似文献